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Review and Compilation of Demand Forecasting Experiences... August 1979
Click HERE for graphic. NOTICE This document is disseminated under the sponsorship of the Department of Transportation in the interest of information exchange. The United States Government assumes no liability for its contents or use thereof. ACKNOWLEDGEMENTS This research was performed under the sponsorship of the University Research Program of the Office of the Secretary of Transportation (Contract No. DOT-OS-60146). The principal investigator was Dr. Yupo Chan, Assistant Professor of Civil Engineering. He was assisted by Messrs. Fong-Lieh Ou, Jossef Perl and Edward Regan, graduate students in transportation. Many professionals in the field have offered valuable advice and assistance during the research. Dr. Charlotte Chamberlain, the Technical Monitor, gave us more than a generous share of her time. Other professionals to whom we wish to express our appreciation include D. Brand, R. Dial, R. D. Dobson, D. Dunlap, D. Gendell, T. Hillegass, J. Horowitz, I. Kingham, B. Nupp, R. Paaswell, P. Patterson, M. Rabins, R. Sheridan, G. Shunk, D. Ward, P. Watson, and E. Weiner. M. Heckard and B. Goodman are thanked for editing and putting the whole document together under genuine pressures of time. EXECUTIVE SUMMARY Introduction It is often felt that the wealth of research and methodology developed in demand forecasting has not yet had its fullest impact on the mission-oriented, policy-directed functions of the transportation planning profession. While decision makers ask for "quick-turnaround" analyses, sophisticated demand forecasting techniques often require months of data collection, calibration, and computations. This research effort, directed at filling that knowledge gap, will compile and evaluate studies in urban travel demand forecasting. The thrust of our research efforts is to synthesize the demand-forecasting experiences in the past decade or two and to come up with a simple estimation procedure which would allow the determination of-passenger travel on an urbanized- arealevel. Instead of the link level or transit line level of specificity, the procedure forecasts overall figures such as vehicle- miles-of-travel and passenger-miles-of-travel corresponding to alternative transportation system implementations. Through the compilation of generalized parameters such as demand elasticities, the research provides a fast-response tool to guide policy decisions such as the levels of investment in "capitalintensive" transit, "low-cost" transit, or highway systems around the urbanized areas in the country. Problem Studied Operationally oriented, the initial research is designed to assist planners in deciding which demand forecasting procedures are applicable for their particular use. Specifically, the following areas are investigated: (a) The validation of ridership and traffic predictions, including comparison with forecasts made by alternative demand estimation procedures as well as data compiled after the implementation of planned transportation systems. (b) The transferability of validated demand forecasting model parameters to other areas and scenarios aside from the ones in which they were calibrated. Realistic evaluations are conducted using data from well over 60 percent of U.S. urban areas. Each unique demand modeling framework is analyzed on the basis of its operational feasibility, socioeconomic input, prediction of future traffic and level-of-service attributes and flexibility of examining policy options. The result is a recommended simple procedure for passenger travel forecasting on an urban areawide level. The first task in our research is to classify the urbanized areas in the United States into groups in which the cities share similar travel patterns and socioeconomic characteristics. A four-cell taxonomy can be hypothesized: the large/multinucleated cities, the large/core- concentrated iii cities, the medium/multinucleated cities, and the medium/core- concentrated cities. Subsequent statistical analysis, using multiple regression and linear goal programming (LGP), supports such a hypothesis. Such a taxonomy scheme parallels some of the findings in the market analyses for alternative transportation systems. Available information indicates, for example, that "capital-intensive" systems such as rapid transit are usually found in large/core-concentrated cities. On the other hand, a highway-based system (including transit and automobile) is one of the more viable systems for the medium/multinucleated cities. The city classification, therefore, works hand-in-hand with our equilibrium framework in which not only the demand but also the supply functions are considered. Our forecasting procedures begin with the approximation of the demand curve. A convenient way to summarize many of the sophisticated demand models and their calibration results is through the use of elasticities. A set of elasticities, calculated according to the four-cell classifica- tion scheme outlined above, would allow a quick determination of the travel responses to a variety of transportation system implementations. Care is taken to include not only calibrated elasticities, but also empirical ones. Attention is also paid to the base conditions under which an elasticity is derived as well as the numerical range of these elasticities under different urban scenarios. With such a table of elasticities and the knowledge about the base conditions in which they can be applied, one can draw linear segments to approximate the shape of the demand function at the vicinity where the analysis is to be performed. After determining the demand function, the next step is to derive the supply curve. Since our unit of analysis is the urbanized area, the commonly available supply curves, which are traditionally defined for a link, need to be aggregated for the city as a whole. This task is to be performed. not only for the highway mode, but also for transit. An aggregation procedure is devised by building upon the previous researches by the principal investigator and the Characteristics of Urban Transportation Systems (CUTS) report from the U.S. Department of Transportation. In accordance with our advocacy of a simple procedure, the number of calculation steps are minimized to a level in which only a hand calculator is necessary. One pays a price for the savings in computational time, however. The aggregate supply curve so derived can only serve as a linear approximation at the vicinity of interest in our analysis. Overall, the impedance/capacity relationship displayed by the aggregate function is deemed accurate enough for the urbanized-area- level of aggregation employed in our travel estimation procedures. Results Achieved Research results indicate that most of the successful demand fore- casting models can be expressed in terms of generalized demand model parameters such as elasticities. In order to apply demand elasticities meaningfully, however, the base conditions under which they are derived are tabulated. Parallel to the tables of elasticities, therefore are, iv two equations which estimate the level-of-service and traffic volume at which the elasticities are valid. In summary, a set of forecasting parameters and steps are specified for the four groups of urban areas of the United States according to the following population size and urban structure: (a) Large/multinucleated (b) Large/core-concentrated (c) Medium/multinucleated or (d) Medium/core-concentrated where a population of 800,000 is found to be the demarkation between a large and medium city. -Cities in each of these two-way classification cells are found to share similar travel patterns thus allowing a set of generalized parameters and forecasting steps to be applied. Since our objective is to come up with a simplified procedure to forecast urban passenger travel, maximum use of previous forecasting experiences (instead of expensive surveys and model calibrations) is our guiding principle. -The compilation of demand model parameters and procedures into a four-cell tabular form is a first step toward this goal. In order to illustrate the compilations in a meaningful and consistent way, an equilibrium" approach is suggested, which synthesizes these seemingly disparate sets of tables into a consistent applicational context. Since pre-vious successful forecasting experiences can be summarized in a demand/ supply paradigm, the researchers recommend that future traffic be estimated as the intersection of the two functions. Such a determination procedure is not only more theoretically satisfying but also more practical in its computational requirements. Instead of using the econometric approach, in which a set of simultaneous equations-may have to be constructed, the demand and supply curves are determined individually based upon our knowledge of the way they shift over time and the way they can be approximated by linear segments. This method also avoids many of the intricate statistical problems such as "identification." Utilization of Results A directory of the potential users for the research has been drawn up, comprised of professionals from local, state and federal levels. One hundred sixty questionnaires were sent out; 110 were returned, in which a majority expressed a good deal of interest in the project. Sixteen professionals also indicated their desire to participate in the project in a coordination capacity, 10 of which were selected in accordance with contract requirements. In general, the amount of enthusiasm expressed by the profession-at-large for our research results has exceeded our expectations. In order to show the profession-at-large (particularly those in the operating agencies) examples of how the generalized parameters and procedures compiled in this report can be used in site-specific applications, three case studies were performed in San Francisco, Pittsburgh, and Reading, Pa. They represent a cross-section of the scenarios in which various transportation systems improvements have been made, including "capital-intensive" transit alternatives, "low-cost" alternatives and the auto-oriented Mode. These case studies also encompass numerous forecast periods spanning the last two decades. This time-span allows us to attest to the temporal stability of such parameters. v Where the generalized elasticities and base condition estimation equations are not specific enough for a particular study area, updating procedures are provided to re-calibrate the parameters according to local socioeconomic and level-of-service conditions. Such updating procedures also offset, to a large extent, any inadequacies in the inferential robustness of the statistical analysis performed thus far. Conclusion Within the limits of the available resources, the research team has assembled an adequate information base from which the successful forecasting models of the past have been summarized in the form of tables and equations. The first-hand data base alone, for example, consists of 150 cities, covering well over 60 percent of all the urbanized areas with a population over 50,000. It is true that the number of valid observations may be quite numerous in one cell of the city classification scheme while meager in another. Rigorous methodological steps have been taken, however, to extract the best available information content out of the sample. Remedial measures are also recommended where the number of observations is relatively scant. Our research findings can be applied directly in a resource allocation context. If several candidate transportation system improvement schemes are contemplated for a number of cities around the country or in a particular state, our procedures serve as a screening tool to rank the alternative systems according to their patronage and usage. vi TABLE OF CONTENTS Page I. PROBLEM STATEMENT AND OVERVIEW. . . . . . . . . . . . . . . . 1 A. Objective. . . . . . . . . . . . . . . . . . . . . . . . . 1 B. State of the Profession. . . . . . . . . . . . . . . . . . 2 C. Case for a More Responsive Procedure . . . . . . . . . . . 4 D. Stability and Transferability. . . . . . . . . . . . . . . 7 E. Updating . . . . . . . . . . . . . . . . . . . . . . . . . 9 F. Summary. . . . . . . . . . . . . . . . . . . . . . . . . .11 II. CLASSIFICATION OF URBAN AREAS FOR DEMAND FORECASTING ANALYSIS... . . . . . . . . . . . . . . . . . . . . . . . . .13 A. Candidate Urban Areas. . . . . . . . . . . . . . . . . .13 B. Infrastructure. . . . . . . . . . . . . . . . . . . . . .15 C. Activity System . . . . . . . . . . . . . . . . . . . . .16 D. Supply Characteristics. . . . . . . . . . . . . . . . . .21 E. Analyses. . . . . . . . . . . . . . . . . . . . . . . . .24 F. Results: A Taxonomy . . . . . . . . . . . . . . . . . .38 G. Summary . . . . . . . . . . . . . . . . . . . . . . . . .45 III. AGGREGATE ESTIMATIONS OF DEMAND ELASTICITIES. . . . . . . . .50 A. Tabulation of Elasticities. . . . . . . . . . . . . . . .50 B. Aggregation of Elasticities . . . . . . . . . . . . . . .73 C. Values of Travel Time . . . . . . . . . . . . . . . . . .84 D. Demand Forecasting Using Elasticities . . . . . . . . . .87 E. Macro Urban Travel Demand Models. . . . . . . . . . . . .92 F. Summary . . . . . . . . . . . . . . . . . . . . . . . . .97 IV. GENERIC CLASSES OF TRANSPORTATION SYSTEMS . . . . . . . . . .99 A. Definition of Modes . . . . . . . . . . . . . . . . . . .99 B. Capacity and Level-of-Service . . . . . . . . . . . . . 100 C. Impedance . . . . . . . . . . . . . . . . . . . . . . . 104 D. Aggregate Supply Curves for Urban Areas.. . . . . . . . 110 E. Summary . . . . . . . . . . . . . . . . . . . . . . . . 125 V. FORECASTING URBAN AREAWIDE PASSENGER TRAVEL . . . . . . . . 128 A. A Demand/Supply Equilibrium Approach. . . . . . . . . . 129 B. Modeling Structure and Parameter Transferability. . . . 142 C. A Case Study of Three Cities. . . . . . . . . . . . . . 148 D. Equilibration and Correlative Forecasting . . . . . . . 160 E. Generalization of the Forecasting Procedure . . . . . . 165 F. Summary . . . . . . . . . . . . . . . . . . . . . . . . 167 VI. CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH. . . . . . 171 A. Research Results . . . . . . . . . . . . . . . . . . . . 172 B. Mission-Oriented Applications. . . . . . . . . . . . . . 176 C. Conclusions. . . . . . . . . . . . . . . . . . . . . . . 178 D. Extensions . . . . . . . . . . . . . . . . . . . . . . . 179 vii TABLE OF CONTENTS (Continued) Page BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . 183 APPENDICES APPENDIX l: DESCRIPTION OF DATA BASE AND DATA TABULATIONS. . 200 APPENDIX 2: LINEAR GOAL PROGRAMMING. . . . . . . . . . . . . 228 APPENDIX 3: AREAWIDE SUPPLY AGGREGATION PROCEDURE. . . . . . 231 APPENDIX 4: BAYESIAN UPDATING. . . . . . . . . . . . . . . . 236 APPENDIX 5: A CASE STUDY OF SPATIAL TRANSFERABILITY: PITTSBURGH . . . . . . . . . . . . . . . . . . . 245 APPENDIX 6: A CASE STUDY OF TEMPORAL TRANSFERABILITY: SAN FRANCISCO. . . . . . . . . . . . . . . . . . 266 APPENDIX 7: A CASE STUDY OF SPATIAL AND TEMPORAL TRANSFERABILITY: READING, PA. . . . . . . . . . . . . . . . . . . 296 APPENDIX 8: HOUSEHOLD, ZONAL, VS AREAWIDE ELASTICITIES . . . 314 APPENDIX 9: DEMAND ELASTICITIES VS MODAL-SPLIT ELASTICITIES. 319 APPENDIX 10: AGGREGATION OF ELASTICITIES. . . . . . . . . . . 323 viii LIST OF TABLES Table Page 2-1 RELATIONSHIP BETWEEN TRAVEL DEMAND AND SIZE OF THE URBAN AREA. . . . . . . . . . . . . . . . . . . .17 2-2 RELATIONSHIP BETWEEN TRAVEL DEMAND AND SPATIAL DISTRIBUTION OF SOCIOECONOMIC ACTIVITIES . . . . . . . . . . . . . . . . .18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19 2-3 NINE-GROUP LEVEL CLUSTERING . . . . . . . . . . . . . . . . .22 2-4 NINETEEN CLASSIFICATIONS OF URBAN AREAS . . . . . . . . . . .29 2-5 ALTERNATIVE CITY CLASSIFICATIONS FOR TRIP FREQUENCY ANALYSIS... . . . . . . . . . . . . . . . . . . . . . . . . .30 2-6 ALTERNATIVE CITY CLASSIFICATIONS FOR TRIP DURATION ANALYSIS. . . . . . . . . . . . . . . . . . . .31 2-7 DOMINANT CLASSES IN TRIP FREQUENCY ANALYSIS . . . . . . . . .33 2-8 DOMINANT CLASSES IN TRIP DURATION ANALYSIS. . . . . . . . . .40 2-9 RELATIONSHIP BETWEEN AVERAGE TRIP FREQUENCY PER DWELLING UNIT AND AVERAGE AUTO OWNERSHIP PER DWELLING UNIT ACCORDING TO URBAN SIZE AND URBAN STRUCTURE. . . . . . . . . . . . . . . . . . .42 2-10 RELATIONSHIP BETWEEN AVERAGE TRIP DURATION AND THE POPULATION SIZE ACCORDING TO URBAN SIZE AND URBAN STRUCTURE. . . . . . .44 2-11 TRIP FREQUENCY MODELS OBTAINED USING LINEAR GOAL PROGRAMMING . . . . . . . . . . . . . . . . . . .46 2-12 TRIP DURATION MODELS OBTAINED USING LINEAR GOAL PROGRAMMING . . . . . . . . . . . . . . . . . . .47 3-1 EMPIRICAL TRANSIT DEMAND ELASTICITIES FOR OVERALL TRIPS . . .53 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .55 3-2 TAXONOMY OF EMPIRICAL TRANSIT DEMAND ELASTICITIES FOR OVERALL TRIPS . . . . . . . . . . . . . . . . . . . . . . . . . . . .57 3-3 WORK TRIP DEMAND ELASTICITIES CALIBRATED BY AGGREGATE DEMAND MODELS AND AGGREGATE DATA . . . . . . . . . . . . . . . . . .60 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61 3-4 NONWORK TRIP DEMAND ELASTICITIES CALIBRATED BY AGGREGATE DEMAND MODELS AND AGGREGATE DATA . . . . . . . . . . . . . . . . . .62 3-5 WORK TRIP DEMAND ELASTICITIES CALIBRATED BY DISAGGREGATE DEMAND MODELS AND DISAGGREGATE DATA. . . . . . . . . . . . . . . . .63 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66 ix LIST OF TABLES (Continued) Table Page 3-6 NONWORK TRIP DEMAND ELASTICITIES CALIBRATED BY DISAGGREGATE DEMAND MODELS AND DISAGGREGATE DATA. . . . . . .67 3-7 MEAN VALUES OF VARIABLES FOR DERIVING ELASTICITIES. . . . . .69 3-8 RANGE OF CALIBRATED WORK TRIP ELASTICITIES,.AAs and .DDs . . . . . . . . . . . . . . . . . . . . . . . . . . . .75 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76 3-9 DEMAND ELASTICITIES WITH RESPECT TO THE OVERALL TRIPS FOR LARGE/MULTINUCLEATED CITIES . . . . . . . . . . . . . . .79 3-10 DEMAND ELASTICITIES WITH RESPECT TO THE OVERALL TRIPS FOR LARGE/CORE-CONCENTRATED CITIES. . . . . . . . . . . . . .80 3-11 DEMAND ELASTICITIES WITH RESPECT TO THE OVERALL TRIPS FOR MEDIUM/MULTINUCLEATED CITIES. . . . . . . . . . . . . . .81 3-12 DEMAND ELASTICITIES WITH RESPECT TO THE OVERALL TRIPS FOR MEDIUM/CORE-CONCENTRATED CITIES . . . . . . . . . . . . . . .82 3-13 VALUES OF TRAVEL TIME . . . . . . . . . . . . . . . . . . . .83 3-14 VALUES OF TRAVEL TIME FOR OVERALL TRIPS . . . . . . . . . . .86 4-1 EXAMPLE LEVEL-OF-SERVICE ATTRIBUTES . . . . . . . . . . . . 107 4-2 TOTAL IMPEDANCE IN TERMS OF TRAVEL COSTS AND TRAVEL TIME. . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4-3 T-CAPACITY AND OPERATING SPEED ON VARIOUS ROADWAYS PER LANE. . . . . . . . . . . . . . . . . . . . . . . . . . 112 4-4 MAXIMUM CAPACITIES OF TRANSIT SYSTEM. . . . . . . . . . . . 126 5-1 PARAMETERS FOR MODAL SPLIT IN PITTSBURGH. . . . . . . . . . 161 5-2 PARAMETERS FOR MODAL SPLIT IN SAN FRANCISCO . . . . . . . . 163 LIST OF FIGURES Figure 1-1 CLASSIFICATION SCHEME OF URBAN AREAS. . . . . . . . . . . . .10 2-1 EXAMPLE CLASSIFICATION OF STUDY AREA. . . . . . . . . . . . .20 x LIST OF FIGURES (Continued) Figure Page 2-2 NUMBER OF DAILY PERSON TRIPS PER DWELLING UNIT VERSUS AVERAGE TRIP DURATION . . . . . . . . . . . . . . . . . . . .25 2-3 TRIP DURATION VERSUS POPULATION IN URBAN AREAS WITH POPULATION BETWEEN 50,000 AND 800,000 . . . . . . . . . . . .27 2-4 AVERAGE NUMBER OF TRIPS PER DWELLING UNIT VERSUS AVERAGE AUTO OWNERSHIP PER DWELLING UNIT IN CITIES WITH POPULATION OVER 50,000 . . . . . . . . . . . . . . . . .28 2-5 AVERAGE NUMBER OF TRIPS PER DWELLING UNIT VERSUS AVERAGE AUTO OWNERSHIP PER DWELLING UNIT IN LARGE CORE-CONCENTRATED CITIES WITH POPULATION SIZE OVER 800,000 . . . . . . . . . . . . . . . . . . . . . . . . . . .34 2-6 AVERAGE NUMBER OF TRIPS PER DWELLING UNIT VERSUS AVERAGE AUTO OWNERSHIP PER DWELLING UNIT IN MEDIUM CITIES WITH POPULATION SIZE BETWEEN 50,000 AND 800,000. . . .35 2-7 AVERAGE NUMBER OF TRIPS PER DWELLING UNIT VERSUS AVERAGE AUTO OWNERSHIP PER DWELLING UNIT IN LARGE CORE-CONCENTRATED CITIES WITH POPULATION OVER 800,000. . . . . . . . . . . . . . . . .36 2-8 AVERAGE NUMBER OF TRIPS PER DWELLING UNIT VERSUS AVERAGE NUMBER OF PERSONS PER DWELLING UNIT IN MEDIUM CITIES WITH POPULATION BETWEEN 50,000 AND 800,000. . . . . . . . . . . . . . . . . .37 2-9 TRIP DURATION VERSUS POPULATION IN URBAN AREAS WITH POPULATION BETWEEN 50,000 AND 800,000 . . . . . . . . . . . .39 3-1 Cross Demand .a. . . . . . . . . . . . . . . . . . . . . . .90 3-2 CROSS DEMAND .t. . . . . . . . . . . . . . . . . . . . . . .90 3-3 PERCENT PERSON TRIPS BY TRANSIT VERSUS TOTAL TRANSIT MILES IN CORE-CONCENTRATED CITIES . . . . . . . . . . . . . .95 4-1 TYPICAL TRANSIT AND HIGHWAY SUPPLY CURVES . . . . . . . . . 102 4-2 THEORETICAL SUPPLY FUNCTIONS FOR TRANSIT SERVICE. . . . . . 103 4-3 PLOTTING THE TOTAL SUPPLY CURVE . . . . . . . . . . . . . . 105 4-4 SUPPLY CURVES OF CORRIDORS. . . . . . . . . . . . . . . . . 113 4-5 URBAN HIGHWAY CLASSIFICATION SCHEME . . . . . . . . . . . . 114 4-6 AVERAGE SPEEDS AT V/C RATIO = 0.00. . . . . . . . . . . . . 117 xi LIST OF FIGURES (Continued) Figure Page 4-7 AVERAGE SPEEDS AT V/C = 1.00. . . . . . . . . . . . . . . . 119 4-8 PLOTTING THE AGGREGATE SYSTEM SUPPLY CURVES . . . . . . . . 121 5-1 SUPPLY DEMAND EQUILIBRIUM FOR BASE CONDITIONS . . . . . . . 131 5-2 SHIFT OF SUPPLY CURVE . . . . . . . . . . . . . . . . . . . 131 5-3 SHIFT OF DEMAND CURVE . . . . . . . . . . . . . . . . . . . 133 5-4 SHIFT OF BOTH THE DEMAND AND SUPPLY CURVES. . . . . . . . . 133 5-5 APPROXIMATING THE SUPPLY CURVE. . . . . . . . . . . . . . . 137 5-6 SUPPLY/DEMAND EQUILIBRIUM . . . . . . . . . . . . . . . . . 137 5-7 CALIBRATION OF DAP. . . . . . . . . . . . . . . . . . . . . 140 5-8 DIFFUSED PRIOR STATE. . . . . . . . . . . . . . . . . . . . 145 5-9 COVERAGE OF THE CASE STUDIES. . . . . . . . . . . . . . . . 149 5-10 THE SPATIAL TRANSFERABILITY OF TRAVEL FORECASTING PARAMETERS IN PITTSBURGH. . . . . . . . . . . . . . . . . . 151 5-11 THE TEMPORAL STABILITY OF TRAVEL FORECASTING PARAMETERS IN SAN FRANCISCO . . . . . . . . . . . . . . . . . . . . . . . 152 5-12 EVALUATIONS OF DAP TRANSFERABILITY IN TIME AND SPACE. . . . 154 5-13 THE COMPARISON. . . . . . . . . . . . . . . . . . . . . . . 168 5-14 RELATIONSHIP BETWEEN CIRCUMSTANTIAL SETS AND COMMON SETS. . 169 6-1 GENERALIZED DEMAND FORECASTING PARAMETERS BY POPULATION SIZE AND BY URBAN STRUCTURE. . . . . . . . . . . 173 xii CHAPTER I PROBLEM STATEMENT AND OVERVIEW It is often felt that the wealth of research and methodology develop- ment in demand forecasting has not had a full impact on the mission- oriented, policy-decision-oriented functioning of the transportation profession. While decisions typically have to be-made under pressing deadlines, sophisticated demand-forecasting techniques require the process of data collection, calibration and sensitivity analyses, which often entails a time span longer than what the real time decision and policy formulation can afford. Several keen observers in the profession, including the developers of the Urban Transportation Planning System (UTPS), have recognized the need for research focused on "quick-turnaround" forecasting techniques. Few research efforts have been successful in fulfilling the need. The current research is undertaken to fill a gap in the knowledge base. A. Objective The research reviewed and compiled the empirical experiences in the multi-modal demand forecasting of the past two decades, during which a number of the early urban transportation studies, such as those in Philadelphia, Pittsburgh and Chicago, were conducted and a large number of demand-forecasting methodologies developed in the process. During the same time period, a sequence of events in the development of the national transportation system occurred, from the implementation of the interstate highways to recent emphasis on energy conservation and clean air. The time-series data for this era constitutes a wealth of information for addressing the following issues: (a) Have the original demand forecasts been validated by other studies (including the actual traffic counts) after the implementation of the planning transportation system? (b) For the successful forecasts, how can one transfer the demand model calibration parameters to other urbanized areas? regions and scenarios of similar characteristics, and with what confidence level? It is an opportune time, in the authors, opinion, to collect these successful parameters into one forum. This study Is Intended to contain validated forecasting parameters for "similar" geographic groupings, such as large and medium urbanized areas with core-concentrated or multinucleated urban structures. The tabulations also include demand parameters for a range of transportation supply alternatives with implementation potentials. The results are to be used for "policy- sensitive," multimodal urban demand forecasting, with the focus placed on fast-response decision Analyses in which an approximate projection of the vehicle-miles-of-travel (VMT) or passenger-miles-of-travel (PMT) in an urbanized area is to be made. B. State of the Profession The transportation planning profession is still in its embryonic stages. Unlike its sister professions, such as traffic management and engineering, much of the existing body of knowledge in transportation planning was accumulated over the past three decades, during which time both methodological development and empirical studies took place. In the 1940s and 1950s, trip generation models were developed to predict "generated" traffic from facilities. The early 1950s and 1960s saw ground breaking studies such as the Penn-Jersey study, the Chicago Area Transportation Study (CATS), and the Pittsburgh Comprehensive Renewal Program (CRP). During these and other milestone studies, a number of demand-forecasting techniques were developed. These include early versions of the Urban Transportation Planning (UTP) process consisting of generation, distribution and modal split on the one hand and direct demand models such as Baumol-Quandt/Abstract Mode varieties on the other. The UTP process consists of models applied sequentially and uses as input data aggregate values of zonal population, employment, average values of zonal incomes, car ownership, and interzonal travel times and costs. Tracing through the more recent developments, one finds literature on disaggregate behavioral formulations and modeling techniques of the simultaneous variety. The issue of aggregate versus disaggregate "probability" 'models permeates the above discussion. Hoot urban travel forecasting procedures are still being continuously developed both by researchers and 2 by operating personnel "in the field. " For example, research is under way with disaggregate models. in several universities and in selected consulting firms. The generally strong arguments for using disaggregate models are associated with the criticism of the aggregate models. An implicit aggregated data is that the characteristics of assumption in using households within zones are relatively homogeneous compared with differences between zones. However, several studies have shown just the opposite to be true--that more variation occurs within zones than between zones (McCarthy 1969). One potential problem of zonal-level analysis is the risk of ecological fallacy, in which aggregate level correlations are mistakenly attributed to individuals. Another problem is the loss of-variability in the data used for estimation. Since a model's coefficients are determined by explaining variations in observed travel behavior, the less variation to be explained, the less reliable the model will be. This reduced variability in aggregated data also results in a high level of collinearity between variables at the aggregate level which does not exist at the disaggregate level. There is always room for further theoretical development in the difficult subject of demand modeling. The current study is undertaken to verify many of the state-of-the-art techniques in an empirical setting. It is felt that a number of the forecasts made in the early 1950s and 1960s have been either validated or negated by subsequent measurements after the proposed transportation systems have been implemented. Meaningful verification of the forecasting methodologies can therefore be performed by comparing the forecasts with actual traffic and patronage counts. Aside from an evaluation function, such a comparison will point toward directions for future research. There are efforts being undertaken to accomplish similar objectives, albeit disparate in nature. Putting the discussion in the paradigm of supply/demand equilibrium, one can make the following review of related projects. On the demand side , one can cite the recent work of Dunbar (1976), in which a fair amount of emphasis is placed on observing demand elasticities on a national household sample survey. Similarly, one can 3 cite the work of Holland (1974). who concisely provides an empirical review on urban public transit demand elasticities reported on aver the last 19 years. The parallel work of Levinson (1976) is to the best of the authors' knowledge, still in the development stages. One of the more notable works on the supply side is the Characteristics of Urban Transportation System (CUTS) report by the U.S. Department of Transportation (.1974) in which seven factors ranging from speed to fuel consumption, are discussed as the attributes of the supply systems. Finally, pointing toward the equilibration side, a modest undertaking was made by Pratt (1977) to review the literature on the effect of supply changes on demand. Therefore, while projects are carried out on compiling the experiences in demand forecasting, the emphasis thus far has been placed most heavily on the demand or supply side individually, rather than on the equilibration between the two. The only project that comes close to equilibration is focused on literature review instead of compiling site-specific research and demonstration findings available from practice archives. C. Case for a More Responsive Procedure The current research places emphasis on fast-response demand forecasting under an equilibrium and empirical framework, providing the profession with a set of parameters (and procedures) to perform urban areawide forecasts of Vehicle-Mileage-of-Travel (VMT) and/or the PassengerMileage-of-Travel (PMT). This is undertaken in response to the inadequacies of previous approaches. Responsiveness to Problem-Solving One major problem of the conventional sequential model's of urban travel demand (UTD) is the amount of calibration required and, therefore, the large amounts of time and money involved in their operation. Simplicity has been used as a major criterion in the synthesis of past findings. As a result, its application requires few data items and does not require calibration (unless updating is necessary). The report attempts to develop an approach which will make use of the repertoire of the past twenty years of empirical experience in travel-demand forecasting. Such development is accomplished through the use of previous empirical experiences in 4 demand forecasting, as summarized In the demand elasticities. Elasticities of demand are recommended as one of the key parameters in determining the imp act of various changes in the level-of-service on transport demand. -,Independent variables will be selected which have been found by previous studies to be the most important in explaining total trip frequency (Smith and Cleveland 19761 and average travel impedance (Voorhees 1968), both of which serve as base conditions under which. the tabulated elasticities can be meaningfully applied. Another problem involved in the application of the traditional UTD models is their inadequate response to changes in the transportation systems. An equilibrium approach is followed in our research where the forecast equilibrium traffic is compared with other projections and/or the actual traffic volume after the implementation. Both the level-of- service variables.and the socioeconomic characteristics after the implementation are taken into account when the equilibrium traffic is forecast. The approach is, in this manner, much more responsive to changes in transportation systems. Policy-Oriented Analysis One of the objectives of this study is to develop a "quick-turn- around" technique for policy-oriented analyses, such as resource allocation between urban transportation investments. Toward this end, the forecasting is performed on an areawide basis. In a study by Koppelman (1972), an urbanized area aggregate model was developed based on the same modeling structure as the sequential UTD models. The analysis was based entirely on a correlative type of analysis, and the forecasts in this case are, therefore, based on the assumption that the trend established between the equilibrium points in different urban areas In the past years will perpetuate into the future. Statistical inferences were drawn from 22 urban areas that were treated as a homogeneous group. Studies mentioned previously (including Koppelman's) suggest four areas of emphasis for our research: (a) First, stratification of cities into classes such as large, medium or small (rather than treating them as a homogeneous group) facilitates a more policy-oriented and accurate urban areawide forecasting procedure. 5 (b) Second, a structurally sound analysis based on demand and supply functions is more likely to result in a more reliable forecast than a purely correlative projection would be. (c) Third, a larger data base than, for instance, Koppelman's 22 cities is mandatory in order to draw any meaningful statistical inferences. (d) Finally, a method to synthesize the models which were calibrated in different levels of data aggregation, from household, zonal, to urban areawide, needs to be discussed. While the first three points have been covered thus far, the last is yet to be addressed. It is toward this last issue that the reader's attention is directed. Aggregation of Previous Experiences Three types of model parameters, encompassing calibrations from household-level data, zonal-level data and urban areawide data respectively, have been compiled in our current study. Urban areawide models calibrate the parameters by using areawide-average data, while parameters calibrated by zonal-level models and household-level models use zonal-average and household-average data respectively. To different degrees, the three types of parameters assume that the response of demand with respect to various attributes is homogeneous over the geographic unit-of-analysis (whether it is the household, the zone or the city). Many practictioners recognize, however, that this assumption may be weak in numerous "realworld" circumstances, and the use of aggregated data has been subjected to active discussions among the profession. Recognizing the data aggregation issue, we find it is necessary to adjust these three types of parameters into a common denominator so that the aggregation error can be reduced to a minimum. An estimation on the aggregation error is made, albeit on a very limited data base. Actual parameters from zonal-level calibrations are also established as upper limits of the equivalent parameters aggregated from their householdlevel counterparts. With these steps taken, we feel that our aggregation errors are acceptable for the forecast of city wide VMTs and PMTs. Once a set of demand model parameters has been synthesized and aggregated from previous experiences, two new issues surface which require our attention. First is the stability and transferability of 6 these parameters, both spatially among diverse cities and temporally over different planning periods. Even when parameters are shown to be transferable, a second question arises regarding the necessity to update them prior to site-specific applications. These issues will be discussed below. D. Stability and Transferability The sequential and direct models of urban travel demand (UTD) require three basic assumptions for use in forecasting: (a) Independent variables can be accurately forecast. (b) The models provide an accurate, behaviorally correct simulation of base-year travel demand. (c) Model variable structure and parameters are stable over time. These assumptions should also hold with respect to our approach. Two other specific assumptions for the development of the approach are: (i) Model variables, structure and parameters are spatially stable; and (ii) Both elasticities and cross-elasticities are tempor ally and spatially stable. The temporal and spatial stability assumptions in this research are based on findings of previous researchers which are briefly discussed here. The introduction of the updating issue later in this section will render the temporal and spatial stability assumption less restrictive than they may appear at this point. Previous Findings In recent years, much work has gone into the development of disaggregate travel demand models which are based on household (rather than zonal) data. It has been suggested that such models are more temporally and spatially stable than aggregate models based on zonal characteristics. Kannel and Heathington (1973) examined the form of household travel relations to determine the stability of these relations over time and to evaluate the ability of household (disaggregate) trip generation models to estimate future travel. The results indicated that the household trip generation models based on the 1964 data could successfully predict household travel reported by the same households in 1971. 7 The spatial stability of the trip generation relations has also been shown. Both the household and zonal models were estimated from household-level variables based on 200 observations in Indianapolis and 305 observations in the tri-state area. The magnitudes of the household model parameters for the independent variables are strikingly similar for the two study areas even though the areas themselves would not be considered as comparable in nature. The parameters of the model in the zonal-level of analysis, using independent variables from the household- level, have also been shown to be relatively stable. Along this line of investigation, Smith and Cleveland (1976) identified the two most important types of independent variables in explaining total trip generation: (a) some measure of household size; and (b) some measure of household economic status--typically car ownership. The total number of person trips as a function of cars available and number of persons in the household showed temporal stability when non- trip-making households were removed. Smith and Cleveland also showed that, as a general rule, the stability of each of the coefficients in an equation does not sufficiently guarantee the overall time stability of the equation. The research by Atherton and Ben Akiva (1976) was concentrated on the spatial transferability problem. In their work, the researchers re- estimated an existing mode choice model, based on 1968 Washington, D.C. data, using a data set representative of New Bedford, Mass. in 1963 and Los Angeles, Calif. in 1967. The original Washington models provided surprisingly good performance on both New Bedford and Los Angeles data. This is particularly noteworthy in view of the fact that the New Bedford and Los Angeles data sets represent very different travel conditions than those existing in the Washington data. Trip Frequency, Trip Duration and Demand Elasticities The assumption of temporal and spatial stability in our current research holds with respect to three different travel parameters: trip frequency, average trip duration and demand elasticities (including cross-elasticities). While the spatial stability of the three sets of parameters is not found over identical groups of cities, the result of 8 our classification analysis of urban areas according to size and struc- ture points definitively toward a four-cell taxonomy. Our classification scheme of urban areas is shown in Figure 1.1. From our trip duration analysis, the urban areas can be classified into two groups according to their sizes. The large cities are those cities with population over 800,000, while the medium cities are those with populations between 50,000 and 800,000. Together with the additional analyses on trip frequency, each group is again classified according to their urban structure (core-concentrated or multinucleated). Core- concentrated cities have the development centered around the Central Business District (CBD), while multi-nucleated cities have a dispersed land use-pattern. The four-cell classification, according to population size and urban structure, is shown to have grouped cities into similar clusters as far as travel patterns are concerned. Finally, the elasticities and cross-elasticities which are derived from the modal split model are also found in this study to be spatially stable within as well as across the cells. This is in agreement with the work of Atherton and Ben-Akiva (1976) and other disaggregate travel demand research. Representative of the latter category are the numerous values-of-travel-time studies (Transportation Research Board 1976) which are often referenced in many modal split calibrations. E. Updating Although there is a considerable amount of agreement concerning the temporal and spatial stability of the model structure and the explanatory power of selected variables (Smith and Cleveland 1976), a few researchers have not agreed on the direct transferability of parameters such as individual regression coefficients. This non- transferability of parameters is mainly due to the fact that there are extreme differences between the cities where the model was estimated and those for which the model is applied. These dissimilarities may be caused by differences in the levels-of-service and socioeconomic variables. In these cases, the model should be updated before it can be applied to the urban area under consideration. The motivation behind updating is clear. If a successful model in one area can be updated instead of re-estimated, the amount of data 9 Click HERE for graphic. FIGURE 1-1. CLASSIFICATION SCHEME OF URBAN AREAS 10 needed to develop a travel demand model in the new area could be greatly reduced, and, as a result, the cost of conducting the transportation study in that area will be minimized. Updating also allows one to improve the accuracy of a forecast where the inferential robustness of a general model, with respect to a specific site, is in doubt. Simple updating procedures are identified In this Project. It can be noticed that an additional contribution of this research will be parameter updating. The spatial and temporal stability established for our models and parameters facilitate the updating process to a large extent. One should bear in mind, at the same time, that while we are forecasting on an urban areawide basis, many of our analyses use the household-level data results. This provides parameters that are more temporally and spatially stable than traditional zonal analysis. F. Summary The objective of this chapter is to review the previous experiences in the demand-forecasting profession and to incorporate these experiences in a consistent and succinct form for more effective travel forecasting. The discussion plan parallels the historical development of demandforecasting techniques. Our chapter starts with a summary of the many previous experiences in trip generation and trip distribution. The review leads toward the base-condition equations on trip frequency and duration which serve as discriminants for classifying cities according to their travel pattern. Then modal-split models developments are captured in the discussion of elasticities, which summarizes many of the findings (and calibration results) regarding modal choice models. The aggregation of previous results--which are typically performed on a zonal or household level-into an urban areawide travel forecast is a main task of this study. This emphasis permeates our whole report and many of the discussions are devoted to the synthesis of past findings. Take the use of elasticities, for example; our synthesis shows that demand elasticity alone, being a point estimate, cannot be used to forecast effectively. This is because elasticity is defined only for a particular base condition which is often characterized by a particular level-of-service and traffic volume. In addition, it reflects only 11 short-term changes where no drastic system implementation and shift in socioeconomic activities take place. To use parameters such as elasticities meaningfully, one must employ an equilibrium framework to put the various pieces of information together in a consistent manner, whether they be elasticity tabulations, city classification schemes or base travel conditions. There are other attempts to perform urban areawide forecasts, most notable of which is the Macro Urban Demand Models (Koppelman 1972). It utilizes a purely correlative type of analysis and does not employ demand/supply structural equations. Our aggregation and synthesis differ from others in the following respects: (a) It is a simple procedure based on the tabulations of demand forecasting parameters such as elasticities and base-condition travel characteristics. (b) The parameters are tabulated for each homogeneous group of cities sharing similar travel characteristics. (c) The transferability of these parameters to specific sites is ensured by considering the need for updating. (d) It takes into account demand/supply equilibrium--a desirable feature in forecasting where major transportation system improvements took place. 12 CHAPTER II CLASSIFICATION OF URBAN AREAS FOR DEMAND FORECASTING ANALYSIS The following analysis deals with forecasting travel demand on an areawide level. Before any demand-forecasting experiences can be compiled, a logical and effective way of identifying cities that are similar in their travel demand characteristics is essential. For example, cities may be grouped into large, medium, versus small categories. Such a grouping, while appealing at first sight, may not represent all the classification factors that need to be considered. Two large cities with similar population sizes may turn out to have drastically different land development patterns, thus generating totally different travel volumes. A more refined classification scheme is, therefore, necessary to result in meaningful demand forecasts. In the sections which follow, not only is a taxonomy scheme developed out of these and other a priori or theoretical considerations, but the data availability problem is also discussed at the same time. A. Candidate Urban Areas A candidate set of cities needs to be selected as a data sample for our city classification analysis. In this regard, whether there is adequate travel information becomes as much a determining factor in the final selection as regional science or urban planning considerations. The following two criteria were specifically referenced in selecting the cities which were included in our classification analysis: (a) Availability of data and development of demand forecasting experiences in the candidate city. (b) Proportional sampling based on the number of cities of each classification in the United States; thus there are more medium than large cities in our sample because there are more of them in the nation. Either data is gathered directly from the field or can be obtained indirectly. The former is often referred to as "primary data," while the latter encompasses both "secondary" and "tertiary level data." As the title indicates, this project, by its nature, is based mostly on secondary and tertiary data. "Secondary data" is defined here as information obtained 13 "off-the shelf" from another party. Survey returns obtained from an organization which conducted the actual survey are examples of secondary data. Tertiary data, on the other hand, is processed data--data that has been tabulated, abstracted, or calculated from primary data. Empirical elasticities calculated from the patronages before and after a fare increase (Holland 1975) or the trip generation rates per household (Oi and Shuldiner 1962) are examples of tertiary data. A fourth level data set can also be defined. This consists of the calibrated parameters from demand models that have been operationalized in the past for selected cities. These coefficients, whether they are elasticities from direct demand models or coefficients of the logit model, can conceivably be updated to reflect present scenarios or be transferred to a similar geographic setting after the appropriate adjustments have been made (Kannel and Heathington 1973, Atherton and Ben-Akiva 1976). They serve as a rather accessible set of demand parameters where a complete model cannot be obtained. The need for compiling areawide level data can be realized from a review of travel demand models which-show that only a very few attempts have been made to develop urbanized area aggregate models. Koppelman (1972) states, "Despite the massive acquisition of travel data in urbanized areas during the 1960s, little has been done to develop a consistent set of data in different areas which could be used to estimate a highly aggregate set of relationships for directly estimating total travel in urbanized areas." At the early stage of the research, the use of tertiary information seemed particularly desirable for a project of this nature where synthesis is involved. However, as one can understand from the above statement by Koppelman, the availability of areawide level data from tertiary sources was so scarce that the above strategy was changed. It was understood that the reliability of our findings would depend on a great extent on the amount and reliability of the data available. As a result, a significant portion of the research effort was allocated to data acquisition. As a first step in the data acquisition process, a questionnaire was designed and mailed to transportation planning agencies across the country. Appendix 1 gives a detailed description of both the acquisition process and the actual data base. The second step consisted of extracting the data pertinent to the calibration analysis and reorganizing it according to the 14 specified format. The final product of this step is given in full in the same Appendix. We believe that the travel demand-forecasting experiences compiled from the survey consist of one of the largest collections of such data in existence. The availability of such a data set to transportation planners is of great importance to the development of urbanized area aggregate models in the future. It is for this reason the data tabulation is included as part of the Final Report. The last step was to finalize the city classification analysis into a set of three tasks. Task 1 was the referencing of the way cities are grouped in the institutional frameworks of transportation planning, whether it be the Comprehensive, Cooperative, and Continuing (3C) process or otherwise. Task 2 was the categorization of cities according to their sizes and development pattern (collectively referred to as the Activity System). Task 3 was the grouping of cities into families according to their transportation systems. B. Infrastructure The classification of cities has to be responsive to the overall policy framework of the nation. Section 134 of the Federal-Aid Highway Act of 1962, for example, specifies that urban areas of more than 50,000 population have underway Comprehensive, Cooperative, and Continuing (3C) planning programs. In many local planning contexts, this legislative action draws a sharp distinction between cities of different sizes--thus the cities with 50,000 or more population forms a logical group because of their common planning guidelines, while those below 50,000 constitute a second grouping. Another distinction (albeit a less prominent one) is made for urbanized areas over 250,000 in population, most of which have performed multimodal planning programs including long-range transit planning. Thus, it would appear that urban areas over 250,000 population would constitute one grouping, those between 250,000 and 50,000 could be referred to as a second, and those under 50,000 a third. Finally, recent developments in Transportation Systems Management (TSM) improvement programs call for TSM plans for urban areas with population of 200,000 and above. It can be seen, therefore, that infrastructural guidelines for grouping cities are numerous and varied. It will suffice to say at this juncture that these guidelines will be taken into account in our city classification analysis. 15 C. Activity System Urban travel demand has long been recognized as derived from the execution of socioeconomic activities such as work and recreation. Koppelman (1972) suggests that the socioeconomic variables to explain travel demand in an urban area can be grouped into two categories: (a) Area characteristics including overall size, density of development and commercial and industrial characteristics (b) Population characteristics including income, age, auto- ownership, population, household size, and occupation status. There tends to be a larger amount of traffic, for example, in a larger size urbanized area (than in a smaller area). A core-concentrated city, which is by definition more densely developed in the center, would likewise have a different travel pattern than a multinucleated city. Classification of cities according to their activity system has been performed by a number of researchers (see Ellis and Chan [1975], for example). Few of them, however, have related specifically to the size, shape, and spatial distribution of urban activities. A review of the pertinent findings regarding the relationship between travel demand and activity system is given in Tables 2-1 and 2-2 which are discussed below. Relationship Between Demand and Urban Size Some theoretical relationships between trip lengths and the size of an urban areas have been compiled in Table 2-1. There seems to be a general agreement that larger cities report longer average trip lengths. The equations from both empirical and simulation studies bear this out, where the mean trip length (measured either in time or in miles) are positively related to either the population or the developed land area of a city. Another intuitively appealing result is the observation on the trip frequencies that more areawide travel is reported in bigger cities. A special relationship, however, is found regarding the auto trip demand per household: small urbanized areas have a generally higher auto ownership and most trips are executed via auto (due to the absence of a competitive mode). The reliance on the auto as the only means of transportation is heavier in small urban areas but becomes less so in larger cities where transit emerges as a viable alternative. 16 TABLE 2-1. RELATIONSHIP BETWEEN TRAVEL DEMAND AND SIZE OF THE URBAN AREA SIZE (Population, Land Area) SOURCE Empirical Results _ 0.2 t = 0.98 P _ where t = mean trip length, minutes P = population _ 0.2 1.49 L = 0.003 P S Voorhees (1968) _ where L = mean trip length, miles S = average network speed ______________________________________________________________ Maximum auto trip length and number of auto trips occur in cities of 5,000 - 25,000 population. Gilbert and Dajani Thereafter, auto trip demand per household declines (1974) steadily as population increases. ______________________________________________________________ Simulation Study Results _ 1.5 L = K P Goldmuntz K = constant (1974) ________________________________________________________________ _ L - k A A = developed land area k = constant Edwards and Schofer (1975) However, this relationship is not independent of the activity distribution. Source: Adapted from Clark (1975). 17 TABLE 2-2. RELATIONSHIP BETWEEN TRAVEL DEMAND AND SPATIAL DISTRIBUTION OF SOCIOECONOMIC ACTIVITIES ACTIVITY DISTRIBUTION SOURCE Empirical Results __ _ _ _ 0.5 t / t = [ O / O ] 1 2 2 1 _ Voorhees O = mean opportunity trip length, which implies (1968) closeness between trip ends is low travel. __________________________________________________________ Comprehensive Transportation Study Results Mean Trip length increases with centralization of employment. Hansen and Morrison (1968) __________________________________________________________ Extreme concentration of employment requires most travel. Limited dispersion (within the political city, but not Toronto throughout the entire region) leads to minimum travel study (1975) requirements. __________________________________________________________ Simulation Study Results Low travel: weak centralization of employment and shopping (multinucleated) High travel: strong centralization of employment and Hemmens shopping (core-concentrated) (1967) Residential distribution: little effect on travel Low travel: Locate population and employment at least central location; minimize the disper- Schneider sion in the zone-to-zone ratio of population and Beck to employment. (1974) Minimize travel Concentrate growth of population and Clark increase: employment at the regional center. (1975) (continued) 18 TABLE 2-2. RELATIONSHIP BETWEEN TRAVEL DEMAND AND SPATIAL DISTRIBUTION OF SOCIOECONOMIC ACTIVITIES (Continued) Minimum travel: Concentrate population at center. More sensitive to population than employment distribution. More generally, cluster Edwards and activities. Schofer(1975) Spread pattern can be made fairly efficient, and can offer high accessibility but requires reliance on auto for trips that might be made on foot in compact concentration. __________________________________________________________ Large concentration of employment in CBD requires 6 percent Levinson greater mean trip length than moderate concentration. and Roberts (1963) __________________________________________________________ Locate 50,000 new jobs: _ - concentrated in CBD L = 10.8 miles _ - in 12 satellite centers L = 8.2 miles Harkness _ (1973) - in 50 neighborhood centers L = 2.3 miles ___________________________ Source: Adapted from Clark (1975). 19 Dimension I Population Size Dimension II Large Medium Core- Atlanta Salt Lake City Concentrated Pittsburgh El Paso Milwaukee Tucson Multi- Chicago Springfield Nucleated Philadelphia Richmond Dallas-Fort Worth Oklahoma City FIGURE 2-1. EXAMPLE CLASSIFICATION OF STUDY AREAS 20 Relationship Between Demand and Spatial Distribution Travel demand is also found to be determined by the layout of activities such as population and employment in the study area (Table 2- 2). For example, the amount of travel (measured in VMT) is less when employment centers are dispersed than when they are concentrated in one location. This can be explained. When there are multinculeated activity centers, the average trip length tends to be shorter due to a closer proximity between residential, work, and non-work locations. For a given trip making frequency, the amount of vehicle-miles-of-travel (or passenger-miles-of-travel) is smaller in multinucleated cities (where trip durations are shorter) than in core-concentrated cities. All these findings lead us to hypothesize a four-cell city classification to explain the different travel patterns. As can be seen in Figure 2-1, a column vector can be used to identify the study area as large or medium, and a row vector can be employed to define a given area by its urban structure, whether it be core-concentrated or multinucleated. Three examples are given for each of the classification cells. Thus, while Pittsburgh exemplifies a core-concentrated large city, Oklahoma City illustrates a multinucleated, medium city. D. Supply Characteristics Aside from considerations of travel patterns, the city classification scheme should ideally reflect the distinct families of urban transportation systems. Heavy rail, for example, tends to have an association with only the very large/core-concentrated cities. Demand- responsive systems, on the other hand, are more suited for the lower density/multinucleated communities. One wishes to classify cities, therefore, on the grounds not only of their activity systems, but also according to their transportation supply characteristics. Classification of cities according to their arterial transportation needs and requirements has been performed by Golob et al. (1972). They classified 80 urban areas into nine groups (see Table 2-3). Groups one and two reflect the uniqueness and dominance in the urban hierarchy of first, New York, and secondly, Chicago and Los Angeles. Group three consists of large northeastern cities characterized by high residential density and transit orientation. Group four consists of southern cities with high residential density and low income. Group five contains cities not highly industrial, 21 TABLE 2-3. 9-GROUP LEVEL CLUSTERING Group 1 Group 5 Group 7 Group 9 New York Denver Beaumont Albuquerque Indianapolis Dallas Davenport Kansas City El Paso Dayton Group 2 Oklahoma City Fort Worth Duluth Portland Houston Flint Los Angeles Providence Phoenix Lansing Chicago Seattle San Antonio Madison Springfield San Bernardino Minneapolis Tacoma San Diego Newport News Group 3 Tulsa San Francisco Omaha San Jose Tucson Baltimore Utica Boston Group 6 Wichita Detroit Group 8 Youngstown Philadelphia Akron Pittsburgh Albany Fort Lauderdale St. Louis Bridgeport Miami Washington Buffalo Orlando Cincinnati Tampa Cleveland West Palm Beach Group 4 Columbus Grand Rapids Atlanta Hartford Birmingham Milwaukee Charlotte Richmond Honolulu Rochester Jacksonville Sacramento Knoxville Salt Lake City Louisville Syracuse Memphis Toledo Mobile Wilmington Nashville Worcester Mew Orleans Norfolk ___________________________ Source: Golob et al. (1972) 22 with their residents earning average personal income and older families. Group six consists of mideastern industrial cities, with high personal income and high residential density. The Cities in this group are oriented toward public transit. Group seven includes young south- western areas with the lowest residential density and public transit orientation, Group eight consists of the Florida areas with significant retired population and low residential densities. Finally, group nine consists of young northern industrial areas with high personal income. In grouping cities, Golob et al. used a cluster analysis technique which is a version of a method developed by Friedman and Rubin (1967). A variety of cluster analysis techniques are available for the purpose of classifying items into relatively homogenous groups, and they differ in their criteria for optimality and solution methods. Basically cluster analysis is a heuristic algorithm in which relatively homogenous groups containing 'contiguous" items are found through a sequence of steps. In each step the solution is improved with respect to the criteria of optimality. If one examines our proposed city- classification scheme carefully, he will recognize that both urban size and urban structure are embedded within the Golob classification, in that core-concentrated and multinucleated cities are actually associated with higher and lower density levels. One can, therefore, notice that the Golob classification and the proposed taxonomy are in agreement, since both use population size explicitly as a factor in classifying cities, and differentiating cities according to urban structure is equivalent to urban density. Each city grouping should ideally represent a logical cluster of cities with similar transportation systems characteristics (aside from socioeconomic ones). Predictions made from such a cluster have a correspondingly higher statistical validity than "fits" made on more than one cluster. The classification scheme outlined in the previous section is responsive to the clustering scheme. Large/core-concentrated cities, for example, represent scenarios where more elaborate transit systems such as heavy rail (typically radial at the CBD) are found and transit modal split is significant, On the other end of the spectrum, small/multinucleated cities have shorter trip lengths and are typically auto-oriented. 23 E. Analyses The purpose of classifying urban areas is to group areas with similar travel behavior and transportation system characteristics. A number of city classification techniques are investigated. We have investigated cluster analysis in the previous section. Such a technique is not used explicitly in our study for several reasons. First, the cluster analysis technique is rather involved and time consuming, which by definition works against the research objective of simplifying demand- forecast procedures. A large amount of time is consumed during the cluster analysis procedure in defining: (a) a meaningful measure of association between variables, (b) a measure of similarity for every pairwise combination of the entities to be clustered, and (c) a clustering criterion. It is also questionable if the above effort is Justifiable in view of the small number of factors dealt with. Most importantly, preliminary analyses, such as those shown in the plot of Figure 2-2, show no logical cluster pattern among a number of variables. It is decided that such an approach be taken into account explicitly by the urban size and structure classification scheme following some of the findings by Golob et al. Having considered cluster analysis as a city classification technique, the researcher proceeds to examine other pertinent methodologies, factor analysis, linear regression and a technique related to linear regression, "linear goal programming." Factor analysis is a technique of data reduction that identifies a selected set of underlying dimensions of data reduction that identifies a selected set of underlying dimensions out of a larger pool of variables. Another method for reducing the dimensions out of a large pool of variables is the regression analysis. While no explicit distinction ismade between independent and dependent variables in factor analysis, regression analysis explains a dependent variable in terms of a set of independent ones. Linear goal programming (Ignizio 1976) can perform a similar statistical fit between dependent and independent variables. It differs from ordinary regression in that the sum of the absolute values of the residuals Alt228|ri| are minimized instead of the squared of the residuals Eri 2 (see Appendix 3). It is felt that the use of "quadratic loss function" in the regression method results in allocating inflated weights to "outliers," since the weights are proportional to the square of the residual instead of being proportional 24 Click HERE for graphic. FIGURE 2-2 NUMBER OF DAILY PERSON TRIPS PER DWELLING UNIT VERSUS AVERAGE TRIP DURATION 25 to the residuals themselves. This error is avoided in the LGP method, since it minimizes the sum of the absolute values of the residuals. It has been pointed out that the difference in travel patterns between cities can be characterized by two attributes trip frequency and trip duration. The difference in frequency rate and average trip duration among cities was explained in terms of urban size and structure. Preliminary analyses (Figures 2-3 through 2-4 and Tables 2-4 through 2-6) indicate that trip frequency and trip duration are good discriminants between city groups. Trip frequency is a function of variables such as income, auto-ownership, etc., while trip duration is correlated most significantly with population, both of which are activity system variables. By grouping cities according to similarities regarding trip frequency and trip duration relations, we actually obtain a taxonomy according to both activity system and supply characteristics. It is concluded that while there are quite a few factors which can be used in discriminating between cities, our review of previous studies and preliminary analyses indicate that differences in urban travel patterns can be explained using very simple bivariate relationships. This finding, together with our emphasis on a fast-response demand estimation procedure, eliminates the need for factor analysis and points toward regression and linear goal programming as the most suitable techniques for city classification. Trip Frequency Trip frequency (generation) rates are the first element of trip making patterns according to which cities are classified. Together with average trip lengths, trip frequency rates are required for calculating total vehicle-miles-of-travel. To guarantee the stability and transferability of the equations used to estimate trip frequency, the trip frequency rates are represented by "average number of person trips per dwelling unit." The two types of independent variables that have been found to be the most important in explaining total number of trips per household are persons per household, and autos per household. However, the above findings are based on analysis in the household level; whether the two independent variables presented above are also closely associated with the number of trips per 26 Click HERE for graphic. FIGURE 2-3. TRIP DURATION VERSUS POPULATION IN URBAN AREAS WITH POPULATION BETWEEN 50,000 and 800,000 27 Click HERE for graphic. FIGURE 2-4. AVERAGE NUMBER OF TRIPS PER DWELLING UNIT VERSUS AVERAGE AUTO OWNERSHIP PER DWELLING UNIT IN CITIES WITH POPULATION OVER 50,000 28 TABLE 2-4. NINETEEN CLASSIFICATIONS OF URBAN AREAS No. Class Population Urban Size Range Structure 1 Large over 250,000 x 2 Medium 50,000-250,00 x 3 Large over 500,000 x 4 Medium 50,000-500,000 x 5 Large over 800,000 x 6 Medium 50,000-800,000 x 7 Large over 250,000 Core-Concentrated 8 Large over 250,000 Multinucleated 9 Medium 50,000-250,000 Core-Concentrated 10 Medium 50,000-250,000 Multinucleated 11 Large over 500,000 Core-Concentrated 12 Large over 500,000 Multinucleated 13 Medium 50,000-500,000 Core-Concentrated 14 Medium 50,000-500,000 Multinucleated 15 Large over 800,000 Core-Concentrated 16 Large over 800,000 Multinucleated, 17 Medium 50,000-800,000 Core-Concentrated 18 Medium 50,000-800,000 Multinucleated 19 Overall over 50,000 x 29 TABLE 2-5. ALTERNATIVE CITY CLASSIFICATIONS FOR TRIP FREQUENCY ANALYSIS Classi- Population Intercept Car Ownership R t Se fication Range Coefficients Overall --- 2.569 5.022 0.368 7.40 1.18 Large Over 500,000 3.072 4.030 0.407 4.72 1.07 Medium 50,000-500,000 0.974 6.887 0.409 6.83 1.26 Large Over 800,000 3.132 3.611 0.503 4.60 0.922 Medium 50,000-800,000 1.262 6.591 0.412 7.43 1.21 30 TABLE 2-6. ALTERNATIVE CITY CLASSIFICATIONS FOR TRIP DURATION ANALYSIS Classi- Population Model* Intercept Population R t Se fication Range Type Coefficient Overall --- (a) 9.077 0.003 0.231 4.95 3.55 --- (b) 0.892 0.260 0.320 7.58 0.295 --- (c) -3.574 2.638 0.333 7.18 3.15 Large Over 500,000 (a) 14.180 0.001 0.251 2.01 3.75 Large Over 500,000 (b) 1.629 0.159 0.223 1.85 0.243 Large Over 500,000 (c) -0.657 2.738 0.202 1.74 3.87 Medium 50,000-500,000 (a) 7.123 0.013 0.140 3.21 3.08 Medium 50,000-500,000 (b) 0.660 0.307 0.249 4.57 0.302 Medium 50,000-500,000 (c) -2.818 2.463 0.176 3.67 3.01 Large Over 800,000 (a) 13.980 0.001 0.644 3.69 1.83 Large Over 800,000 (b) 1.396 0.188 0.563 3.11 0.115 Large Over 800,000 (c) -10.540 3.618 0.766 4.43 1.56 Medium 50,000-800,000 (a) 7.235 0.013 0.264 4.97 3.31 Medium 50,000-800,000 (b) 0.629 0.314 0.335 5.90 0.304 Medium 50,000-800,000 (c) -5.181 2.970 0.281 5.19 3.77 ___________________________ * The "model type" refers to the different types of trip duration models that were investigated, where (a), (b) and (c) are defined in the text. 31 dwelling unit in the areawide level of analysis is yet to be investigated. A goodness-of-fit measure to help in the investigation is the partial correlation coefficient between a dependent variable and the particular independent variable under consideration. Table 2-7 shows the partial correlation coefficients between trip frequency and both "average auto ownership" and "average number of persons ,per dwelling unit." The relationship between "average number of trips per dwelling unit" and "average auto ownership per dwelling unit" is : illustrated in Figures 2-3 and 2-5. It can be observed from the partial correlation coefficient in Table 2-7 as well as from Figure 2-3 and 2-5 that there is a high correlation between the "number of trips per dwelling unit" and the "average auto-ownership per dwelling unit." However, Table 2-7 as well as Figures 2-7 and 2-8 show that there is no significant correlation between the "number of trips per dwelling unit" and the "average number of persons per dwelling unit" on the areawide level. The independent variable average number of persons per dwelling unit" is therefore eliminated from the trip frequency model. In an analysis conducted at the early stage of the research using data from tertiary sources, another variable that was investigated as the explanatory variable for the "number of trips per dwelling unit" is "average number of autos per adult." This variable was found to be less successful in explaining "average number of person trips per dwelling unit" than "auto ownership per dwelling unit." In the same analysis, differences in trip duration relations were identified between two groups of city sizes: those over 800,000 and those between 50,000 and 800,000. The report will turn to this issue below. Trip Duration It has long been recognized that among trip makers two primary considerations are time and cost, both of which are related to distance. It is also recognized that travel cost or travel distance has been taken into the consideration of residential location choice, which ultimately determines the urban structure. In this study, a surrogate of trip distance and cost (average trip duration in minutes) is therefore used in differentiating travel characteristics among urban classifications. 32 TABLE 2-7. DOMINANT CLASSES IN TRIP FREQUENCY ANALYSIS Click HERE for graphic. ___________________________ 1 - Intercept 2 - Car Ownership Coefficient 3 - Partial Correlation Coefficient between trip frequency and car ownership 4 - Persons Per Dwelling Unit Coefficient 5 - Partial Correlation Coefficient between trip frequency and persons per dwelling unit. 6 - Coefficient of Determination * The coefficient of multiple determination (R), which measures the percentage of total variation in a dependent variable that is explained or accounted for by the combination of the independent variables included in the equation, is adjusted to the number of degrees of freedom. ** The number corresponds to the classification number in Table 2.4, 33 Click HERE for graphic. Figure 2-5 AVERAGE NUMBER OF TRIPS PER DWELLING UNIT VERSUS AVERAGE AUTO OWNERSHIP PER DWELLING UNIT IN LARGE CORE- CONCENTRATED CITIES WITH POPULATION SIZE OVER 800,000 34 Click HERE for graphic. FIGURE 2-6. AVERAGE NUMBER OF TRIPS PER DWELLING UNIT VERSUS AVERAGE AUTO OWNERSHIP PER DWELLING UNIT IN MEDIUM CITIES WITH POPULATION SIZE BETWEEN 50,000 and 800,000 35 Click HERE for graphic. FIGURE 2-7. AVERAGE NUMBER OF TRIPS PER DWELLING UNIT VERSUS AVERAGE AUTO OWNERSHIP PER DWELLING UNIT IN LARGE CORE- CONCENTRATED CITIES WITH POPULATION SIZE OVER 800,000 36 Click HERE for graphic. FIGURE 2-8. AVERAGE NUMBER OF TRIPS PER DWELLING UNIT VERSUS AVERAGE NUJMBER OF PERSONS PER DWELLING UNOT IN MEDIUM CITIES WITH POPULATION BETWEEN 50,000 AND 800,000 37 A study by Voorhees and Associates (1968) indicates that primary determinants of trip duration are the size and physical structure of the urban areas, and average city density. Two models are suggested by Voorhees and Associates (1968) to explain the average trip duration in an urban area. In both models, average trip duration is explained by the urban population: _ (a) t = a + bP _ (b) t = P where: _ t = average travel time in the urban area in minutes P = the population size (thousands of persons) a, b, , = calibration coefficients The above models are based on the hypothesis that trip duration should increase with population--that the larger the city the longer the trips. It is to be noted that although population is the only independent variable in the model itself, the other determinant variables, physical structure and average city density, are incorporated through the classification scheme presented in the previous section. It is our belief that a third model that has not yet been investigated should be taken into consideration. Intuitively and from trip duration data (Figure 2-4 and 2-9), it appears that when population grows, travel time grows at a decreasing rate. Hence the following model is suggested: _ (c) t = c + d 1n(P). Similar to the trip frequency analysis, alternative linear regressions were performed to estimate trip duration. The results are summarized in Table 2-8. F. Results: A Taxonomy It was previously stated that the purpose of the taxonomy is to identify similarities in average trip frequency and average trip duration relations among cities. Such similarities can be identified from plotting the observations as a first step. Then the coefficient of determination is used as a more quantitative measure of the extent to which the trip frequency and duration of a group of cities can be explained by a common set of explanatory variables. Thus, if there are similar travel characteristics between a group of urban areas they are reflected by a larger coefficient-ofdetermination within this group when compared to other ways of grouping these cities. Note that the coefficient-of-determination at this stage is not used 38 Click HERE for graphic. FIGURE 2-9. TRIP DURATION VERSUS POPULATION IN URBAN AREAS WITH POPULATION BETWEEN 50,000 and 800,000 39 TABLE 2-8. DOMINANT CLASSES IN TRIP DURATION ANALYSIS Click HERE for graphic. 40 as a measure of the "goodness-of-fit" or as an indicator of forecasting ability but rather as an indicator of the existence of a relationship among cities that can be represented by the same linear model. For example, if we review the plot of trip duration against population (Figure 2-2) the large cities with population size over 800,000 and the medium cities with population between 50,000 and 800,000 form two well defined groups with distinctly different relationships between average trip duration and population. Our hypothesis regarding the four-cell classification scheme is now to be investigated. An alternative to this hypothesis is that both size and structure are not influential factors on travel behavior and, therefore, all the urban areas can be considered as a single group with respect to their travel characteristics. Another alternative is to classify cities according to their size only. These alternatives have been covered in our analysis as shown in Table 2-4. A major part of the results regarding the above alternative is demonstrated in Tables 2-5 and 2-6. One can notice that similarities regarding travel relations exist among cities with population within a certain range. This is indicated by a larger portion of the variations explained by both the trip frequency and trip duration models when the overall group of cities is classified according to population size. The second step is to test the significance of urban structure as an underlying determinant of travel relations. The trip frequency models shown in Table 2-7 indicate that classifications with stratification according to urban structures were found dominant over those classifications presented in Table 2-5, where urban areas are grouped only by their population size. One can notice that a significant portion of the variations in trip frequency relations in large urban areas could be explained by differences in structure. Similarly, a significant portion of the variations in trip duration relations in medium size cities should be attributed to the difference in their structure. This can again be concluded from a parallel comparison between the results in Table 2-6 and 2-8. The results of the analysis, as exemplified by Table 2-7 and 2-8 and the corresponding plots, can be summarized below: (a) The classification of urban areas according to trip frequency characteristics results in these groupings (Table 2-9): 1. Large/core-concentrated urban areas with population size over 800,000 41 TABLE 2-9. RELATIONSHIP BETWEEN AVERAGE TRIP FREQUENCY PER DWELLING UNIT AND AVERAGE AUTO OWNERSHIP PER DWELLING UNIT ACCORDING TO URBAN SIZE AND URBAN STRUCTURE Urban Structure Population Size Core Concentrated Multinucleated _ _ _ _ Large Y = 2.242 + 3.761 X Y = 2.831 + 4.117 X with Population R=0.842 Se=0.673 df=6 R=0.842 Se=0.542 df=7 over 800,000 _ _ _ _ t = 5.30 Se/Y = 0.098 t = 4.27 Se/Y = 0.073 _ _ Medium with Y = 2.831 + 4.117 X Population between R = 0.842 Se = 0.673 df = 6 50,000 and 800,000 _ _ t = 5.30 Se/Y = 0.098 where: _ Y = average number of daily trips per dwelling unit _ X = average auto ownership per dwelling unit. 42 2. Large/multinucleated urban areas with population size over 800,000 3. Medium urban areas with population size between 50,000 and 800,000. Notice that differences in trip frequency characteristics among medium urban areas could not be attributed to difference in structure. b. The classification of urban areas according to trip duration characteristics (Table 2-10) on the other hand, results in these groupings (which are slightly different from those above): 1. Large urban areas with population size over 800,000 2. Medium/core-concentrated urban areas with population size between 50,000 and 800,000 3. Medium/multinucleated urban areas with population size between 50,000 and 800,000. A study by Perl (forthcoming) has investigated the temporal and spatial stability of the trip frequency and trip duration models estimated using linear goal programming (Appendix 2) versus the stability of the corresponding models calibrated by regression analysis. The results indicated that, although our areawide models are not as temporally stable as disaggregate trip generation models (Downes and Gyenes 1976), the models calibrated on our data,which dates from 1953 to 1964, could provide a good representation of travel data for the period 1965 to 1976. It should be stated that our trip frequency has shown greater stability than the trip duration models. Our models have also provided an accurate forecast of trip frequency and trip duration in urban areas not included in the models' calibration. Notice that for large cities with population over 800,000, the difference in trip duration relations between core-concentrated cities and multinucleated cities could not be identified. The above results with respect to trip duration are illustrated in Figure 2-4 which shows that cities with population over 800,000 consist of well identified groups with different relations between population size and average trip duration. In order to obtain a more detailed display of the trip duration relations among cities with population size between 50,000 and 800,000 one should refer to Figure 2-9. This figure shows that two well defined groups can be identified within the category of medium 43 TABLE 2-10. RELATIONSHIP BETWEEN AVERAGE TRIP DURATION AND THE POPULATION SIZE ACCORDING TO URBAN SIZE AND URBAN STRUCTURE Urban Structure Population Size Core-Concentrated Multi-nucleated _ Large with t = -10.54 + 3.618 1n P Population over R= 0.766 Se=1.56 df=6 800,000 _ _ Se/Y = 0.094 t = 4.43 _ _ Medium with t = 6.715 + 0.017 P t = -3.748 + 2.134 1n P Population between R=0.477 Se=2.56 df=59 R=0.832 Se=0.821 df=8 50,000 and 800,000 _ _ Se/Y = 0.262 t = 7.34 Se/Y = 0.108 t = 6.30 where: _ t = average travel time in minutes P = population size in thousands of persons. 44 cities. As expected, the multinucleated cities are characterized by shorter trip duration than the core-concentrated cities. Regarding trip frequency, Figure 2-3 illustrates three well defined groups: large/core-concentrated cities large/multinucleated cities and medium cities. The illustration in Figure 2-3 is in agreement with the theoretical basis of our classification scheme: that higher trip rates should be expected in large/multinucleated cities compared to large/ core-concentrated cities as a result of the proximity to the activity centers (which tend to encourage more travel). By the same reasoning, higher trip rates per dwelling unit can be expected in medium cities compared to large cities for dwelling units with the same number of autos. The fact that 800,000 was found to be a significant demarkation point for both trip frequency and trip duration is significant for policy decision making in which distinctions often need to be drawn between large and medium cities. This finding is also in agreement with other studies (Fogarty 1976). Furthermore, it is to be noted that all the regression results obtained above are substantiated by parallel analyses using linear goal programming (see Tables 2-11 and 2-12). G. Summary The results of the above analysis can now be summarized in terms of the model structure which best represents the trip frequency and trip duration processes for the different groups of cities as defined by our taxonomy. The trip frequency model is (Tables 2-9 and 2-11) _ _ Y = + X _ where: Y = average number of trips per dwelling unit _ X = average auto ownership per dwelling unit , = calibration coefficients The trip duration models are (Tables 2-10 and 2-12) _ (a) t = a + b 1n (P) for large cities with population over 800,000, _ (b) t = a + b P for medium/core-concentrated cities with population between 50,000 and 800,000; and _ (c) t = a + b 1n (P) for medium/multinucleated cities with population between 50,000 and 800,000 45 TABLE 2-11. TRIP FREQUENCY MODELS OBTAINED USING LINEAR GOAL PROGRAMMING Urban Structure Population Size Core-Concentrated Multinucleated _ _ _ _ Large Cities Y = 1.782 + 4.034 X Y = 3.101 + 3.761 X with Population _ _ over 800,000 a = 3.039 a = 3.225 Medium Cities _ _ with Population Y = 1.635 + 6.201 X between 50,000 and _ 800,000 a = 76.478 ___________________________ _ Note: a denotes the total sum of absolute residuals (see Appendix 2) Source: Perl, J. (forthcoming) 46 TABLE 2-12.. TRIP DURATION MODELS OBTAINED USING LINEAR GOAL PROGRAMMING Urban Structure Population Size Core-Concentrated Multinucleated _ Large Cities t = -19.09 + 4.756 1n P with Population _ _ over 800,000 a = -6.04 df = 6 a = 9.398 Medium Cities _ _ with Population t = 6.941 + 0.0207 P t = -5.308 + 2.4077 1n P between 50,000 _ _ and 800,000 a = 125.01 df = 59 a = 5.58 df = 8 ___________________________ _ Note: a denotes the total sum of absolute residuals (see Appendix 2) Source: Perl, J. (forthcoming) 47 _ where: t = average trip duration P = population size a,b = calibrated coefficient. The calibration results regarding trip frequency are given in Table 2-9. Similarly, the calibrated trip duration models are given in Table 2-10. The good statistical performance of all the models can be recognized by looking at the "t"-statistics and R -values, All the "t"-statistics values show a high level-of-significance (over 99 percent). Most of the coefficients-of-determination are surprisingly high in view of the number of independent variables and the nature of the models. Even the coefficientsof-determination for trip frequency in medium cities can be considered relatively high, given the high level of aggregation and compared to other studies in the areawide level (Koppelman 1972). For example, Koppelman suggested the following frequency model: Y = 0.516 + 0.0025 X - 0.000013 X + 0.0057 X + 0.00064 X 1 2 3 4 where: X.1 = size of the area (square miles) X.2 = population density (persons per square mile) X.3 = supply of roads (freeway land miles x 1750 + arterial lane miles x 650 per person) X.4 = supply of public transportation (bus miles of travel + 4.0 rail car miles of travel per person) The above model was capable of explaining only 13 percent of the variation within the data. In the trip length model suggested by Koppelman, which is equivalent to the trip duration model presented in this study, the area size expressed in square miles was used as a single independent variable. This model was capable of explaining 10 percent of the variations within the data. Considering the fact that the amount of variations explained by a regression model tends to increase as more independent variables are added, our equations (which include only one independent variable) are statistically far superior to Koppelman's. Similar comparison with the results by Voorhees and Associates C1958). substantiate the quality of our statistical results. It should be recalled at this point that our basic assumption was that cities with similar size and structure consist of a group with similar travel 48 characteristics, In other words, we assumed that large/core-concentrated cities, large/multinucleated cities, medium/multinucleated. cities, and medium/core-concentrated cities consist of four city-groups where significant similarities regarding travel behavior can be identified. The validity of our basic assumption is shown by the recommended classification scheme. While the analysis for trip frequency and duration has shown slightly different results individually (see Table 2- 9 and 2-10), the results, when taken as a whole, establish the four-cell city classification scheme. 49 CHAPTER III AGGREGATE ESTIMATIONS OF DEMAND ELASTICITIES In this chapter previous demand estimation parameters will be compiled in the four-cell city classification framework. The successful forecasting experiences are to be summarized in key parameters such as demand elasticities. Together with the base condition equations on trip duration and frequency, linear approximations of the segment of the- demand function of interest can be made. The elasticities provide the travel responses to changes in levelof-service, while the bivariate equations identify the base conditions under which the elasticities can be applied. In the urban transportation planning profession, two types of demand models are often used. They are named "aggregate" and "disaggregate" respectively. Dependent on the types of model and data, demand forecasting may be carried out using: (a) Aggregate model and aggregate data; (b) Aggregate model and disaggregate data; (c) Disaggregate model and aggregate data; and (d) Disaggregate model and disaggregate data. To date all demand model calibration parameters fall into the aforementioned categories. The conventional sequential models of urban travel demand (UTD) models, for instance, belong to the first category. On the other hand, a disaggregate modal-split model can be classified in the fourth category. Both the first and fourth category forecasting methodologies have been widely developed and used in the profession. The present chapter will focus on these types of models. The discussions will include demand elasticities, values of travel time and macro-urban travel demand models. A. Tabulation of Elasticities Demand elasticities are often used in conjunction with urban travel forecasting. They have been applied frequently, however, under circumstances that are inconsistent with the assumptions under which they were derived. It is the intent of this chapter to report some of these inconsistencies and to provide guidelines for a consistent application of elasticities in demand estimation. 50 There are three areas where inconsistencies may be introduced. First, elasticities are often applied in a scenario that is quite different from the base situation under which the elasticities were empirically derived. For example, if a fare elasticity of .13 was measured during the New York subway fare-increase of January 1970, it refers specifically to the base conditions that existed at that time, including the patronage and fare level. To apply the elasticity indiscriminantly for other fare and patronage levels without modification is a meaningless exercise at best. While such a point is almost elementary and well understood, we found (regretably) many cases where elasticities are cited out-of-context and, hence, erroneous inferences are drawn. Second, demand elasticities found in a large metropolis such as New York City provide little information on other cities of more modest size or even of similar size since they may have drastically different urban structures. Very limited research has been performed in relating elasticities to cities classified according to size and other urban characteristics. Until a better understanding of such a relationship is obtained, our knowledge about elasticities in specific cities cannot help us in demand forecasting in other cities. Third, the measurement of elasticities was performed using a variety of ways ranging from areawide empirical tabulations to disaggregate demand modeling. These various levels[-of-aggregation can often lead to very different estimates of demand elasticities for the same study area. A case study in Chicago, for example, shows that the difference between areawide and household elasticities can be as high as 40 percent, depending on the homogeneity of travel behavior among households in the area (refer to Appendix 8). Citing an elasticity without specifying the level-of-aggregation can therefore result in estimates significantly out-ofkilter with actuality. All these conditions point to the fact that guidelines for applying demand elasticities need to found. Elasticity as a Point Estimate Recent transportation systems analysis often explains travel on the basis of economic theory. It postulates that traffic flow pattern is a 51 result of the equilibration between supply and demand. Correspondingly, the demand elasticities, n, are defined for mode m with respect to the level-of-service X as Click HERE for graphic. where n(m,X.m,b,V.m,b) is the percentage change in demand of mode m with respect to one percent change of its own service characteristics, with service volume V m,b and the level-of-service (LOS) X.m,b at the point of time b. On the other hand, if the demand elasticities of mode m are expressed as the percentage change in demand with respect to the percentage change in LOS of its competing mode h, the cross-elasticity can be defined correspondingly by changing the subscripts of expression (3-1). It is important to note that elasticity measures are defined for a particular base condition, which is characterized by attributes such as a fare and patronage level if a transit system is considered. The measures cannot be directly applied to a scenario with a different base condition unless steps are taken to guarantee its transferability. Elasticity as an Arc Estimate An empirically-derived set of elasticities are compiled in Table 3-1 where transit ridership experiences are recorded for 26 cities both here in the United States and abroad. For each city, the elasticities over the years corresponding to the various fare level increases (such as in New York City) are recorded. Some of the measurements were performed during the peak hours, some off peak (as shown in St. Louis), and different numbers are reported corresponding to the various trip purposes such as work, shop, and personal business (as is evident from the experiences in San Francisco). Because of the empirical nature of this measurement, these figures were estimated by the arc elasticity formula (Kemp 1973 and Bly 1976): Click HERE for graphic. 52 TABLE 3-1. EMPIRICAL TRANSIT DEMAND ELASTICITIES FOR OVERALL TRIPS Demand Elasticities With Respect to Excess Total Travel In-Vehicle (Headway) Urban Area Year Cost Time Time Time 1. Atlanta, Ga. 1963 -.28 N.A. N.A. N.A. -.20* N.A. N.A. N.A. 2. Baltimore, Md. 1958 -.08 N.A. N.A. N.A. 3. Boston, Mass. 1955 -.19 N.A. N.A. N.A. 1962-64 N.A. N.A. N.A. -.60 4. Chesapeake, Va. 1960 N.A. N.A. N.A. -.83 5. Chicago, III. 1957 -.30 N.A. N.A. N.A. 6. Cincinnati, Ohio 1959 -.24 N.A. N.A. N.A. 1973 -.60 N.A. N.A. N.A. 7. Detroit, Mich. N.A. N.A. N.A. -.20 8. Milwaukee, Wis. 1955- 1970 N.A. N.A. N.A. -3.80 9. New York, N.Y. Rapid Transit 1948 -.13 N.A. N.A. N.A. 1953 -.19 N.A. N.A. N.A. 1966 -.07 N.A. N.A. N.A. 1970 -.13 N.A. N.A. N.A. 1950- 1974 -.15 N.A. N.A. -.24 Surface Lines 1948 -.13 N.A. N.A. N.A. 1950 -.22 N.A. N.A. N.A. 1953 -.25 N.A. N.A. N.A. 1966 -.29 N.A. N.A. N.A. 1970 -.14 N.A. N.A. N.A. 1956- 1974 -.31 N.A. N.A.' -.63 10. Philadelphia, Pa. Bus 1954 -.14 N.A. N.A. N.A. Rail 1965- 1966 N.A. N.A. N.A. -.9.0 11. Portland, Maine 1958 -.28 N.A. N.A. N.A. 12. St. Louis, Mo. Daytime -.47 N.A. N.A. N.A. Evening -.43 N.A. N.A. N.A. Weekday Morning Peak -.14 N.A. N.A. N.A. Weekday Evening Peak -.18 N.A. N.A. N.A. 13. Salt Lake City, Utah 1963 -.12 N.A. N.A. N.A. 14. San Diego, 1972 -.64* N.A. N.A. N.A. Calif. (Continued) 53 TABLE 3-1. EMPIRICAL TRANSIT DEMAND ELASTICITIES FOR OVERALL TRIPS (Continued) Demand Elasticities With Respect to Excess Total Travel In-Vehicle (Headway) Urban Area Year Cost Time Time Time 15. San Francisco, Calif. 1952- -.14 N.A. N.A. N.A. 1969 All Trips -.11 -.55 N.A. N.A. "Noncaptive trips" All Purposes -.19 -1.29 N.A. N.A. Work -.87 -1.16 N.A. N.A. Personal -.00 -.89 N.A. N.A. Visits -.77 .18 N.A. N.A. Convenience/ Shopping -.15 -.65 N.A. N.A. Comparison/ Shopping .34 -2.35 N.A. N.A. 16. Springfield, Mass. 1949 -.29 N.A. N.A. N.A. -.34# 17. Tulsa, Okla. 1973 -.25* N.A. N.A. N.A. 18. York, Pa 1948 -.46 N.A. N.A. N.A. -.65# 19. Auckland, New Zealand -.30* N.A. N.A. N.A. 20. Birmingham, 1963- Great Britain 1970 -.32 N.A. N.A. N.A. 21. Hamburg, West Germany -.41 N.A. N.A. N.A. 22. London, 1953- Great Britain 1973 -.30 N.A. N.A. N.A. 23. Montreal, 1956 Canada -.15 N.A. -.27 .54 24. Paris, France -.20* N.A. N.A. N.A. 25. Rome, Italy -.08* N.A. N.A N.A. 26. Utrecht, -.60* N.A. N.A. N.A. Netherlands ___________________________ N.A. - Data not available. * These values were obtained from observed patronage changes over a period of a few months only. For Atlanta, Ga., the value was calibrated by attitude survey. # Range from central city to suburban. 54 TABLE 3-1. EMPIRICAL TRANSIT DEMAND ELASTICITIES FOR OVERALL TRIPS (Continued) Note: Elasticities for U.S. Cities and Montreal, Canada were estimated by the shrinkage ratio: v - v x x f b f b = -------- / -------- (3-3) T X b b where: V.b, V.f = transit patronage in years b and f X.b, X.f = level-of-service in year b and f Elasticities for cities out of the U.S., except Montreal, Canada, were. estimated by logarithmic arc elasticity. log V - log V f b = ----------------------- (3-4) log X - log X f b When changes in level-of-services and demand are not very large these two types of elasticities as shown in equations (3-3) and (3-4) can still be regarded as point elasticity. More discussion about this point will be addressed in Ou.(Forthcoming). Source: Bates (1974), Bly (1976), Curtin (1968), Holland (1974), Kemp (1973, 1974), Lassow (1968), Scheiner (1974), Sosslau (1965), Tri-State Regional Planning Commission (1976) and R. H. Pratt Assoc., Inc. (1977). 55 In (3-2), (m, X.m,y, V.m,y) is the demand elasticity of mode m when its own volume and service characteristics change from year b to f are V.m,b-f = V.m,f - V.m,b and X.m,b-f = X.m,f - V.m,b respectively. The variation of these empirical measurements for various trip purposes range from -3.80 to +.34 (Table 3-1) although all of them are transit demand elasticities with respect to various components of the level-of-service. An explanation of such a degree of difference is needed. Much of the remainder of this chapter provides such an explanation. Transferability In order to apply elasticities to travel forecasting, it is required that a group of elasticities be compiled for cities that share common socioeconomic and behavioral characteristics. It is postulated that such a stratification may, at least in part, explain some of the variations observed in Table 3-2. Correspondingly, the transportation planners can use the compilation (if the elasticities remain stable in time) to infer from elasticities obtained at one location to travel behavior at other similar locations. Spatial Transferability. A stratification scheme according to city size is an intuitively appealing one since the frequency of trip making is different in large, medium versus small cities. Travel demand is also found to be affected by the urban structure. For example, the amount of travel is probably greater when employment and shopping centers are dispersed than when they are concentrated in one location (in which the main movements are from the suburbs to the city center). A stratification of cities into multinucleated versus core-concentrated categories is therefore advisable in explaining the variations. A rearrangement of the elasticities in Table 3-1 is performed according to this taxonomy in Table 3-2. Cities with population larger than 800,000 are classified as large cities while cities with population between 800,000 and 50,000 are medium sized cities. We have also broken down level-of-service into its three components: trip cost, linehaul time and excess time; at the same time, transit is identified as either bus or rail. Such an approach is to introduce into a collection of empirically derived numbers some plausible explanation of their variations. The two-way classification by city size and urban structure, groups the set of numbers into four cells. 56 TABLE 3-2. TAXONOMY OF EMPIRICAL TRANSIT DEMAND ELASTICITIES FOR OVERALL TRIPS Large Multinucleated Core-Concentrated (Population Transit Transit 800,000 or ________________________ _____________________ Greater) Total Bus Rail Total Bus Rail Linehaul Time}-.55(15) -.27(23) Excess Time -.20(7) -.60(3) -.90(10) -.54(22) -3.80(8) -.63(9) -.24(9) Cost -.30(5) -.28(1) -.08(2) -.13(9) -.19(3) -.24(6) -.19(9) -.14(10) -.60(6) -.07(9) -.64(14) -.13(9) -.13(9) -.14(15) -.22(9) -.11(15) -.25(9) -.41(21) -.29(9) -.30(22) -.14(9) -.20(24) -.47(12) -.08(25) -.15(23) -.32(20) -.15(23) -.60(26) Medium (Population between 800,000 and 50,000) Linehaul Time Excess Time -.833(4) Cost -.12(13) -.28(11) -.29-> -.34(16) -.25(17) -.46-> -.65(18) -.30(19) ___________________________ } Total travel time. Note: Number in parentheses are codes of urban areas as shown in Table 3-1. 57 With this classification, the largest variation in each of the cells with respect to bus fare elasticities, for example, amounts to -.08 to -.64 which is a substantial improvement over the -3.80 to +.34 range pointed out earlier. Temporal Transferability. The use of demand elasticities as a measurement of demand changes (with respect to changes in travel time and travel cost) is predicated upon a hypothesis that these elasticities are stable over time. If we define .b as the demand elasticity of base year b, and .f for the forecast year f, the assumption of temporal transferability amounts to equating .b with .f. Obviously such an assumption needs to be verified. An examination of Table 3-1 reveals that the range of elasticities reported for the New York Rapid Transit system ranges from -.07 to -.19 over the period from 1948 to 1970, which, at first sight, indicates that elasticities may not be temporally stable. However, we can see, upon closer examination, that such a range of variation is much more narrow than those cited above. Further investigations, to be outlined below, will uncover the situations under which elasticities are, in fact, temporally transferable. Procedures are also defined to transfer elasticities from one time period to another. Taxonomy of Calibrated Demand Elasticities A possible way to address the transferability problem is to develop mathematical models to explain the various determinants of demand. Some of the efforts of the modelers over the last decade can be abstracted in tables of calibrated elasticities (to be differentiated from the empirically measured elasticities discussed thus far). It is observed that there are more drastic reductions in spatial and temporal variations in calibrated elasticities than in their empirically measured counterparts. In the demand modeling developments over the past two decades, both models and data used by planners can be divided into two categories: aggregate versus disaggregate, where the disaggregate approach is founded on an individual or household unit of analysis, while the aggregate is based on zonal data. According to this taxonomy calibrated demand elasticities can be classified into four groups: (a) .AA = those calibrated by aggregate data using an aggregate model; (b) .AD = those calibrated by aggregate data using a disaggregate model; 58 (c) .DA = those calibrated by disaggregate data using an aggregate model; and (d) .DD = those calibrated by disaggregate data using a disaggregate model. The classification of demand elasticities can be further defined by trip purposes (whether it be work, shop, socio-recreation-or other). Two groups of demand elasticities will be discussed in this study: namely .AA and .DD. .DD tends to overestimate the magnitude of demand response (after it has been aggregated to a zonal basis) while .AA will underestimate individual demand elasticities on the average. The relationship can be expressed by equation (3-5): .DD > .real > .AA; or .DD - = .real = .AA + S. 0, S 0. The difference between .DD and .AA could reach around 40 percent (Appendix 8). Without empirical study one cannot know whether the real elasticity, .real is the average of the two or not. However, at this time it is assumed and S in the above equation are approximately equal so that we can progress with our analysis. Shown in Tables 3-3, 3-4, 3-5 and 3-6 are the calibrated elasticities .AA and .DD which are obtained using aggregate direct demand model and disaggregate demand model respectively. Mean values of the variables used to derive those calibrated elasticities are presented in Table 3-7. When one compares both types of work demand elasticities as contained in these tables, it is found that in many cases the assumptions of .DD > .AA are not necessarily true because both types of elasticities-have already been aggregated to the areawide level. Any attempt to incorporate both tables in one is improper. Also the number of modal alternatives will affect the value of elasticities (as one may expect). For example, as shown in the upper left cell of Table 2-5, demand for both auto and bus is more elastic than after a third mode--the BART system--is introduced. In our classification 59 TABLE 3-3. WORK TRIP DEMAND ELASTICITIES CALIBRATED By AGGREGATE DEMAND MODELS AND AGGREGATE DATA Transportation Large/Multinucleated A Large/Multinucleated B System Variables ______________________ _______________________ Para- Transit Auto Para- Transit Auto transit____________ transit_____________ Total Bus Rail Total Bus Rail ParaTransit Linehaul Time N.A. N.A. N.A. N.A. N.A. Excess Time N.A. N.A. N.A. N.A. N.A. Cost N.A. N.A. N.A. N.A. N.A. Transit Total Linehaul Time -.39 0 -.20 N.A. N.A. Excess Time -.709 .373 -.69 N.A. N.A. Cost -.09 .138 -.38*N.A. N.A. Bus Linehaul Time N.A. N.A. N.A. -1.10 .23 Excess Time N.A. N.A. N.A. -1.84 0 Cost N.A. N.A. N.A. - .51 0 Rail Linehaul Time N.A. N.A. N.A. 1.02 -.80 Excess Time N.A. N.A. 1.15 -2.06 Cost N.A. N.A. 0 -1.80 Auto Linehaul Time N.A. -.82 .37 N.A. N.A. Excess Time 0 -1.437 0 N.A. N.A. Cost 0 -.494 .80 .36 1.34 ___________________________ * - As calibrated by Lave (1973) and Warner (1962) transit cost elasticity was respectively -.7 and -.8 for the year of 1956 for overall trips, while by Lisco (1967) was -A for 1964 for non-captive riders only. 0 - Zero-cross-elasticities represent situations where the preimposed constraints on parameter values were binding. The elasticities were not estimated to be zero. Study Areas: Large/Multinucleated City A - Boston, 1963 (Domencich, et al., 1968) Large/Multinucleated City B - Chicago, 1969 (Telvities, 1973) 60 TABLE 3-3. WORK TRIP DEMAND ELASTICITIES CALIBRATED BY AGGREGATE DEMAND MODELS AND AGGREGATE DATA (Continued) Transportation Medium/Multinucleated Medium/Core-Concentrated System Variables ____________________ __________________ Para- Transit Auto Para- Transit Auto transit ___________ transit __________ Total Bus Rail Total Bus Rail ParaTransit Linehaul Time N.A. N.A. Excess Time N.A. N.A. Cost N.A. N.A. Transit Total Linehaul Time N.A. N.A. Excess Time N.A. N.A. Cost N.A. N.A. Bus Linehaul Time -.19 N.A. Excess Time -.38 N.A. Cost -.40 .15 Rail Linehaul Time N.A. N.A. Excess Time N.A. N.A. Cost N.A. N.A. Auto Linehaul Time N.A. -.39 Excess Time N.A. N.A. Cost N.A. -.12 ___________________________ N.A. - Data not available. Study Area: Medium/Core-Concentrated City - Louisville, K.Y., 1975 (Fulkerson, 1976) 61 TABLE 3-4. NONWORK TRIP DEMAND ELASTICITIES CALIBRATED BY AGGREGATE DEMAND MODELS AND AGGREGATE DATA Large Transportation Multinucleated System Variables__________________________________ Para- Transit Auto transit_____________________ Total Bus Rail ParaTransit Linehaul Time N.A. N.A. Excess Time N.A. N.A. Cost N.A. N.A. Transit Total Linehaul Time -.593# .095 Excess Time N.A. 0 Cost -.323@ 0 Bus Linehaul Time N.A. N.A. Excess Time N.A. N.A. Cost N.A. N.A. Rail Linehaul Time N.A. N.A. Excess Time N.A. N.A. Cost N.A. N.A. Auto Linehaul Time 0 -1.02 Excess Time 0 -1.44 Cost 0 -1.65 Income Level N.A. N.A. ___________________________ N.A. - Data not available # - Includes transit access time @ - Includes transit access cost 0 - Zero-cross-elasticities represent situations where the preimposed constraints on parameter values were binding. The-elasticities were not estimated to be zero. Note: Non-work demand elasticities are only available for large/multinucleated cities. The data reported here comes from Boston, Mass., 1963 (Domencich, et al., 1968) 62 TABLE 3-5. WORK TRIP DEMAND ELASTICITIES CALIBRATED BY DISAGGREGATE DEMAND MODELS AND DISAGGREGATE DATA Large Transportation Multinucleated A Core-Concentrated System Variables ____________________ ______________________ Para- Transit Auto Para- Transit Auto transit ___________ transit _________ Total Bus Rail Total Bus Rail ParaTransit Linehaul Time N.A. N.A. N.A. -.59 .22 N.A. Excess Time N.A. N.A. N.A. -.28 .10 N.A. Cost N.A. N.A. N.A. -.10 .04 N.A. Transit Total Linehaul Time N.A. N.A. N.A. N.A. N.A. N.A. Excess Time N.A. N.A. N.A. N.A. N.A. N.A. Cost N.A. N.A. N.A. N.A. N.A. N.A. Bus Linehaul Time -.60 .23 .14 N.A. -.78 .25 (-.46) (.15) Excess Time -.19 .06 .05 N.A. -.94 .30 (-.17) (.06) Cost -.58 .28 .12 N.A. -.20# .06 (-.45)* (.15) Rail Linehaul Time .13 -.60 .10 N.A. N.A. N.A. Excess Time .03 -.12 .02 N.A. N.A. N.A. Cost .25 -.86 .13 N.A. N.A. N.A. Auto Linehaul Time .36 .41 -.22 N.A. .17 -.18 (.39) (-.13) Excess Time N.A. N.A. N.A. N.A. .33 .35 Cost .81 .82 -.47 N.A. .15 -.16 (-.32) Socio-Economic Variables Income Level -.25 -.29 .15 (-.28) (.09) * As calibrated by McGillivray (1969) transit cost elasticity for 1955 for overall trips was -.10. # As calibrated by Sosslau, et al. (1965) transit cost elasticity was -.12 for 1955 for overall trips. N.A. Data not available. ( ) Figures in parentheses are for auto vs. bus only, July 1972. Study Areas: Large/Multinucleated City A - San Francisco Bay Area, 1973 (McFadden 1974) Large/Core-Concentrated City - Washington, D.C., 1968 (Atherton and Ben-Akiva 1976) 63 TABLE 3-5. WORK TRIP DEMAND ELASTICITIES CALIBRATED BY DISAGGREGATE DEMAND MODELS AND DISAGGREGATE DATA (Continued) Medium Transportation Multinucleated Core-Concentrated System Variable __________________ _________________ Para- Transit Auto Para- Transit Auto transit ___________ transit_____________ Total Bus Rail Total Bus Rail ParaTransit Linehaul Time N.A. N.A. -.315 N.A. N.A. Excess Time N.A. N.A. -.189 N.A. N.A. Cost N.A. N.A. -.057 N.A. N.A. Transit Total Linehaul Time N.A. N.A. N.A. N.A. N.A. Excess Time N.A. N.A. N.A. N.A. N.A. Cost N.A. N.A. N.A. N.A. N.A. Bus (Total Linehaul Time Time)-2.80 1.11 N.A. -.373 N.A. Excess Time N.A. N.A. N.A. -1.555 N.A. Cost -.51 .60 N.A. -.852 N.A. Rail Linehaul Time N.A. N.A. N.A. N.A. N.A. Excess Time N.A. N.A. N.A. N.A. N.A. Cost N.A. N.A. N.A. N.A. N.A. Auto (Total Linehaul Time Time)2.81 -1.11N.A. N.A. -.138 Excess Time N.A. N.A. N.A. N.A. -.138 Cost 1.39 -.55 N.A. N.A. -.092 ___________________________ Study Areas: Medium/Multinucleated City Richmond, 1973 (Kavak and Demetsky, 1975) Medium/Core-Concentrated City New Bedford, Mass., 1963 (Atherton and Ben-Akiva 1976) 64 TABLE 3-5. WORK TRIP DEMAND ELASTICITIES CALIBRATED BY DISAGGREGATE DEMAND MODELS AND DISAGGREGATE DATA (Continued) Large Transportation Multinucleated B Multinucleated C System Variables _______________________ _____________________ Para- Transit Auto Para- Transit Auto transit ___________ transit___________________ Total Bus Rail Total Bus Rail ParaTransit Linehaul Time -.664 N.A. N.A. -.02 .27 N.A. Excess Time -.122 N.A. N.A. N.A. N.A. N.A. Cost -.092 N.A. N.A. -.01# .06 N.A. Transit Total Linehaul Time N.A. N.A. N.A. N.A. N.A. N.A. Excess Time N.A. N.A. N.A. N.A. N.A. N.A. Cost N.A. N.A. N.A. N.A. N.A. N.A. Bus Linehaul Time N.A. -.653 N.A. .04 -.73 .04 Excess Time N.A. -1.024 N.A. .10 -2.28 .08 Cost N.A. -.378 N.A. .03 -.65 .02 Rail Linehaul Time N.A. N.A. N.A. N.A. N.A. N.A. Excess Time N.A. N.A. N.A. N.A. N.A. N.A. Cost N.A. N.A. N.A. N.A. N.A. N.A. Auto Linehaul Time N.A. N.A. -.026N.A. .27 02 Excess Time N.A. N.A. -.027N.A. N.A. N.A. Cost N.A. N.A. -.047N.A. .06# -.01 Socio-Economic Variables Income Level N.A. N.A. -.36 -.33 .15 ___________________________ N.A. Data not available # Parking cost only Study Areas:. Large/Multinucleated City B - Los Angeles, Calif. 1976 (Atherton and BenAkiva 1976) Large/Multinucleated City C - San Diego, Calif. 1966 (Peat Marwick Mitchell and Co., 1972). 65 TABLE 3-5. WORK TRIP DEMAND ELASTICITIES CALIBRATED BY DISAGGREGATE DEMAND MODELS AND DISAGGREGATE DATA (Continued) Transportation Multinucleated D* System Variables _______________________ Para- Transit Auto transit__________________ Total Bus Rail ParaTransit Linehaul Time N.A. N.A. Excess Time N.A. N.A. Cost N.A. N.A. Transit Total Linehaul Time N.A. N.A. Excess Time N.A. N.A. Cost N.A. N.A. Bus Linehaul Time -.719 .047 Excess Time -.326 .027 Cost -.688 .047 Rail Linehaul Time N.A. N.A. Excess Time N.A. N.A. Cost N.A. N.A. Auto Linehaul Time .252 -.254 Excess Time .815 -.089 Cost .209 -.164 ___________________________ * Cross-elasticities are derived from sensitivity test. Study Area: Large/Multinucleated City D - Minneapolis-St. Paul, Minn., 1970 (R. H.Pratt 1976) 66 TABLE 3-6. NONWORK TRIP DEMAND ELASTICITIES CALIBRATED BY DISAGGREGATE DEMAND MODELS AND DISAGGREGATE DATA Transportation Multinucleated System Variables _______________________ Para- Transit Auto transit__________________ Total Bus Rail ParaTransit Linehaul Time X X Excess Time X X Cost X X Transit Total Linehaul Time X X Excess Time X X Cost X X Bus Linehaul Time -.419 .004 Excess Time -.379 .006 Cost -.476 .014 Rail Linehaul Time X X Excess Time X X Cost X X Auto Linehaul Time .06 -.054 Excess Time 1.40 -.041 Cost .12 -.033 ___________________________ Note: 1. Cross Elasticities are derived from sensitivity test. 2. Nonwork Demand elasticities are only available for large/multinucleated cities. The data reported here comes from Minneapolis-St. Paul, Minn., 1970 (R. H. Pratt, 1976). 67 scheme, it is required that the elasticities are tabulated for the corresponding cities under the same transportation modal choices (which are auto, bus and rail in our case). Transferability of Calibrated Elasticities In many studies it has been found that calibrated elasticities, .DDs, which are derived by disaggregate model with household (disaggregate) data, are more temporally and spatially stable than .AAs which are computed by aggregate model using zonal (aggregate) data. The transferability of .DDs and .DAs lies somewhere in between. As mentioned before, Kannel and Heathington (1973) used an aggregate demand model to examine the temporal stability of household travel relations and to evaluate the capability of this type of model to estimate future travel. The results of their study indicated strongly that the .DAs calibrated from the 1964 household data could successfully predict household travel reported by the same households in 1971. Besides temporal transferability, spatial transferability of .DAs has also been shown. With the same trip generation model the calibration was made by using two sets of disaggregate data from two different geographic areas: Indianapolis and the Tri-State area. The .DDs in both cases are comparable, even though the areas themselves are disparate in nature. The temporal transferability of demand models was further demonstrated by McFadden (1976) and Train (1976). In their works, parameters DD (including .DD ) which were calibrated in the pre-BART time period, were used to predict post-BART modal choice among six travel modes. All the predicted shares among six modes are within one standard error of the corresponding observed shares. The forecasting error in total BART patronage is 2.3 percent. The research by Atherton and Ben-Akiva (1976) provides more evidence of both spatial and temporal transferability. In their study, the .DDs calibrated by 1968 Washington, D.C. data provided surprising similarities to those obtained from both 1963 New Bedford data and 1967 Los Angeles data. The ad hoc manner in which empirical elasticities were compiled makes meaningful comparison with the calibrated values difficult. However, such comparison is still useful as a check as long as we keep in mind that work demand elasticities are more inelastic by nature than elasticities for overall 68 TABLE 3-7. MEAN VALUES OF VARIABLES FOR DERIVING ELASTICITIES Type of Linehaul Time Excess Time Cost Urban Area Trip (minutes) (minutes) Chicago, III. Work Rail 96.9 26.4 179.5 Bus 79.2 23.1 173.6 Washington, D.C. Work Auto 43.71 16.7 130 Paratransit 52.07 19.3 61 Transit 67.15 36.32 99 New Bedford, Mass. Work Auto 15.5 6.4 21 Paratransit 25.5 6.3 8 Transit 20.1 33.6 71 Los Angeles, Calif. Work Auto 44.09 N.A. N.A. Paratransit 53.50 N.A. N.A. Transit 61.47 N.A. N.A. Minneapolis-St. Paul, Minn. Work Auto 13.92 3.55 37.39 Transit 30.47 28.33 48.15 Minneapolis-St. Paul, Minn. Non-work Auto 10.03 2.93 25.66 Transit 22.71 27.24 45.82 Source: Talvities, 1973, Atherton and Ben-Akiva 1976 and R. H. Pratt 1976. 69 trip purposes. This means that empirical elasticities, which are generally measured for overall trips, should be generally lower in absolute value than the calibrated work elasticities. It is also observed that empirical elasticities are often extracted from the short- term effects of level-of-service changes, while calibrated elasticities have taken into account long-term effects such as changes in car ownership and land use patterns. In this regard, the former can be used as a lower limit of the latter. For example, let us take a look at the cost elasticities for bus transit. The calibrated elasticity (Table 3-5) for bus is -.58 (in large multinucleated city A) while the equivalent empirical elasticities (Table 3-2) ranged from -.08 to -.64, which are lower in average absolute value. Another example can be found in the other cell (large/core-concentrated) of the same two tables. The empirical excess time elasticity for bus of -1.555 compares well with the lower absolute value of the calibrated elasticity -.833 for excess time. Generally speaking, the calibrated elasticities are consistent with the empirical findings. General Characteristics of Elasticities When one regards urban transportation as a service to the consumer, one can assign a price to purchasing such a service in terms of cost and time. Since demand elasticity is a measure of the responsiveness of travel demand to changes in the various aspects of level-of-service (LOS), it evaluates the marginal demand contribution of a change in cost or time. It is expected that, while individual travel demand elasticity in a class of urban areas often share some common characteristics, the elasticities among groups of cities are disparate. The difference between aggregate demand elasticities among different groups of urban areas can be explained by the following factors. Income Level. Travel demand is related to the socioeconomic status of the trip maker (such as his income or auto ownership). Tables 3-3, 3-4, 3-5, and 3-6 show a set of demand elasticities compiled from a number of cities. It is observed that the demand for both auto and transit are inelastic with respect to income. Both San Diego and San Francisco Bay Area studies, at the same time, indicate that transit demand is much more sensitive to income than the auto demand. In a three-mode case, both income elasticities in large/multinucleated city groups A and C (Table 3-5) for auto are .15, while 70 for bus they are -.20 and -.33 respectively. These two studies suggest that income elasticities with respect to travel demand are relatively stable for cities in the same grouping. Because income elasticities of transit are more elastic than those of auto, the change of income level will result in change of modal split, with high income levels tending to favor auto and vice versa. Saturation of Demand. According to the theory of demand, the marginal utility of additional trips tends to diminish when demanded trips approach served trips. This explains why, in the larger urban area where served trips often fall short of demanded trips, demand is highly sensitive to changes in LOS. As shown in Table 3-3, the results of three case studies in Boston, Massachusetts; Chicago, Illinois; and Louisville, Kentucky strongly support this theory. Bus demand elasticities with respect to linehaul time, excess time and cost are respectively -1.10, -1.84, and -.51 for a large city such as Chicago and -.19, -.38, and -.40 respectively for a smaller city such as Louisville. The comparison of auto demand elasticities with respect to its own linehaul time and cost in Boston (a large city) and Louisville (a smaller city) shows the same tendency, i.e., -.82 and -.494 versus -.39 and -.12. Level-of-Service Attributes. According to consumer behavior, when the price of commodity is high the response of demand to a change in price is more elastic. This leads to a corollary which states demand elasticities are smaller where LOS is high. In large cities where the LOS is generally higher, demands are less elastic than in smaller cities. Table 3-5 gives us some evidence on bus demand elasticities. Comparing bus demand elasticities of Richmond and New Bedford with that of San Francisco and Washington, D.C., it appears that the bus ridership in medium cities such as Richmond and New Bedford are more sensitive to changes in travel time and travel cost. Another example of transit schedule frequency can be cited.. Large cities have generally higher levels-of-service in terms of schedule frequency. The headway change of buses from 5 minutes to 10 minutes has less impact on ridership compared to the same percentage change in medium cities from 15 minutes to 30 minutes. This is shown in the findings of Chesapeake, Virginia, a medium-sized city and several large cities such as Boston, 71 New York, Detroit and Montreal (except Milwaukee, Wisconsin). The headway elasticity for the former is -.83 and for the latter are -.60, - .20, -.63 and -.54 respectively. This reasoning is further supported by empirical findings in New York, where ridership impacts corresponding to change in schedule frequency of bus and subway were measured (Table 3- 1). The bus (with lower LOS) has an elasticity of -.63, while the subway (with higher LOS) has an elasticity of -.24. Captive Ridership. It is recognized that the urban activities are much more scattered in large cities than in mediumm-size cities, and that the income variation among people is also higher in large cities. This often means that the increase of urban size will increase the proportion of transit captive ridership for the elderly and low income people whose demand on transit is less elastic with respect to changes in LOS. However, this study has no data to support or negate this hypothesis. New Mode. Based on modal choice theory, the demand elasticities are more elastic if the trip maker has more than one choice of mode. This is shown in two different observations. The first case is the BART study. As shown in Table 3-5, the bus demand elasticities for variables of linehaul time, excess time and cost are -.46, and -.17, and -.45 for preBART and -.60, -.19, and -.58 for post-BART. The auto demand elasticities with respect to changes in linehaul time and cost are -.13, -.32, and -.22, -.47 corresponding to the two different points of time. The second piece of evidence is shown in an attitudinal homeinterview survey in Ottawa-Carleton and in Quebec, Canada (Recker and Golob 1976) where travel is predominantly auto-oriented. The survey indicates that the bus demand elasticity with respect to bus-availability is very elastic with a demand elasticity of 2.022. Summary. Due to the difference of social and economic background, different areas have different levels of income, "saturation" of demand, levels-of-service, captive ridership volumes, modal choices and many unobserved variables. These lead to the differences of demand elasticities among areas. One of the objectives of this research is to identify a common set of elasticities according to city groupings. Updating procedures are outlined to transfer a set of generalized demand elasticities to a particular site, thereby reflecting the socioeconomic pattern specific to the area. 72 Classification of Elasticities: An Examination Preliminary analyses were performed on classifying the elasticities by the four-cell taxonomy of cities. Available information suggests that it is an acceptable approach. This can be explained if one remembers that elasticity is a point estimate. It is only meaningful if applied in a scenario similar to the base conditions upon which it is derived, Such base conditions are characterized by the then existing travel trip impedance and the travel volume, which are derivatives of trip duration and trip frequency. Since the trip duration and frequency equations show distinct differences among city groups (Tables 2-9 and 2- 10), it is not surprising to find similar patterns among the point elasticities. Until more and better data are available, the four-cell classification scheme appears to be the most logical framework to tabulate the elasticities. Twelve sets of elasticities from ten different case studies were compiled into four generic sets of elasticities according to our urban classification scheme. Areas from which calibrated elasticities are extracted are shown in Tables 3-3, 3-4, 3-5, and 3-6 respectively. Among these elasticities, four sets of .AA, which are calibrated by direct demand model and by zonal data, will be used as the higher limits (upper bounds) on the generic sets of elasticities (remembering that .AAs are by definition higher estimates than .DDs. In addition, empirical demand elasticities of transit in twenty-six cities (both here in the United States and abroad) are used collaterally to verify the calibrated elasticities. These empirical elasticities reflect short- term travel response to level-of-service change. They can often serve as lower limits on the calibrated elasticities which have taken into account long-term effects such as changes in car ownership and land use patterns. The complete elasticity data base is shown in Appendix 1. B. Aggregation of Elasticities The geographic unit-of analysis targeted for this research is the urbanized area, which is again grouped into four cells. At the same time, since overall VMTs and PMTs are our concern, trips are forecasted without trip purpose stratifications. Our data base, however, is assembled from calibrations performed on a zonal or household level in a number of cities, and they are stratified by trip purposes--a majority of them being work 73 elasticities. The next task, therefore, is the aggregation of demand elasticities. Due to the lack of information on non-work trips, the transformation of demand elasticities from work to the "overall" trip purpose involves a great amount of judgment. Our best available aggregation procedure is outlined below: Step 1. Both work and non-work trip elasticities are aggregated into overall trip elasticities. The elasticities by trip purpose are combined by a weighting procedure, where the weights are the percentage of trips by purpose. Thus W W NW NW M + M X,i i X,i i = ----------------------------- Xi W NW M + M i i where .X,i is the overall trip demand elasticity with respect to LOS attribute X in city i; .W.X,i, .NW.X,i is the demand elasticity with respect to the LOS attribute X for work and non-work trips respectively in city i; and M.W,M.NW is the percentage of work and nonwork trips in city i. Step 2. An aggregate overall trip elasticity for each cell of the city classification is obtained by taking the weighted average of the elasticities from individual cities, where the weights are the respective urban population. P i X,i i = ----------------- X P i where .X is the aggregate demand elasticity with respect to LOS attribute X for overall trips; .X,i is the demand elasticity with respect to LOS attribute X for overall trips in city i; and P.i is the total population in city i. While the above formulas compute a "representative" elasticity for each cell of our city classification, the researchers recognize the need to record the values range of these elasticities. For this reason, Table 3-8 is compiled showing such ranges for the elasticity data base. 74 TABLE 3-8. RANGE OF CALIBRATED WORK TRIP ELASTICITIES, s and s AA DD Large (Pop. 800,000 or More) Medium (Pop. 50,000 - 800,000) Transportation System Variables Click HERE for graphic. 75 TABLE 3.8. RANGE OF CALIBRATED WORK TRIP ELASTICITIES, s and s AA DD (Continued) Large (Pop. 800,000 or More) Medium (Pop. 50,000 - 800,000) Transportation System Variables Click HERE for graphic. 76 An examination of Table 3-8 shows that most of these elasticities are for work trips. The elasticity for non-work trips is only found in the Boston and Twin Cities case studies. The comparison between the work and non-work elasticities will be used as the base for aggregation. For example, in Boston auto trip demand elasticities, with respect to auto travel cost for work and non-work trips, are -.494 and -1.65, while the modal split for work and non-work are 40 percent and 60 percent respectively. According to our aggregation procedure, the elasticity for overall trips is therefore -(.198 +.99) or -1.19. The factor for converting work elasticity to overall trip elasticity is -1.19/.494 = 2.4. Similarly, the adjustment factors for auto trip demand elasticities with respect to auto linehaul time and excess time are 1.16 and 1.00, respectively. On the other hand, these adjustment factors for Twin Cities are respectively 4.91, 4.70, and 2.17. Although the values of factors in Twin Cities are two to three times higher than those in Boston, the Boston factors will be used for this aggregation because, according to our previous findings, the elasticities calibrated by zonal direct demand models service as the upper limits of elasticity aggregation, although in the present case with the limited amount of data, the reverse appears to be true. The adjustment factor to convert work to overall transit demand elasticities is assumed to be 1.0. This assumption is made according to .the following reasons. First, in Boston the calibrated transit time elasticity for work is -0.49 and for overall trips is -0.56. The ratio between the two is about 0.9. Second, in the Twin Cities study, the transit elasticities with respect to transit linehaul time, excess time and cost are -0.72, -0.33 and -0.67 for work trips and -0.57, -0.35 and -0.57 for overall trips. The ratios between work and overall trips for these three attributes are 1.26, 0.93 and 1.20 respectively. These comparisons, viewed in the light of extreme data limitations, suggest that transit demand responses with respect to changes of its own LOS have little difference between work and overall trips. In general, the relations between work trip elasticities and overall trip 77 elasticities for transit are consistent in both the Boston and Twin Cities studies. until better information becomes available we may have to be satisfied with equating work and overall trip elasticities. The development of elasticity adjustment factors to allow for a redefinition of the number of modes is based on the San Francisco case. It is apparent that the increase of the number of modal alternatives will increase the absolute values of elasticities. For example, bus demand elasticities with respect to bus linehaul time, excess time, and cost are respectively -.46, -.17, and -.45 for bus/auto case, but -.60, -.19, and -.58 for bus/rail/auto case. The adjustment factors from bus/rail/auto to bus/auto are .77, .89, and .77, respectively. Adjustment factors for other types of elasticities with respect to other LOS attributes are derived similarly. On the other hand, the development of adjustment factors to convert work to overall trips for cross-elasticity have to rely heavily on the Minneapolis-St. Paul case study. In general, the absolute values of crosselasticities (in contrast to direct elasticities) are relatively small. The procedure of deriving adjustment factors for cross- elasticities, however, is similar to that for direct elasticities. For example, in 1970 the ratio between work/non-work trips in the Minneapolis-St. Paul region was .57/.43, and the cross-elasticities of auto with respect to the bus linehaul time were .004 for non-work trips and .047 for work trips. The aggregate crosselasticity of auto overall demand with respect to bus linehaul time is (.57 x .047 + .43 + .004) or .03. When one compares the overall crosselasticity of .03 with the work trip cross-elasticity of .047, the adjustment factor of a cross- elasticity from work to overall trips is .64. Similarly we can derive adjustment factors for other cross-elasticities. For example, the factors for auto demand with respect to excess time and cost of bus are computed to be .74 and .64 respectively, while the factors for bus demand with respect to linehaul time, excess time and cost of auto are .44, 1.52 and .72 respectively. When these adjustment f actors and the use of empirical values as lower limits are applied, four generic sets of demand elasticities can be developed. They are shown in Tables 3-9 through 3-12. For large cities each 78 TABLE 3-9. DEMAND ELASTICITIES WITH RESPECT TO THE OVERALL TRIPS FOR LARGE/MULTINUCLEATED CITIES Click HERE for graphic. 79 TABLE 3-10. DEMAND ELASTICITIES WITH RESPECT TO THE OVERALL TRIPS FOR LARGE/CORE-CONCENTRATED CITIES Click HERE for graphic. 80 TABLE 3-11. DEMAND ELASTICITIES WITH RESPECT TO THE OVERALL TRIPS FOR MEDIUM/MULTINUCLEATED CITIES Bus/Auto Paratransit/Bus/Auto __________________ ___________________ Transportation Para- Transit Auto Para- Transit Auto System transit transit Variables TotalBus Rail Total Bus Rail Para-Transit Linehaul Time N.A. N.A. -.32 .11 N.A. Excess Time N.A. N.A. -.19 .05 N.A. Cost N.A. N.A. -.14 .02 N.A. Transit Total Linehaul Time N.A. N.A. N.A. N.A. N.A. Excess Time N.A. N.A. N.A. N.A. N.A. Cost N.A. N.A. N.A. N.A. N.A. Bus Linehaul Time -.29 .71(Total N.A. -.37 .64# Excess Time -1.38 . Time) N.A. -1.55 N.A. Cost -.39 .36 N.A. -.51 .30 Rail Linehaul Time N.A. N.A. N.A. N.A. N.A. Excess Time N.A. N.A. N.A. N.A. N.A. Cost N.A. N.A. N.A. N.A. N.A. Auto Linehaul, Time .16(Total -.74 N.A. .10 -1.23 Excess Time 1.24 Time) N.A. .15 Cost .72 -.60 N.A. .64 -.96 # Total Time 81 TABLE 3-12. DEMAND ELASTICITIES WITH RESPECT TO THE OVERALL TRIPS FOR MEDIUM/CORE-CONCENTRATED CITIES Bus/Auto Paratransit/Bus/Auto ________________________ _______________________ Transportation Para- Transit Auto Para- Transit Auto System transit transit Variables Total Bus Rail Total Bus Rail Para-Transit Linehaul Time N.A. N.A. -.32 .11 N.A. Excess Time N.A. N.A. -.19 .05 N.A. Cost N.A. N.A. -.14 .02 N.A. Transit Total Linehaul Time N.A. N.A. N.A. N.A. N.A. Excess Time N.A. N.A. N.A. N.A. N.A. Cost N.A. N.A. N.A. N.A. N.A. Bus Linehaul Time -.19 N.A. N.A. -.37 .64# Excess Time -.38 N.A. N.A. -1.55 N.A. Cost -.40 N.A. N.A. -.85 .30 Rail Linehaul Time N.A. N.A. N.A. N.A. N.A. Excess Time N.A. N.A. N.A. N.A. N.A. Cost N.A. N.A. N.A. N.A. N.A. Auto Linehaul Time .16 -.22 N.A. .10 -.25 Excess Time 1.24 -.35 N.A. .15 -.59 Cost .72 -.22 R. A. .64 -.32 # Total Time 82 TABLE 3-13. VALUES OF TRAVEL TIME Click HERE for graphic. ___________________________ * Site locations were found in Florida, Illinois, Kansas, Kentucky, Maine, New Jersey, Oklahoma, Pennsylvania, Texas and Virginia. ** After tax wage. Note: This table is adapted or derived from the following sources: McFadden (1974), PMM & Co. (1972), R. H. Pratt Association, Inc. and D & M, Inc. (1976), Atherton and Ben-Akiva (1976), Thomas and Thompson (1971), and Kavak and Demetsky (1975). 83 set has three subsets of elasticities which reflect the existing transportation systems: bus/auto, paratransit/bus/auto and bus/rail/auto (Tables 3-9 and 3-10). For medium cities each generic set is further divided into two subsets:- bus/auto and paratransit/bus/auto (Tables 3- 11 and 3-12). C. Values of Travel Time Another step of aggregation for our elasticities is still to be performed. Instead of keeping time and cost elasticities separate, our level of analysis calls for the combination of both into an "impedance elasticity," where impedance is the weighted sum of trip time and trip cost. The aggregation procedure requires information on the valuation of travel time. There are other reasons to review travel time values. Values of travel time have long been used as criteria to verify the validity of forecasting, particularly when disaggregate modal split models are used. Aside from elasticities, they are very concise parameters which summarize the successful calibration experiences of the past. In this report the analysis of values of travel time perceived by travelers will cover both linehaul time and excess time--two of the most important trip time components. Linehaul Versus Excess Time Shown in Table 3-13 are values of travel time derived from eight case studies. As can be seen, the values of time perceived by tripmakers are varied from location to location. The value per hour of travel ranges from $0.57 in New Bedford to $3.35 in Washington, D.C. for linehaul time and from $0.87 in New Bedford to $5.17 in San Diego for excess time. Since the income levels are different from one area to another, the difference in value of time is expected. One way to avoid the influence of regional income inequality on values of time is to assume that values of time are transferable over time and space. To achieve this end the dollar value of time is represented in terms of a ratio of hourly earning. When the dollar value of hourly travel time is expressed as a percent of hourly earning rate, the variation has been reduced to a 27 to 99 percent range for linehaul time and 41 to 156 percent range for excess time. On the other hand, it is found that the traveler's perception of values of time between linehaul time and excess time is consistent among areas. The ratio of values of time between excess time and linehaul time ranges from 1.26 in Washington, D.C. to 2.51 in San Francisco. 84 Most of the data compiled in this table is for work trips. The value of travel time for non-work trips is only found in the Minneapolis-St. Paul case study. It shows that travelers. weigh linehaul time for work trips and non-work trips with equal value, but they regard the non-work- trip-excesstime as 77 percent more valuable than the work trip-excess time. It should be noticed that the different value assigned to excess time in both types of trips is a result of the users' time schedule. Since the work trip demand is less elastic, the excess time for a work trip is more tolerable. On the other hand, because the non-work trip demand is more elastic, the users are more sensitive to the excess time on a comparative scale. If we use Minneapolis-St. Paul study area as a typical example, we may derive the value of excess time for overall trips (remembering that the excess time for non-work trips is valued 70 percent above the work trips). The procedure of aggregation is shown in (3-6): i i i U = U ( R + 1.77 R ) (3-6) E W W NW where U.i.E = value of excess time for overall trips of mode i U.W = value of excess time for work trips R.W = ratio of work to overall trips for mode i R.i.NW = ratio of non-work to overall trips for mode i. The aggregate values of linehaul time and excess time for Minneapolis-St. Paul are respectively 44 percent and 97 percent of wage rate. These values are comparable to results found in Richmond where values for both attributes are 44 percent and 86 percent respectively. The ratios of values between excess time and linehaul time for both areas are 1.95 and 2.20 with a mean value of about 2.0. The Richmond figures strongly indicate that the adjustment factors derived from Minneapolis-St. Paul are reliable. The values of travel time for overall time for overall trips are shown in Table 3-14. Although there are not enough data points for classifying these values according to our city classification scheme, the Table makes two points clear. First, the larger the urban area the higher the values of travel time travelers perceive. Second, the value of excess time is about, two times the value of linehaul time. These results are consistent with the findings elsewhere (Heggie, 1976). 85 TABLE 3-14. VALUES OF TRAVEL TIME FOR OVERALL TRIPS Click HERE for graphic. ___________________________ Note: This table is adjusted according to work vs. non-work trips which accounted for all modes. If modal split is required, the values of excess time for individual modes such as auto, transit, etc. should be adjusted respectively. Source: Table 3-2. 86 It is recommended that the weights of time value between linehaul and excess with a ratio of 1:2 are appropriate, while the value of either attribute has to be decided by the user. For example, if a transportation planner feels the value of linehaul time in his area is $2.67/hour or twothirds of wage (e.g., $4.00/hour) then the value of excess time for his area is $5.33/hour. Or, if the planner decides to use 90 percent of wage as the value of excess time, i.e., $3.60/hour, then the value of linehaul time will be $1.80/hour. Generally speaking, the use of values of excess time is equal to the wage rate and the value of linehaul time equal to half of wage rate. Such usage should be adequate for our synthesis approach With the valuation of travel time, the cost and time of executing a trip can now be collapsed into an impedance measure expressed in dollars. Computing Impedance Elasticities After the time and cost of executing a trip has been combined by converting travel time into a dollar value, further aggregation of elasticities into a composite impedance elasticity is possible. A recommended aggregation procedure is shown as follows: i i I j j j = ----------------------- (3-7) i I j j where .i is the composite impedance elasticity of mode i with respect to all components, such as time or cost, of its own LOS, and .i.j is the elasticity of mode i corresponding to its own component of LOS j. The I's are impedance expressed in dollar value. The details of elasticity aggregation are discussed in Appendix 10. Examples of the calibration and application of impedance elasticities can be found in the case studies of Pittsburgh, San Francisco and Reading, Pennsylvania (Appendices 5, 6 and 7). D. Demand Forecasting Using Elasticities Elasticities are often used to estimate future demand. Such a fore- casting method is operationalized by the elasticity tabulations assembled throughout this Chapter. Since the availability and accuracy of crosselasticities are limited, this approach has to be scrutinized before it can be used effectively for modal split. Furthermore, a substantial amount of input data should be available to the user if the modal split for the future 87 year is to be derived using elasticities. The required items are listed below: (a) Elasticities for the various cells of the trip duration classification; (b) The base year modal split between person trips made by various modes (such as auto and transit); (c) The base year level-of-service for each mode in the form of travel time or travel cost depending on the type of analysis; and (d) The future year level-of-service for each mode in the same form as for the base year. If these data are not available, they should be forecasted exogenously by submodels. The concept and formulation of demand elasticities have been defined in previous discussions. Elasticities were classified into two types: directelasticities and cross-elasticities. Direct-elasticity is a measure of responsiveness of travel demand of a particular mode with respect to its own performance or cost, while cross-elasticity is the responsiveness of travel demand with respect to the performance and cost of its competing modes. The concept of direct and cross elasticities therefore lends itself for use as the basis for the modal-split technique (among other forecasting functions). Using direct and cross- elasticities, one can quantify the increases or decreases of trips within the same mode as well as shifts between modes. While direct elasticities are generally quite straightforward, the use of cross- elasticities is much less so. Correspondingly, our discussion will concentrate on cross elasticities. Determination of Cross Demand The term "cross-demand" is used in order to distinguish it from the direct-demand relationships. In an urban area served by auto and transit, two types of cross-demand can be identified: one of which represents the response of auto passengers to alternative level-of- service.of transit, while the other represents changes in transit patronage in response to changes in auto level-of-service. Before the method of computing crossdemand is discussed, a number of variables should be defined: 88 .a = the cross-demand for person trips by auto as a function of transit level-of-service; .t = the cross-demand for person trips by transit as a function of auto level-of-service; T.ab average trip duration by auto for base year b; T.tb = average trip duration by transit for base year b; T.af = average trip duration by auto for future year f; T.tf = average trip duration by transit for future year f; V.ab number of trips per day by auto for base year b; V.tb = number of trips per day by transit for base year b; V.af = number of trips per day by auto for future year f; V.tf = number of trips per day by transit for future year f; (a, X.t, V.a) = demand cross-elasticity which represents the change in auto trips with respect to change in the level-of-service of transit; and (t, X.a, V.t) = demand cross-elasticity which represents the change in transit trips with respect to change in the level- of-service of auto. A cross-demand curve (.a) can now be plotted. First the point (V.ab, T.tb) is located as shown in Figure 3-1. The slope of the cross-demand curve segment of intersect can be obtained from the cross elasticity as shown in (3-8): Click HERE for graphic. Derivation of the Future Modal Split The future modal split determines the values for V.af and V.tf. In Figure 3-1 suppose that the average travel time of transit between the base year and the future year has been reduced by T = T.tb - T.tf because of system improvement. As a result, a shift from auto trips to transit trips by the amount of V.a occurs. In the same way, the change in the number of trips made by transit can be obtained using Figure 3-2. For example, suppose that in this case the highway system has not been improved 89 Click HERE for graphic. 90 and as a result of additional congestion, travel time by auto has increased by T = T.af - T.ab Again this will result in a shift from auto trips to transit trips by V.t. In order now to obtain the future values of the "number of trips by transit (V.tf)" and the "number of trips by auto (V.af)" both direct and indirect elasticities should be employed. This is shown in equation (3- 9): V = nY {1 + (t, T , V ) T + (t, W , V ) W + (t, T , V ) T } tf t a t a a t a t a t (3-9) where: V.tf = the total number of trips made by transit; n = the number of dwelling units in the future year; T.a = the change in the average travel time by auto (with the base auto time T.a); W.a = the change in auto ownership per dwelling unit (with the base ownership W.a); T.t = the change in the average travel time by transit (with the base transit time T.t (t, T.a, V.t) = the direct elasticity which represents the change in transit trips with respect to change in the level-of-service of transit; (t, T.a, V.a), (t, W.a, V.t) = the cross elasticities which represent the change in transit trips with respect to change in the travel time and auto ownership respectively; and Y.t = the number of transit trips per dwelling unit in the base year. Another variable that should be defined is V.f, which is the total number of person trips by all modes for the future year. The value V.f can be obtained from the base condition equations derived in Chapter II. We can now calculate the values of V.af according to equation (3-10), thus completing our modal split calculations: V = V - V . (3-10) af f tf It is to be noted that, in developing the modal-split procedure using cross-elasticities, two stringent assumptions have been made: 91 (a) The base conditions characterized by a level-of-service attribute such as trip duration and travel volumes such a's trip frequency are known, and they are compatible with those under which the elasticities are derived. (b) There is no substantial shift of the demand function due to significant changes in socioeconomic factors, nor are there any overall improvements of the transportation system which would result in a shift of the supply function. In other words, only short-term (rather than long-term) travel responses are addressed. The researchers recognize that these are rather restrictive assumptions which devalue such a method in practical applications. A supply/demand equilibrium procedure is proposed to overcome this, as will be described in Chapter V. E. Macro Urban Travel Demand Models The other systematic technique (besides the elasticity method above) to forecast demand in an areawide fashion is the Macro Urban Travel Demand Model (Koppelman 1972). A distinguishing feature of such a model is the modal split relationship. Previous studies have suggested that three types of measures are expected to influence modal split, and hence future travel, in an urban area: (a) Income or auto-ownership: these two socioeconomic variables are highly correlated (Kassoff and Deutschman 1967), and they effect the modal split the same way;. (b) The supply and/or quality of public transit service; and (c) The supply and/or quality of auto-oriented travel service. Variables such as the level-of-service explain the relative value placed on time, comfort, and convenience by the trip maker, while auto ownership explains the preponderance of using the auto mode. The two socioeconomic variables, income and auto ownership, are highly. correlated; they cannot be included together in the same model. Previous studies have suggested that auto ownership has more direct effect on the trip maker's behavior (Deutschman 1967). Level-of-service variables include rail and bus linear miles, transit time, transit cost, and transit excess time, all of which were found to influence strongly the transit patronage. Obviously, variables which measure the supply of transit service are expected to have a positive 92 influence on the transit market share while variables which are quality measures, such as transit travel time, are expected to have negative influence. Other examples of levels-of-services are miles of highway, auto out- ofpocket cost, parking fare, etc. Here the measures of supply such as miles of highway are expected to have negative influence on the transit patronage, while quality measures are expected to have positive influence. Based on this information, a correlative relationship has been established to estimate modal split using regression analysis. Koppelman (1972), in his study "Preliminary Study for Development of a Macro Urban Travel Demand Model" dealt with the modal-split process in the areawide level and suggested the following model (3-11): % Transit = b.0 - 6.4 1n (Transit Speed) -3.6 (Income) (3-11) + 311 (auto cost-transit cost) + 4.3 1n (persons/square mile) + 0.4 1n (employment/square mile). A similar and equivalent modal-split model following Koppelman's philosophy is calibrated in (3-12) using more up-to-date data: % Transit = a.0 + a.1 (auto-ownership) (3-12) + a.2 (rail linear miles and bus linear miles) + a.3 (highway miles). This model is also calibrated separately for the different clusters of urban areas, as obtained from the city classification analysis with respect to a single level-of-service variable--travel time. Calibrated Results The model was calibrated on 24 observations for which all of the data items are available (see the listing of data in Appendix 1). The distribution of the observations within our city classification scheme is as follows: 2 large multinucleated, 2 1arge core-concentrated, 19 medium core-concentrated, and 1 medium multinucleated. In our judgment, the calibration of the modal-split model should be performed separately for each cell of the classification, as obtained previously for trip duration. While the meager number of observations prevented Koppelman from doing this, the researchers, having acquired a substantially more robust data set, decided to calibrate such a cell-specific model. 93 First, the researchers selected the independent variables which are correlated with the dependent variables in order to explain the percentage of trips made by transit. It is entirely possible for a regression equation to explain observed values with suitable accuracy, as indicated by a low standard error and high value of R, with an independent variable which is structurally unsound. The equation, however, could be improved with the deletion of such a spurious variable. In order to identify the best explanatory variables and best stratification of the data, the above model was calibrated twice. The first calibration included all of the 24 available points. The second included only the stratified data consisting of 21 observations from core-concentrated cities (see data in Appendix 1). The calibrated models are expressed in equations (3-13) and (3-14) respectively: Y = 2.501 - 0.5821 X + 0.00131 X + 1.00026 X (3-13) 1 2 3 R = 0.409 Se = 0.828 t = -0.57 t = 2.00 t = 0.80 1 2 3 d = 19 F = 4.377 Y = 1.868 - 0.1205 X + 0.00224 X - 0.00 X (3-14) 1 2 3 R = 0.548 Se = 0.787 t = 0.12 t = 1.91 t = -0.10 1 2 3 d = 15 F = 6.066 f where: Y = percentage person trips made by transit, X.1 = auto-ownership per dwelling unit, X.2 = total transit miles, and X.3 = total highway miles. Auto ownership, as was-already mentioned, is negatively related to transit trips, and, as was expected, it appears with negative signs; "total transit miles," on the other hand,, should influence positively the number of transit trips, and, as expected, it appears with positive signs. The only unexpected sign is the one associated with "total highway miles" in the second equation, which should influence negatively the transit trips, but appears with a positive coefficient in the calibrated model. We can notice at this point that the stratification according to urban structure improves the calibration. The model can explain a much larger portion of the variations in transit trips when the core- concentrated cities 94 Click HERE for graphic. FIGURE, 3-3. PERCENT PERSON TRIPS BY TRANSIT VERSUS TOTAL TRANSIT MILES, IN CORE--CONCENTRATED CITIES 95 are taken as a group. This can also be seen from the scatter plots of the dependent variable versus the various independent variables. From both scatter plots and correlation analysis, it was seen that both "auto ownership per dwelling unit" and "total highway miles" are not associated with transit trips as transit miles are (see Figure 3-3) and should be eliminated from the analysis. The model obtained now is Y = a + bX (3-15) 2 where Y and X.2 are as defined above. After two variables are eliminated, the number of available points for the calibration of the new model has increased. The model will be calibrated separately on the observations-from core-concentrated cities, multinucleated cities, and for the "overall" category where the cities are treated as a single group. (a) All of the observation grouped together: Y = 1.587 + 0.00368 X (3-16) 2 df = 27 Se = 1.27 R = 0.172 F = 2.14 (b) Core-concentrated cities: Y = 1.616 + 0.00783 X (3-17) 2 df = 21 Se = 1.18 R = 0.456 F = 4.19 (c) Multinucleated cities: Y = 4.691 0.00208 X (3-18) 2 df = 5 Se = 1.98 R = 0.047 F = 0.50 The small number of observations in the multinucleated group (3-18) does not allow us to conclude whether or not a separate model should represent the modal split in multinucleated cities. The core- concentrated cities (3-17), on the other hand, share a well-defined group relationship with respect to modal split. However, the generally poor quality of the fits and the absence of a multinucleated model prompted us to accept the overall model (3-16). A Critique As mentioned previously, a similar type of modal-split model (where the dependent variable was identically defined as the percentage of person trips made by transit) was developed by Koppelman (1972), and was, to the best of our knowledge, the only existing modal-split model for the areawide level-of-aggregation. The model developed by Koppelman is shown in (3-19) for comparative purposes. 96 % Transit = b.0 - 6.4 1n (Road speed/transit speed) -3.6 1n (Income) + 311 (auto cost - transit fare) + 4.3 1n (Person/square mile) + 0.4 1n (employment/square mile). (3-19). The difference in the types of explanatory variables and in the number of independent variables included in Koppelman's model (3-19) and (3-16) does not allow a definitive comparison of the models. However, both models include transit system characteristics. In Koppelman's model the transit system is characterized by transit speed, while in our model the transit system is represented by transit mileage. The philosophy of both approaches and the generally poor quality of the statistical fit are similar. The largest error involved in this method results from the assumption of the temporal stability of modal-split relations. It is also plagued with a problem associated with "identification" in econometrics. It can easily be noticed from the available observations that the percentage of transit trips has been decreased substantially during the last 15 years, indicating a shift of the supply curve. It is to be noted that a general "trend" for the region does not necessarily explain the situation for a specific city in which the supply function is shifted by an amount unique to the area. A correlative analysis which ignores the underlying supply demand relationship has little structural stability. This point is borne out by Koppelman's and this report's findings. These, combined with previous analyses, show that an .equilibrium analysis using the elasticity tabulations and a full set of supply/ demand functions as recommended in Chapter V is the recommended approach. F. Summary After a review of previous experiences in demand forecasting, it is found that successful calibrations can often be summarized by parameters such as elasticities. Since urban areawide travel figures are to be forecasted via a simple procedure, these parameters are transformed into the same level of aggregation through the use of weighting and adjustment factors. For example, the demand elasticities have been aggregated from work and non-work trips to overall trips, which in turn are collapsed into four generic sets of elasticities according to urban size and urban/ regional structure. These parameters provide basic information for deriving a demand curve. 97 We demonstrated that demand elasticity alone, being a point estimate, cannot be used to forecast effectively. This is because elasticity is defined only for a particular base condition, which is often characterized by a particular level-of-service and traffic volume. In order to use elasticities to approximate a linear segment of the demand function, one should use them in conjunction with the base condition equations, which identify the following data: level-of-service and traffic volume commensurate with the elasticity measurements. Demand elasticities reflect only the travel response to short-term level-of-service changes where no drastic system implementation and shift in socioeconomic activities take place. While useful in estimating the effects of system improvements such as frequencies and headways, they alone are inadequate forecasting tools for urban areas where significant transportation system innovations have taken place. At the-same time, our analysis identified some shortcomings of approaches such as the Macro Urban Demand Model (Koppelman 1972)-a parallel effort to forecast urban areawide travel. Such models utilize a purely correlative type of analysis. They lack sound structural relationships, such as the demand/supply equations, to guarantee forecast stability. Our study suggests that it is possible to synthesize the past findings and develop a more responsive forecasting procedure. Parameters such as elasticities, for instance, are to be used in a demand/supply equilibrium framework. Aside from integrating previous successful calibration parameters in a consistent form, this procedure accounts more rigorously for changes in socioeconomic characteristics and level-of-services in the long term when both demand and supply functions are shifted. It supplements the short term forecast procedure outlined in this Chapter, in which only the tabulated elasticities are used. 98 CHAPTER IV GENERIC CLASSES OF TRANSPORTATION SYSTEMS As previously discussed, urban passenger travel is a function of both the level of socioeconomic activity (population, employment, income, etc.) and the level-of-service provided by the region's transportation network. The determinants of travel demand (such as the socioeconomic variables) are discussed in Chapter III collectively as the "demand function," where we include a detailed discussion of elasticities. It is the purpose of this chapter to cover the other major factors that influence urban travel-namely the service provided by the transportation system (usually referred to as the "supply function"). This will be accomplished by defining the various generic classes of urban transport modes and evaluating the level-of-service characteristics of each. Since this analysis is largely concerned with fast-response, region-wide demand forecasting, a method will be presented for aggregating the various modes and facility types within each mode over the entire urban area. A. Definition of Modes Several possible classifications of urban transportation modes were investigated by the research team. Applicational considerations suggest the following modes should ideally be addressed: (a) Automobile, (b) Transit, and (c) Paratransit. The automobile mode shall be defined as all person trips made in an automobile on the highway network of the urban Area under investigation. This would primarily refer to auto drivers but would exclude such conditions as organized ride-sharing (carpooling) which is considered paratransit. The transit category includes all the regularly scheduled public transportation systems including "capital intensive" systems such as rail and "less costly" options such as bus. The forms of bus operation include such categories as linehaul bus systems, local public and contract transit and school buses. The recent comprehensive study by the Urban Institute (1975) gives a clear idea of the range of the paratransit mode. This includes (but is not 99 limited to) carpooling, subscription bus services, car rental services, taxis, demand-actuated shared-ride service and jitneys. The various paratransit forms can be grouped according to their major service characteristics: (a) Those in which travelers hire or rent a vehicle on a daily or short-term basis and operate it themselves; (b) Those in which a traveler calls or hails a vehicle such as a taxi cab, demand responsive bus or jitney; and (c) Those in which travelers-prearrange ride sharing such as carpools and subscription vans and buses. B. Capacity and Level-of-Service The subject of capacity pervades the determination of all transport supply functions, regardless of the mode or the level-of-aggregation. A discussion of this important factor is presented below for each of our generic classes of modes. Auto (Highway) Case While there is a theoretical absolute limit to the number of vehicles that may traverse a given point in a given amount of time, highway capacity is usually expressed in a more "dynamic" fashion, with the various maximum throughputs being expressed at different desired levels- of-service. According to the Highway Capacity Manual (HCM) the capacity is defined as the maximum number of vehicles that can pass a point on a lane or roadway during a given period of time under prevailing roadway and traffic conditions (or prevailing speed). This HCM capacity is referred to as "distance-cross-section-capacity" or "time-capacity (T- capacity)." The T-capacity is usually expressed in terms of the number of vehicles per hour per lane of roadway. When the prevailing speed is S, the T-capacity is denoted as V s alt127 d/t' where Ad is the lane- distance of highway with a value approaching zero and t is a period of time. On the other hand, capacity may be expressed as the maximum number of vehicles that can simultaneously travel on a section of lane or roadway under prevailing speed. This capacity is referred to as "time-cross- section capacity," or "distance-space-capacity (D-capacity)." When the prevailing speed is Sthe D-capacity can be expressed as V sAt/d , where t is a point of time approaching zero, and d is the length of a lane or roadway. The units of D-capacity are the number of vehicles per mile. It should be noted that the 100 final supply function aggregation procedure is, to some extent, a compromise of the T and D-capacities. This procedure will be discussed in detail later in this chapter. It is apparent that the supply function for a link in the highway network would take on the appearance of the hypothetical curve drawn in Figure 4-1. As the amount of traffic using the link increases, the average travel speeds decrease. Since the length of the link remains constant, of course, the time required to travel that length increases with the decrease in speed. Note that the absolute maximum number of vehicles which may be accommodated occurs at a mean speed that is probably much lower than desirable. For this reason, a series of "levels-of-service" (LOS) categories have been devised, ranging from A to F. Generally speaking, the optimum LOS is usually considered to be Level C, at which a comparatively large amount of traffic is moved at a reasonable speed. Level E represents the absolute maximum throughput (point X in Figure 4-1), while Level F denotes disorganized flow characteristics which actually tend to result in a loss of throughput. This section of the supply function is represented by the dashed line in Figure 4-1. Transit Case Unlike the highway case outlined above, where the level of link loading has a significant effect on the travel speed, the shape and slope of the theoretical transit supply curve may be approximated by a vertical line as depicted in Figure 4-1. This is because a conventional transit system typically operates on a fixed schedule and is providing a relatively constant system speed. It is recognized that, strictly speaking, the system speed is not constant; for when peak hour transit demand is high, there may.-be some decline in average speed, although this has been shown to be minimal. However, under these circumstances, transit headways are usually decreased. Some of the above observations are well supported by the findings of Morlok (1974). In a paper dealing specifically with the development of supply functions for public transport systems, he determined that total travel time, including both in-vehicle and out-of-vehicle time, actually decreases for a given trip as the level of loading increases. This is illustrated in Figure 4-2, where corridor flow is plotted against the 101 Click HERE for graphic. FIGURE 4-1. TYPICAL TRANSIT AND HIGHWAY SUPPLY CURVES 102 Click HERE for graphic. FIGURE 4-2. THEORETICAL SUPPLY FUNCTIONS FOR TRANSIT SERVICE Adapted from: Morlock (1974) 103 average total travel time- (It should be noted that the axes in Figure 4-2 are reversed from those in Figure 4-1 and all other graphical representations in this report.) Morlok further suggests that the total impedance of the trip declines even more significantly as loading increases. This is due to the fact that it is the transit excess time which is typically reduced as patronage increases and more vehicles are introduced to supply additional service. To facilitate the aggregation of the various transit supply curves, a principal objective of this research, and for purposes of conservatism, the theoretical supply curve is approximated by a straight line. There is, of course, a practical limit on the capacity in terms of the daily trips which may be accommodated in the transit vehicles. This is shown schematically by point B in Figure 4-1. The capacity afforded by the transit system is merely added "vertically" to the highway supply curve in our analysis. The overall link, or corridor, supply is therefore dependent on the shape, slope, and location of the highway curve, as shown in Figure 4-3. Paratransit Due to the fact that the paratransit mode has only recently assumed a prominent role in urban transportation, little research effort has yet been devoted to the development of its supply function. There are several difficulties associated with this task which may prove to be insurmountable (at least at the present time). For example, many forms of paratransit do not typically operate on fixed schedules and, as such, are not likely to have vertical supply curves. Other forms, such as carpooling, are actually subject to the highway supply function, although they may be somewhat affected by differential routings as dictated by the taking on of new passengers. These intricacies are further complicated when the issue of regionwide system aggregation is introduced. Taking all these difficulties into consideration, it was reasoned that the paratransit option will not be included in this analysis. C. Impedance The discussion of the supply function thus far has centered on the relationship between travel volume and travel time (or average speed). There 104 Click HERE for graphic. FIGURE 4-3. PLOTTING THE TOTAL SUPLY CURVE 105 are, of course, numerous other factors taken into consideration by the tripmaker in determining travel patterns and mode choice. Examples of these level-of-service attributes are included in Table 4-1. While they may certainly exert considerable influence on travel behavior, the elements included under the categories of safety, comfort and convenience are difficult to quantify and the efforts in multidimensional scalings are by-and-large still in their developmental stages. As such, it was reasoned that only those attributes related to time and cost could be included in the recommended aggregate approach with reasonable accuracy while still maintaining a relatively simple, quick-turnaround profile. Travel Time Travel time can be divided into two components: linehaul and excess time. Take transit as an example. Linehaul time refers to the in- vehicle portion of the journey. The excess time, on the other hand, includes elements such as walk or drive time to the station, the wait at the platform, the time spent in transfers, the walk from the terminal to the destination, and schedule delay. Transit excess time is a critical level-of-service characteristic of transit mode and the one that distinguishes it from the auto as far as user convenience is concerned. Chan and Goodman (1976), for example, showed that the travel excess time is valued 3.65 as much as that for linehaul time--indicating that users are most sensitive to the duration of time spent outside the vehicle. Users' valuation on linehaul versus excess time have been discussed in some detail in Chapter III. Travel Cost Travel cost typically consists of three components: out-of-pocket cost, operating cost, and historic or sunk cost. The out-of-pocket cost consists of expenditures such as tolls and parking for the automobile mode and fare for the transit mode. The operating costs are those attributed to manpower, gasoline, insurance, license fees, and repairs. The historic cost is the capital cost involved in the construction or the purchase of the transportation mode under consideration. The historic cost enables one to differentiate a capital intensive system such as heavy rail from a less capital intensive 106 TABLE 4-1. EXAMPLE LEVEL-OF-SERVICE ATTRIBUTES General Attribute Category Specific Attributes Time Total trip time Reliability--subjective estimate of variance in trip time Time spent at transfer points Frequency of service Schedule times Cost (to user) Direct transportation charges Indirect costs (interest, insurance, etc.) Safety Probability of fatality Probability distribution of accident types Comfort and Convenience Walking distance (for user) Number of changes of vehicle Physical comfort Psychological comfort (status, privacy, etc.) Other amenities (baggage handling, ticketing, beverage service, etc.) Enjoyment of trip Aesthetic experiences 107 system such as bus. However, since this expense is, of course, not borne by the user, it often does not influence his travel behavior. In the case of the auto mode, the historic costs are borne by the user but still have little effect on travel decisions once the sunk cost is committed. For these reasons, the researchers decided not to include such costs in the derivation of both the transit and auto supply curves. A simple method has been configured as part of this research effort to combine the travel time and travel cost considerations into one aggregate factor referred to as travel impedance. This value may be directly compared with travel volume when plotting the supply function for a link, corridor or an entire urban area. The procedure used in calculating travel impedance is presented in Table 4-2. The impedance is clearly segmented into two principle categories, those elements pertaining to travel cost and those pertaining to travel time. This segregation is essential to the supply curve aggregation procedure outlined in the next section. The operating cost associated with the cost of making a particular trip by auto is simply the average operating cost per mile (including gas, maintenance, insurance, etc.) times the average length of the trip. An estimate of the parking and/or toll charges must also be made, with the sum of these three items yielding the total cost per vehicle per trip. To permit a consistent evaluation, this value is divided by the auto occupancy rate to estimate the total cost per person-trip by auto. For the transit mode, the operating cost (and the total cost) per person is given simply by the fare. As previously discussed, travel time is composed of two basic elements; in-vehicle time or linehaul time, and out-of-vehicle time or excess time. The monetary value of each of these elements varies from city to city and their precise valuation is subject to considerable debate. Extensive research has been and is being devoted to this issue (see Chapter III, Section C). However, estimates of these values must be provided to compute the travel impedance. For purposes of convenience, it id typically unnecessary to include excess time when considering the auto mode, since this time is usually quite insignificant and routinely is not taken into 108 TABLE 4-2. TOTAL IMPEDANCE IN TERMS OF TRAVEL COSTS AND TRAVEL TIME Total Costs (Per Trip) Mode i i Operating Cost C , y 0 i Parking C , y p i Tolls C t i i i i TOTAL C = C + C + C y 0y p,y t,y i i Cost Per Person (Auto Mode Only) I = C /0 (at 0.y Person/Car) C,y y y Value of Travel Time i Linehaul Time T L i Linehaul Time Cost Rate U L i i i Linehaul Time Cost I = T x U L,y L L Excess Time T E i Excess Time Cost Rate U E i i i Excess Time Cost I = T x U E,y E E i i i Total Travel Time Cost I = T + I Ty Ly Ey i i i Total Impedance I = I + I y C,y Ty ___________________________ Note: If i equals more than one mode, the weighted impedance is computed by the following form: M i i I = I M y i=1 y y where: i = auto, transit, etc. n = number of modes y = any year (e.g., base year; forecast year) M.i = the percent of trips by mode i 109 consideration by the traveler. For this reason, the auto excess time is not included in our analyses here in this study. The sum of values attributed to linehaul time and excess time, if any, yields the total value of travel time and, when added to the total trip cost determined earlier, yields the impedance. D. Aggregate Supply Curves for Urban Areas The derivation of an aggregate supply curve for an entire urban- network is a difficult task. There is a major problem which prohibits an absolute specification of the curve using the simple procedures outlined for use when determining link capacities. As overall travel increases, the distribution of trips between the different types of highway facilities in the network can occur in an infinite variety of forms. This difficulty, which reflects the intricacies involved in determining the aggregate supply curve, will be discussed further after the basic elements of the aggregation procedure have been presented. A simple explanation of the aggregation procedure is included in this chapter, with a more rigorous mathematical derivation presented in Appendix 3. Highway Supply Function The first step in deriving the aggregate supply curve is the classification of the various components of the highway system by their functional classes and according to their location within the urban area. Much of the discussion of supply characteristics thus far has dealt primarily with a single link. Few trips are made in their entirety on a single link, however. It is necessary, therefore, to introduce the concept of highway corridors and the urban network and associated supply functions. A roadway corridor is composed of two or more links. It is a part of a network (or system) of facilities that provides access and movement of motor vehicle transportation. Various types of corridors in the system serve different functions and are generally grouped according to their two major functions: access and traffic movement. Those designed primarily for land access are generally referred to as local streets. Collector facilities serve both access and traffic movement more or less equally. Major arterials must accomodate greater volumes of traffic for longer distances, and, therefore, traffic movement is primarily 110 facilitated, but the land-access function-is also served. The Freeway- type facility is designed for traffic movement, and access is not part of its function. It should also be noticed that the same facility in different locations has different operating conditions and provides different LOS. According to the Characteristics of Urban Transportation (CUTS) Report (U.S. Department of Transportation 1974), roadway facilities can be classified into freeway, expressway and arterial. The latter involves local streets and is further divided into two-way with parking, two-way without parking and one-way. These facilities are identified by their relative locations within the urban area, which include the central business district, fringe, residential and outlying business district (see Table 4-3). A set of assumptions have to be made for each of the roadway corridors in order to operationalize our aggregation procedure A design speed of 60 miles per hour, for example, is assumed for the freeway corridor in the outlying business districts, while a maximum speed of 25 miles per hour, no parking and so on are assumed for the one-way arterials in the Central Business District (CBD). Based on these assumptions, various supply curves are calculated in Table 4-3 and graphed in Figure 4-4. It is seen that for most arterials (including downtown streets) the travel speed drops or travel duration (for a given travel length) increases substantially after the ratio of service volume/capacity reaches 75 percent. Recommended Classification Scheme It should be noted that Table 4-3 includes estimated hourly capacities for each cell of the CUTS classification scheme. If peak hour traffic constitutes 10 percent of the total daily traffic in a corridor (as is usually the case), we can easily determine the estimated T-capacities on a daily basis. In developing the supply function aggregation procedure for a fastresponse demand-forecasting procedure such as ours, it was reasoned that the CUTS classification, in its original form, was too detailed to be practical. The planner would have to carefully quantify those facilities with and without parking, one-way versus two-way, with and without signal progression, etc, For this reason a slightly modified classification scheme was developed by the research team for use in aggregating the various elements of the highway network. As may be seen in Figure 4-5, this revised taxonomy includes the 111 TABLE 4-3. T-CAPACITY AND OPERATING SPEED ON VARIOUS ROADWAYS PER LANE Click HERE for graphic. ___________________________ (1) Capacity calculated at Level of Service E; absolute capacity. (2) First value shows speed assuming lack of coordinated signal progression; second value sh-)ws speea assuming full signal progression. Source: DeLeuw, Cather & Co., CUTS <1965) Table 34. 112 Click HERE for graphic. FIGURE 4-4. SUPPLY CURVES OF CORRIDORS Note: L is assumed travel length. 113 FIGURE 4-5. URBAN HIGHWAY CLASSIFICATION SCHEME Type of Facility ______________________________ Freeway Arterial Collector TOTAL Location Central xxx Business (7) (4) (2) District [8,000] [6,000] [4,000] xxx,xxx Fringe (6) (3) (2) [10,000] [8,000] [5,500] Residential (5) (2) (2) [11,000] [81000] [5,500] Outlying Business (6) (3) (2) District [10,000] [8,000] [5,500] TOTAL ___________________________ Note: Assumes 10% Peak Hour Factor and KEY Level-of-Service E (Absolute Capacity). Arterials are assumed-to be most X.XX Linear Miles of This accurately represented by the "Two-Way Type Per Highway Without Parking" CUTS Classification - (0) Estimated Average Num- half with signal progression, half ber of Lanes without. Collectors are assumed to [00,000]Estimated Daily T- be most accurately represented by the Capacity Per Lane "Two-Way with Parking" CUTS Classifica- XXX.XXX Estimated Daily A- tion-with no progression. Capacity in Terms of VMT Source: U.S. DOT (1974) 114 same breakdown of regional locations (i.e., CBD, fringe, residential and outlying business district) as in the CUTS arrangement. The roadway classifications, however, have been consolidated substantially, based on the assumptions outlined in Figure 4-5 about parking and signal progression. While it is certainly desirable to have as accurate an allocation of highway miles by type and location as possible, in keeping with the quickresponse nature of this research, it is not necessary to make a rigorous inventory of each mile of highway to assure its appropriate allocation. The following approach is suggested: (a) It should be determined which elements of the highway system actually govern the capacity of the network. This would include those links which would be likely to carry the bulk of interzonal travel, namely freeways, arterials and the larger, more significant collectors. (In general, those routes which are deemed critical enough to be included in a typical highway computer network should be included in the inventory.) (b) These important routes should be classified by facility type, as defined earlier in this chapter. (c) The mileage of each facility type between the various locations should be allocated. This may be accomplished, with the aid of a land use map, by simply visually apportioning the control totals among the cells. Aggregation Unless a more accurate value is available, the average number of lanes and daily capacities per lane for each cell of the system classification table may be obtained from Figure 4-5. Naturally where dictated by the local scenario, the planner may wish to substitute different values for either or both of these factors. Multiplying these three numbers together--the linear mileage, number of lanes and capacity per lane--one obtains the estimated absolute A- capacity provided by each highway category in terms of vehicle-miles-of- travel (VMT). The summation of the capacities of the various cells yields the estimated absolute A-capacity of the entire system. From this value, and the average trip length, the maximum number of trips which may be accommodated by the 115 system may be easily determined by the following equation. C A V = -------- m _ L where: V = Maximum number of vehicle trips m C = capacity of the system in terms of VMT A _ L = Average trip length in miles. Since we are concerned with urban passenger travel by all modes, it is desirable that this capacity value be established in terms of person trips by auto. The maximum number of vehicle trips can be easily expanded to person trips by simply multiplying it times the auto occupancy rate. This rate may usually be obtained from base year survey data. If a reasonable estimate of future year average auto occupancy is readily available, it should be used when determining the capacity of the future year network. Otherwise, the same base year value may be assumed to remain constant throughout the forecast period for purposes of analysis. As was previously discussed, the level-of-service provided by a link, which is the inverse of the travel impedance, decreases as the level of loading is increased. Simply stated, the larger the amount of traffic on a link, the lower the speed and the longer the time required to traverse it. To an extent, the same is true in the aggregate sense, except in this case, the "fixed" length is not that of a particular link but rather that of an average trip. As the level of system loading increases, the time required to make that average trip increases. However, at this point, the major stumbling block alluded to earlier in this section comes into play. There will be a different supply function for each cell of our highway classification scheme, and the distribution between these cells of the additional travel can occur in a variety of forms. The aggregation method would enable the precise plotting of the supply curve if each of the cells assumes the same V/C ratio for each observed 'travel pattern in the urban area. In other words, if fringe expressways, residential arterials, and all other categories were loaded at 50 percent capacity during off-peak hours and 100 percent during peak hours precise plotting would be possible. Such an occurrence is not likely. 116 FIGURE 4-6. AVERAGE SPEEDS AT V/C RATIO = 0.00 Type of Facility ______________________________ Freeway Arterial Collector TOTAL Location Central xxx Business (48) (19.5) (17) District [XXX] Fringe (48) (27) (25) Residential (67) (30) (28) Outlying (58) (23) (22) Business District TOTAL ___________________________ AGGREGATE SYSTEM SPEED _ VMT (A-capacity) 000 Absolute A-Capacity S = ------------------- in terms of VMT VHT (A-capacity) (00) Average Speed [000] Absolute A-Capacity SOURCE: U.S. DOT (1974) in terms of VHT 117 There are, however, two locations on the supply curve where a perfectly even distribution between "cells" does take place by definition. These are the end points corresponding to V/C ratios of 0.00 to 1.00. That is, if the system is completely saturated, operating at 100 percent of capacity, every classification cell within that system must be loaded at 100 percent, and likewise for the zero percent loading condition. Average speeds for the different categories are given in the CUTS report (U.S. Department of Transportation 1974) under both of these levels of loading, in terms of the ratios between volume and capacity. These values are reported in Figures 4-6 and 4-7. By dividing the A- capacity of each cell by its corresponding average speed, we determine the A-capacity in terms of Vehicle-Hours-of-Travel (VHT) for the entire system. When the system VMT is divided by the system VHT we obtain an average system speed. Again, a certain amount of discretion should be exercised by the planner in supplying average speeds. In a very diverse, multinucleated region, for example, the average speed of arterial routes in residential areas may be somewhat larger than those suggested by CUTS. After determining the average system speeds at the extreme conditions of loading, the end points of the aggregate supply curve can be easily obtained. The base year average trip length, E, is shown, having been obtained during travel surveys. Therefore, the average trip duration at the end points of the base year supply curve can be calculated by using the following equation: _ _ L x 60 t = ------------- _ S where: _ t = average trip duration at V/C = 0.00 or 1.00, _ L = average trip length, and _ S = average system speed at V/C = 1.00 or 0.00. In keeping with the convention of representing transportation level- ofservice by travel impedance, the trip duration values must be converted to this monetary equivalent. The method for determining the impedance is similar to the approach outlined in Chapter III and earlier in this chapter. The major difference, of course, is the exclusion of the transit element of the system impedance, since we are only concerned with the highway level-ofservice at this point. The impedance at the end points of the supply curve 118 FIGURE 4-7. AVERAGE SPEEDS AT V/C = 1.00 Type of Facility ______________________________ Freeway Arterial Collector TOTAL Location Central xxx Business (28) (12) (12) District [XXX] Fringe (28) (15) (15) Residential (34) (15) (15) Outlying Business (30) (13) (13) District TOTAL ___________________________ AGGREGATE SYSTEM SPEED 000 Absolute A-Capacity in _ VMT (A-Capacity) Terms of VMT S = ----------------- (00) Average Speed VHT (A-Capacity) [000] Absolute A-Capacity in Terms of VHT SOURCE: U.S. DOT (1974) 119 is made up of two basic components: the actual operating cost of making the trip and the value of the time invested by the traveler in making the trip. Since we are assuming a constant trip length, at least in the, base year, the operating cost portion of the impedance does not change over the length of the aggregate supply curve. However, since the trip duration does change, the overall impedance is altered. With the coordinates known in terms of volume of trips and average travel impedance, the end points of the supply curve can now be located. There is one other point on the base year supply curve which is known, represented y point A in Figure 4-8. This corresponds to the actual number of auto person trips and mean travel impedance in the base year as obtained from survey data. (This point is not to be confused with the point representing the total number of base year trips and total average impedance, shown in Figure 4-8 as point B.) Plotting the Aggregate Curve The shape of the aggregate supply curve is undefined between these three points, since it is not clear how the traffic loading will be distributed between the cells of the highway classification. For this reason the overall shape of the curve must be approximated from the three points which are known. Several methods of making this approximation have been investigated by the research team. While the typical downward curving supply curve, routinely encountered when representing the level-of-service characteristics of a link is intuitively appealing, at first sight, it is not possible to clearly define reasonable guidelines for plotting the precise shape of such a curve. The error associated with approximating the shape of the curve can be minimized by plotting the "best-fit" straight line through the three points. This may be most accurately accomplished by employing linear regression techniques, which minimize the deviation of the dependent variable, which is defined as the travel impedance. The resultant straight line supply curve is shown as the solid line in Figure 4-8. One of two courses of action may be taken at this juncture depending on the estimated amount of total travel which is likely to be made on those elements of the highway system included in the original classification. If a good portion of urban highway travel takes place on local streets which have not been included in the aggregation, as was the case in our 120 Click HERE for graphic. FIGURE 4-8. PLOTTING THE AGGREGATE SYSTEM SUPPLY CURVES 121 Pittsburgh case study, the average impedance may indeed be larger than estimated. Simply stated, the higher the percentage of travel made on facilities not included in the classification, the farther the point of actual impedance/volume will be from the aggregate supply curve, usually to the right. In this case, the straight line approximation of the aggregate supply curve should be shifted to the right so that the actual auto impedance/volume point (A in Figure 4-8) lies on the curve. When most of the region's highway system is included, or when the demand and supply functions are being "calibrated" to reflect only interzonal travel made on the highway network included in the classification, as was the case in our San Francisco Bay Area case study, no such shift is required. It should be noted that the aggregate supply curve will not pass through point B, the total system volume/impedance. This is largely because the additional capacity afforded by the region's transit system is not taken into consideration by the highway supply curve. By definition, point B must lie on the "total system" aggregated supply curve. Therefore, a new supply curve, shown as a dashed line in Figure 4-8, representing the total transportation system supply function, may be drawn parallel to the highway curve through point B. This is an acceptable approach because, as discussed earlier in this chapter, transit capacity may be simply added vertically to the highway supply curve and, as such, takes the overall shape of the highway curve. The base year total system aggregate supply curve was generated and calibrated, upon completion of the above steps. Future Year Curves The procedures for approximating the future year supply curve, assuming the highway and/or transit system has been changed substantially, is similar to that employed in the base year. The highway system is to be classified and A-capacities determined in exactly the same manner. The assumption of a constant average trip length over the range of the supply curve in a given year is clearly acceptable. However, there is some question as to the validity of assuming the mean length will remain 122 unchanged over time. For example, the average trip length in the San Francisco Bay Area, one of our case study regions, was found to be 8.59 miles in the base year, 1965. According to forecasts made by traditional means, the 1990 mean trip length is estimated at 9.75 miles, an increase of 1.16 miles per trip. Unfortunately, no clear cut relationship, or even broad brush "rule- of-thumb" method can be postulated for quickly estimating the future trip length short of detailed analysis. This is exemplified by the fact that the actual base year and the estimated design year trip lengths in Pittsburgh, a case study city, are virtually identical. The value associated with the average trip length is crucial to the plotting of the aggregate system supply curve. Since the absolute capacity of the system is calculated in terms of VMT, the average trip length must be used to determine the maximum number of trips which can be made on the network. If the future year average trip lengths are available, or can be roughly approximated with relative ease, this value should be used in the analysis. If not, the assumption of a temporally stable trip length is unavoidable and the base year value may be used in the future year. Using either a new estimate of mean trip length or the same value that was used in the base year, the maximum number of person trips which may be accommodated by the new highway system is calculated in the same way as in the base year. Similarly, the average speeds and, hence, the mean trip durations and impedances, at the end points of the future year curve may also be easily determined. The curve may not be "calibrated" by regression in the future year as it was in the base year since the mid-point, or more precisely, the actual future year volume/impedance value, is, of course, not yet available. This data deficiency may be overcome by simply shifting" the end points of the future year curve to the left or right the same distance as that of the base year, and a straight line can be drawn between the shifted end points. This process is shown in Figure 4-8, where point F.M corresponds to the end points as given by the highway classification procedure. F.M is the shifted future year endpoint, and 123 X equals the shift distance in both the base and future years. It should be noted that the shift distance, X, corresponds to the net shift in the base year after both the regression of the three base year po ints and any shift to make the highway curve pass through point A. Transit Supply Function Once the future year highway curve has been approximated, the additional transit capacity must be added. The first step is to vertically add the transit capacity estimated in the base year, as denoted by "Y." To this aggregate curve is added any new transit capacity provided by the assumed implementation of any major transit improvement. For example, in our San Francisco Bay Area case study, a significant amount of additional capacity was added vertically to the future year supply curve to reflect the implementation of the BART system. Again, this final total system supply curve is shown to be parallel to the future year highway curve. The determination of the additional capacity afforded by a new transit implementation is not a difficult task. Since it has been demonstrated that the slope and shape of the transit supply curve can be assumed to be a vertical straight line in our graphs, whether for a link, corridor or aggregated over an urban area, it is only necessary to find the total capacity. We are not concerned with the level of system loading since its effect on system speed (or impedance for a given trip length) is insignificant. The capacity in terms of seated persons should be readily available to the planner for every major transit implementation, since transit operations are typically governed by fixed routings and schedules and standard vehicle sizes are usually employed. Due to the unlimited number of possible transit-technological and operational options (e.g., various types of vehicles, speeds, headways, etc.) it is not practical to include in this report estimates of transit capacity at all levels of frequency and all modes. These values will depend largely on the local scenario. As a rule-of-thumb, however, it can be assumed that a typical bus can accomodate about 50 seated passengers, while the typical rapid rail transit vehicle seats 70. 124 There are certain maximum hourly capacities of transit systems (busways, exclusive bus lanes, fixed rail, etc.) since the capacity is governed by the guideways or the roadways on which they operate rather than the number of vehicles. These are included in Table 4-4. The entries in this Table, which represent both observed and theoretical values, are taken from the CUTS report (U.S. Department of Transportation 1974). The seat capacity for the new transit implementation, equivalent to the T-capacity in the auto case, must next be transformed into its equivalent.A-capacity value in terms of the seat-miles of capacity. Since the seat-miles are simply the product of the seat capacity per train (or bus, etc.), the daily frequency and the length of each transit line, the maximum number of person trips which may be accommodated by the new service is therefore given by: C s m Maximum Transit Person Trips = ----------- _ L where: C = the capacity of the new transit service in terms of seat-miles s m _ L = the average trip length. With the inclusion of the additional transit capacity, the resultant supply curve, as shown by the dashed line in Figure 4-8, represents the best approximation of the aggregate total system supply function in the future year. E. Summary Needless to say, the derivation of the aggregate transportation supply curve in an urban area is no small task. With there being at least as many possible supply functions as there are classes of roadways, and an infinite number of possibilities of different levels of loading of each class, the curve can actually assume a variety of shapes-between its end points. The research team has developed and presented in this chapter a method for making a reasonable approximation of the slope and location 125 TABLE 4-4. MAXIMUM CAPACITIES OF TRANSIT SYSTEM Rail Service Number of Cars in Train Station Dwell Time (Seconds) Three Six Nine Trains Per Hour (Seated Persons Per Hour)* 10 99 (20,790) 83 (34,860) 74 (46,620) 20 77 (16,170) 67 (28,140) 61 (48,430) 30 63 (13,230) 57 (23,940) 52 (32,760) 40 54 (11,340) 49 (20,580) 45 (28,350) 50 47 ( 9,870) 43 (18,060) 40 (25,200) ___________________________ * Assumes an acceleration rate of 3 fps. Bus Service Volume Per Lane Number of Headway Number of Condition Buses/hr.- (Seconds) Persons/hr. Highway Capacity Manual Freeway - Level-of-Service D 940 3.8 47,000 Highway Capacity Manual Freeway - Level-of-Service C 690 5.1 34,500 Exclusive Bus Lane (Freeway) 490 7.4 26,350 Arterial Bus Lane 170 21.2 8,500 CBD Curb Bus Lane 160-120 23.0-30.0 8,000-6,000 Bus Lane-On Line Stops 120 30.0 6,000 CBD Bus Streets, Contra Flow, Median Lanes 100 36.0 5,000 Source: U.S. DOT (1974) 126 of the aggregate system supply curve, encompassing both the highway and transit elements of the system. The recommended approach, considered perhaps one of the more significant findings of this research endeavor, is based largely on both accepted transportation principles and sound mathematical reasoning. Although it is not claimed that the suggested process is totally foolproof, the level of accuracy of the expected results is consistent with the aggregate, fast-response method of demand forecasting currently being investigated. As with any approach of this type, a good deal of judgment and intuitive input is required of the user. This is especially true concerning the classification of the highway system, the average speeds supplied for the various cells of the classification scheme under the different levels of loading, and the average trip length employed when deriving the future year supply curve. The aggregate supply curves are used in conjunction with the regionwide travel demand curves (see Chapter III) in an equilibrium approach to fast-response demand forecasting. The process is designed to yield aggregate city-wide estimates of total person trips, mean trip duration, VMT, etc. These aspects will be discussed in greater detail in Chapter V. 127 CHAPTER V FORECASTING URBAN AREAWIDE PASSENGER TRAVEL As mentioned in previous Chapters, very few attempts have been made to develop urban areawide forecasting procedures. This study is undertaken in recognition of the fact that urban areawide travel estimates are valuable information for nationwide or statewide policy- related analyses, particularly when transportation system investments are contemplated for alternative candidate cities. Thus far, demand elasticity has been tabulated and the general base conditions (namely the level-of-service and traffic volume) have been quoted for their valid applications. A city classification scheme is used to stratify these parameters into logical generic groups. Furthermore, supply functions are derived to represent the alternative transportation systems. In order to validate these parameters and classification schemes, a selected number of case studies will be performed in this Chapter. It is through these case studies that an approach will be presented which integrates the seemingly disparate components into a coherent framework and illustrates how they can be used for site specific forecasting We remember, for example, that the classification scheme enables us to obtain a more refined representation of travel behavior than by treating all the urban areas as a homogenous group. Such a scheme also takes into account criteria variables that otherwise would have to be included in the models themselves, and thereby reduces data requirements. Supply/demand relationships have been suggested for quite some time as the theoretical representation of the relationship between the socioeconomic activities, the transportation system, the level-of- service, and the travel volumes (Manheim 1973). The supply function, for example, is a site-specific representation of the transportation system, enabling us to quantify the changes in the transportation system as a result of investments. Similar site-specificity applies to the demand function also, when parameters such as elasticities are to be updated in accordance. with a set of guidelines to be outlined in this Chapter. 128 The advantages of such an approach are brought out by the case studies where the forecast using our synthesis approach is compared with: (a) the traditional UTP methodologies, (b) The actual post-implementation traffic, (c) the forecasts using elasticities alone, and (d) urban areawide forecasts using a purely correlative type analysis. Also illustrated is the procedure in which a set of generalized parameters such as elasticities, trip frequency, and durations can be transferred to and used in a particular study area. After these site- specific case studies, the readers may agree that our equilibrium approach is not only more theoretically consistent and satisfying, but also a lot less "data-hungry" and simpler to use than a number of other approaches. A. A Demand/Supply Equilibrium Approach The demand approximation procedure (DAP) is a technique designed to estimate the effects of changes in the level-of-service (LOS), and socioeconomic characteristics (SEC) on urban passenger travel demand. The development of the DAP technique requires information on the supply function (the performance of the transportation system), the demand function and the process of equilibration. The supply function, being determined to a large extent by the characteristics of the transportation services, is responsive to changes in the transportation system. On the other hand, the demand function, being determined to a large extent by the socioeconomic characteristics of the study area, is affected by the urban development pattern.. The establishment of the equilibrium between the supply and demand functions is not a trivial task since it involves the identification of their precise functional forms (or in our case, their linear segment approximations). However, equilibration is such a key element in travel forecasting that any step forward would contribute significantly toward the state-of-the- profession. The development of DAP, described below, was undertaken to accomplish this mission. 129 Demand Function The travel demand curve represents mathematically the response of trip-making to alternative levels-of-service (LOS) of a particular travel mode and to socioeconomic characteristics (SEC) of the trip- makers themselves. The demand function alt237 (.), such as the one sketched in Figure 5-1, when constructed for a particular mode, expresses the expected demand for that particular mode if the LOS of that mode (or its competing modes) is changed. When both dimensions of LOS and SEC are taken into consideration, a travel demand function can be symbolically expressed as follows: V = (L,A) where: V = number of trips, L = vectors of the levels-of-service (LOS) for a particular mode and its competing modes, and A = vector of the socioeconomic characteristics (SEC) for the trip makers, reflecting the activit system of the study area. Linear segments of the demand function can be approximated by the tabulation of elasticities in Chapter III and the base condition equations derived in Chapter III. We will come back to this in subsequent sections. Supply Function A supply function is defined as a curve showing the various levelsof- service at different traffic volumes. The supply function is derived from system performance. In Figure 5-1, curve f(.) illustrates the relationship between the volume of traffic and the performance of the transport system in a corridor or an urbanized area. At the traffic volume V, for example, the level-of-service is I, the travel impedance. The positive slope of the supply curve indicates that as volume increases, the level-of-service deteriorates. For example, speed drops and travel time increases. The supply function can be mathematically shown by the form: L = f(V,T) 130 Click HERE for graphic. 131 where: L = level-of-service rendered, and T = characteristics of a transportation system. An approximation of the areawide supply function can be made following the procedures outlined in Chapter IV. Equilibrium A rigorous analysis of the response of urban passenger travel to the performance of the transportation system involves the system supply curve and a travel demand curve. The forecast travel volume and the level-of-service (LOS) are determined by the intersection of the two curves. Figure 5-1 shows a supply/demand diagram for a transportation system. The equilibrium occurs at the point of intersection, E, of the two curves, (.) and f(.), as characterized by (I, V). This is the equilibrium system performance/traffic volume combination. The equilibrium point E will move according to the shift of the supply curve and/or the demand curve. A shift of equilibrium point E can result from three types of changes. Case 1: Change of Supply Curve. In Figure 5-2, let the supply curve f.1 (.) show the relationship between the performance of the trans- portation system and the volume of traffic in an urban area in the base year. The supply curve f.2 (.) expresses the same relationship in a forecast year after the system has been improved and its capacity increased. The travel volume in this case will be increased from V.1 to V.2 correspondingly. At the same time, the level-of-service is upgraded from I.1 to I.2 Case .2: Change of Demand Curve. In Figure 5-3, illustrates the alternative demand for travel in an urban area at different service levels. Demand curve ..2(.) shows the same relationship at a forecast year except that the demand has been increased corresponding to a change of the socioeconomic characteristics or the activity system (A). Without an improvement of the supply of transportation services, there will be more traffic and more congestion in the forecast year, as shown by V.2I.2 in the figure respectively. 132 Click HERE for graphic. 133 Case 3: Changes of Both the Demand and Supply Curves. Now suppose that curve f represents the existing transportation system and an increase in capacity to f.2(.) is being considered (Figure 5-4), and suppose that curve .1(.) illustrates the existing demand and .2(.) represents the demand in the forecast year corresponding to some change in the activity system. In this case, the forecast travel and the corresponding level-of-service are shown as V.4 and I.4 in the figure respectively. The Information Base to Operationalize the Demand/Supply Paradigm Before DAP can be operationalized, the necessary information base has to be available. The previous three Chapters have provided us with precisely this information--ranging from demand elasticities to the representation of areawide transportation systems. Demand Elasticities. Demand elasticity is of importance in trying to evaluate the responsiveness of travel demand to various aspects of performance and cost. It can be expressed as the aggregated overall elasticity n(-, I, V) elasticity and where I is the impedance which is the weighted sum of time and cost, and V is the base traffic volume. Notice that both the trip purpose and the modes have been aggregated in such a definition of the elasticity. Appendix 10 documents in detail the actual aggregation procedure. In our synthesis approach the demand elasticities will play an important role in determining the linear segment approximation of the demand function. For instance, if the elasticity is n(, I, V), the slope of demand function at the base conditions can be obtained by: V S(I,V) = (,I,V) ---. I It is to be noted that elasticities, being point estimates, are only meaningful when cited with respect to the base conditions upon which they are derived. Quantification of these base conditions is accomplished by the bivariate equations which determine a base level-of- service attribute such as the trip duration and the base traffic volume such as the trip frequency (see Chapter II). Unless both the base conditions 134 and the corresponding elasticities are available, linear segment approximations of the demand curve cannot be made. Base Condition Equations. The regression and linear goal programming analyses performed in Chapter II have shown a strong relationship between a socioeconomic factor such as auto ownership and trip frequency. The assumption of spatial and temporal stability is apparently sound as discussed in previous Chapters and will be demonstrated in the case studies to follow. At first glance, temporal- stability might appear questionable, since travel in our urban areas has been increasing at a much greater rate than the population of these areas. It is important to note, however, that auto ownership has also been increasing much faster than population, providing the basis for the increased mobility of urban society and thus supporting the assumed relationship. The average trip duration in a city was found to be adequately explained by another socioeconomic variable: the population in the area. One should notice that the trip duration, expressed in minutes of time, needs to be combined with the trip cost in order to determine the total trip impedance. It is also to be noted that while the relationship between population and trip duration has been shown to be temporally stable, some local refinement is required to ensure spatial transferability. This is because trip duration is largely affected by local level-of-service characteristics which are not taken into account in the simple bivariate equations. The actual refinement procedure, referred to as "updating," is described in more detail later in this Chapter. The form of the bivariate equations employed for determining trip frequency and trip duration follows: y = a + bx where: y = the dependent variable in question (trip duration and trip frequency per household); x = the independent variable (auto ownership per household or population in thousands); and a,b = calibration coefficients. Notice the equations are simple algebraic relationships in keeping with the emphasis on a fast-response methodology. 135 Representation of Transportation Systems Improvements. The services rendered by the transportation system in the study area have to be quantified in terms of a supply function before the equilibrium approach can be used. Chapter IV outlines the procedures to accomplish this, not only for the base year, but also the forecast year after the system has been improved. Computation Procedure Now that we have reviewed the necessary information to operationalize the equilibrium forecast procedure, detailed computational steps will be described in the following paragraphs. They are parallel to the previous discussions on demand and supply. (i) Derivation of the Demand Curve. The demand function in the range of interest is to be approximated by a linear segment. The input which is required for the derivation of the linear segment consists of the following data items which are obtainable from previous Chapters: (a) the average trip duration for the base year (T.b); (b) the total number of trips per day for the base year (V.b) (c) the dollar values of travel time; and (d) the "composite" elasticity for the base year b (.b) for a particular vector of level-of-service. (Reference Appendix 10 for the definition of composite elasticity.) If the total number of trips V.m is not given explicitly, it can be derived from the trip frequency (F.b) by V = F x D b b b where F.b is the trip-making frequency per day per dwelling unit and D.b is the number of dwelling units for the base year b. The trip frequency (F.b) can be obtained from the corresponding bivariate equation which varies according to the size and the structure of the urban area under consideration. If the average trip duration (T.b) is not available, it can be obtained from the trip duration equation which in turn should also be selected according to the size and the structure of the urban area under consideration using appropriate city classification. The equilibrium point E.b (I.b, V.b) (See Figure 5-5) can now be located. The slope of the demand curve segment of interest is obtained from the elasticity as: Click HERE for graphic. 136 Click HERE for graphic. 137 (ii) Derivation of Supply Curve. The determination of the supply curve is based on the physical inventory of the transportation system and a set of aggregation procedures (as described in Chapter IV). Such an aggregate curve is used directly in DAP for both the base year and future year. However, a substitute (or "default") procedure for deriving the supply curve, which saves a fair amount of computation, is outlined below. First, one determines a future equilibrium point Ef (If, Vf) on the basic demand curve via the trip duration and trip frequency models which determine If and Vf respectively. Given the temporal stability of the bivariate equations and the fact that both equations employ only socio- economic variables, Ef represents the intersection of a future demand curve and the existing supply curve. The line segment connecting Eb and Ef, therefore, constitutes an approximated supply curve. This short-cut procedure to determine the supply curve, while computationally convenient, is not recommended where the supply curve can be derived explicitly,,since econometric identification problems may arise when the temporal stability of the bivariate equations are not strictly guaranteed. (iii) The Equilibrium Diagram. The next step is to coordinate the full set of supply and demand curves obtained thus far into a DAP framework. Aside from the functions .f(.), the forecast year equilibrium must be found. The equilibrium point in the future year is the point of intersection between the future demand curve and the future supply curve. In order to sketch the future demand curve, the assumption that the elasticity of the future demand curve at the equilibrium point E.f is the same as the elasticity of the base year demand curve is made. Such an assumption is acceptable as long as the temporal stability of demand elasticity (given an unchanging transportation system) can be established. The slope of the future demand curve is given by: Click HERE for graphic. 138 It is to be noted that E.f (shown as point D in Figure 5-7) is determined via the base condition equations assuming there is no change in the supply curve. Using the assumption that: b t I I T T ---- = ---- _ _ t t b f which says that the valuation of the base and the future travel time is approximately the same, one can obtain the time portion of the trip impedance for the future year. The total impedance is obtained by adding to I.f.t the cost portion of the trip impedance (I.f.c ) which is assumed to be the same as the base year (i.e., I.b.c = I.f.c ) under a constant base year dollar value. On the other hand, in the rare event that the future supply curve cannot be obtained exogenously, a similar approximation can be made for the supply curve as well. However, in this case a consistent slope (instead of a stable elasticity) is assumed. This assumption is defensible given the aggregate nature of our analysis and the linear approximation made on the supply curve. Together with the information about the additional capacity due to system improvement, the future supply curve can be located. (iv) The Equilibration Process. The computation of DAP can be illustrated in Figure 5-7. In a two-mode case, automobile versus transit, for instance, we may locate actual base year total person trips/impedance and auto person trips/impedance at A and C, respectively. From A the demand curve for base year .b(.) can be drawn and the curve intercepts the base year automobile supply curve f.b(.) at B. From points A and C, we can approximate the total number of transit trips by taking the difference between the ordinates of points C and A, in other words: Base Year Transit Trip = V - V . a c With the inclusion of point B, the total transit trips can be broken down into "captive" versus "choice" riders. Thus, by taking the difference between the ordinates of point B and A, we obtain the estimated volume of "choice" transit trips: Base Year "Choice" Transit Trips = V - V . a b 139 Click HERE for graphic. FIGURE 5-7. CALIBRATION OF DAP 140 "Captive" transit trips, on the other hand, can be obtained from the ordinate difference between B and C: Base Year "Captive" Transit Trips = V - V . b c Similarly, the amount of total person trips and the amount of "choice" transit trips may be graphically determined for the forecast year as follows. After the location of point D is decided by the base condition equations, which help to determine the trips and the average impedance, the forecast year demand curve .f(.) can be drawn. This is shown to intersect the forecast year auto supply curve f.f(.) at E and the total supply curve (including transit) at F. The forecast year "choice" transit trips is obtained by: Forecast Year "Choice" Transit Trips = V - V . f e Since available literature indicates that captive ridership can be explained by auto ownership rates, a straightforward method of estimating captive trips is to use the ratio of forecast year captive trips to base year captive trips and the ratio of forecast year auto ownership and base year auto ownership. That is: Forecast Year Base Year Base Year Auto Ownership = x -------------------------------- Captive trips Captive Trips Forecast Year Auto Ownership The total number of forecast year transit trips is then the sum of captive and choice trips. Total Transit Trips = Forecast Year (Captive Transit Trips + Choice Transit Trips) Forecast Year The number of auto person trips is obtained by subtracting transit trips from the total. (Auto Trips) Forecast Year = V - Total Transit Trips f Forecast Year The mean trip duration can be estimated from the impedance value of I.f in the graph via simple algebraic approximations. The approximations are based on the value of travel time being constant b f _ _ (i.e., I / I = t / t t T b f Then, by the valuation of the linehaul and excess times of the base year trip, as discussed in Chapter III, Section C, an average value of travel time in terms of cents per minute, u, is Computed. At future year levels, that element attributable to travel cost, I.c,(which is assumed to be the same as the base year in constant dollars) is subtracted from the impedance. The remaining impedance, I.T, consisting of only the value 141 of the time associated with making the average trip, may then be divided by the value of time per minute to obtain the mean trip duration in minutes. This simple procedure is presented mathematically below: I = I - I . T f C Therefore, the trip duration for the forecast year is: I _ T t = -------- f u The entire set of computational procedures are illustrated in three case studies which will be discussed later in this Chapter. B. Modeling Structure and Parameter Transferability The thrust of the present chapter is to illustrate how the city classification scheme, the demand elasticities and the network aggregation procedure can be used in a consistent manner to forecast urban travel. A general approach named the demand approximation procedure (DAP) was outlined above to accomplish this objective. In this section, DAP is examined in greater detail, particularly with respect to the accuracy of such a procedure to forecast site-specific travel with reasonable accuracy. Such an undertaking is necessary since a set of generalized parameters (such as elasticities and thier base condition equations) are compiled in this Project. Positive steps are necessary to ensure that such parameters are applicable in specific sites. One objective of this chapter is to examine carefully the demand approximation procedure (DAP) and to provide alternative solutions where there are areas of inadequacy in the methodology. Second, in order to keep the estimation procedures simple, the researchers singled out socioeconomic factors such as auto ownership and urban population size as the only explanatory variables to estimate the base conditions for which the elasticities are to be applied. It is recognized that the explanatory power of socioeconomic variables (SE) alone are deficient at times. Steps are also taken under these circumstances to introduce level-of-service (LOS) factors into the estimation procedure. An example will make this clear. Suppose a city has an inordinately slow travel speed due to congestion, indicating a poor level-of-service. The trip duration base condition equation, being a generalized correlative relationship for a group of cities based on population alone, may estimate 142 an unacceptably short average trip time in the study area. The equation certainly must be updated to reflect local LOS factors, to render it transferable to the specific site of interest. Updating Procedures In the following discussion, emphasis will be placed on data requirements in updating our generalized parameter and equation set for site-specific applications. Several possible approaches for updating have been suggested (Atherton and Ben-Akiva 1976). The various approaches are different in many respects, but they fall into one of two broad categories: those requiring a small sample of observations from the new population and those not requiring such a sample. Data requirements can therefore be considered as the main attribute in distinguishing between the available updating procedures. A brief outline of the individual methods is given below: Method A: Use the original parameters, thus involving no updating. Method B: Adjust the constant term using aggregate data of travel in the study area. Method C: Re-estimate all parameters using a small disaggregate sample. Method D: Re-estimate only the constant terms using a small disaggregate sample. Method E: Update the parameters using Bayes' Theory. An approach based on Bayes' theorem has been suggested by Atherton and Ben-Akiva (1976) as an effective updating method. Bayes' theorem is an inferential procedure through which the posterior distribution of a parameter is updated from the prior distribution through the sample likelihood function. Bayes' theorem can be written as follows: P(~ = / ~ = )P(~ = ) s i i P(~ = / ~ = ) = ------------------------------------ J P(~ = /~ = )P(~ = ) j=1 s j j where: .s = the sample statistics which represent the new sample information P(~ = .s/~ = .i) = the likelihood determined from the conditional distribution of .s given different values of .1 . . . .j of ~ P(~ = .i /~ = .s) = the revised probability that = .i given the new sample information. 143 In the continuous case Bayes' Theorem can be written as: f() f( /) s f (/ ) = ---------------------- s f()f( /)d _ s Methods A and B are those which do not require small samples from the new population, while Methods C, D, and E are those which require a small sample. However, there are differences in data requirements among the updating methods which need a small sample. An example of such a difference can be obtained by comparing Methods C and E. The Bayesian approach tries to avoid a decision that is based only on small samples and tries to gain information on the parameters of interest by using valuable prior information represented by the prior distribution. If the prior information is not used, Method E becomes Method C. In other words, Method C is equivalent to the Bayesian method which gives zero weight to the prior parameter. This is an extreme case of diffuse prior state where the prior information is completely overwhelmed" by the sample information. The above case occurs when the variance of the prior distribution is large compared to the variance of the sample information such as the example shown in Figure 5-8. If the prior state is not diffuse, Method C requires a large sample in order to obtain the same amount of information as Method E. Similarly a comparison between Methods C and D would show that Method D can be applied with a smaller sample if both models have to be calibrated on the same amount of information, since Method D uses previous information to calibrate the model's coefficient, and only the constant has to be recalibrated using the small sample. Obviously, this method is based on the assumption that only the factors not explicitly explained by the mode, which the constant terms account for, vary between areas or over time. Bayesian Updating Bayesian updating has been shown to be an effective updating method (Atherton and Ben Akiva 1976) and is therefore worth investigating whenever the data required by this approach is available. A more formal description of the Bayesian methods as applied to the updating of linear regression models and elasticities (including its mathematical formulation), is given in Appendix 4. 144 Click HERE for graphic. f(.s/) = the likelihood function f() = the prior distribution function FIGURE 5-8. DIFFUSED PRIOR STATE 145 The Bayesian statistician views the unknown parameter as a random variable generated by a distribution which summarizes his information about . Some researchers argue that the above assumption is not valid in the travel demand context (J. Horowitz 1977). Whether the assumption is valid or not has been a subject of argument between the Bayesian and the classical statistician for some years and is beyond the scope of this research. More pertinent is the data availability problem, which dictates whether such an approach is relevant to our forecasting procedure. At this point the specific models related to DAP which may have to be updated should be examined. The data required by the Bayesian updating method in our specific context have to be examined as well. As a result of these examinations, the proper updating methods for the actual models, given the actual data availability, will be suggested and investigated through several case studies. The results are then evaluated in the conclusion sections. Trip Frequency and Trip Duration Among the basic building blocks of DAP are the estimation equations for trip frequency and trip duration, which help us in grouping urban areas according to their size and their structure. Each grouping consists of urban areas with similar characteristics with respect to trip frequency and trip duration. Since both the temporal and spatial stability of the trip frequency and duration equations have been established, the city classification scheme allows one to simplify the travel forecasting procedure by using a set of generalized parameters for the urban areas under the same grouping. There are situations, however, in which a city may be different enough from others in the same grouping to warrant site-specific updating. Updating is a way of recalibrating the existing model to better represent exceptional characteristics regarding travel behavior in the urban area under consideration. One could suggest that the areawide model for certain cells, for example, should be updated by the Bayesian method and using sample information taken from the households in the urban area under consideration. It has been shown previously, however, that a substantial difference exists between the coefficient of disaggregate models calibrated on household level data and aggregate models calibrated on zonal level data (Kassof and Deutschman 1969). Our trip frequency model, while adopting household level variables, is 146 actually an areawide model using average household rates. Using household level data to update the areawide model, therefore, is equivalent to adding meters to feet. it is equally obvious that the trip duration model cannot be updated using household level models, since it is based entirely on an areawide level variable: city population. The correct way of applying the Bayesian updating procedure for the areawide model is by using sample information form the urban area level. This idea can best be illustrated by a hypothetical example. Suppose the city under consideration were a large/multinucleated city, and it constituted an outlier with respect to trip duration. There may be a number of reasons for that city to be an outlier. In the trip duration case, a particularly low system speed might result in an estimate of a long average trip duration.. If the Bayesian procedure were to be applied, the sample information should consist of observations from similar cities with the same travel characteristics and observations which are not included in the original calibration of the equation for large/multinucleated cities. By doing so, one would isolate the exceptional characteristics and incorporate them into the model. One can easily realize, however, that the Bayesian procedure is not applicable in this case due to its data requirement. The total number of U.S. cities with population size over 800,000 is 41 according to census data from 1970. It is quite likely that, even if data are available for all the large cities, the number of cities with similar characteristics (such as extremely low system speeds) is limited. It should also be mentioned that our survey results show that, for many urban areas, average trip duration is not available. On the other hand, there are cases where the Bayesian method is applicable. Suppose that the city under consideration were a medium size city for which the trip frequency model needs updating temporally. Suppose our observations were taken over a period of 20 years. Observations should be grouped into two periods of 10 years each, and the observations from the later period should be used as sample information in the Bayesian method. As mentioned previously, the need to update a model is due to factors not explicitly accounted for by the model, which consists of exceptional characteristics of the urban area under consideration. In a regression equation, the constant term accounts for factors not explicitly accounted for by the model. The presence of these constants indicates that, in fact, the model has not captured all aspects of the given travel behavior process. 147 The updating should therefore be focused on these terms. Referring to the beginning of this section, one can realize that the best updating method in our case, for both data requirements and level of aggregation points of view, is method B. According to this method, the aggregate base year data are used to adjust the constant to reflect better the situation in the given area. The adjustment is performed by applying the model to the new area in the same way in which it would be applied for forecasting. The constant s are then "calibrated" until the model replicates existing aggregate data. For example, in Pittsburgh, the lack of freeway type facilities in 1958 resulted in exceptionally low average travel speed and high trip duration. The updating of the constant term is performed as follows: _ t = 23.1 = a + 3.616 1n 1169 u where a.u is the updated constant term for the city of Pittsburgh. Solving the equation results in: a = 23.1 - 3.616 1n 1169 = -2.44. u The updated model for the city of Pittsburgh is, therefore: _ t = -02.44 + 3.616 1n P. Three case studies are employed to verify the transferability properties of DAP, representing large/multinucleated, large/core- concentrated and medium/core-concentrated cities respectively. These study sites represent the three most significant cells of the four cell city-classification. C. A Case Study of Three Cities This case study demonstrates the mechanics of forecasting city-wide traffic such as vehicle-miles-of-travel and passenger-miles-of-travel using our compilations of parameters and procedures in a supply/demand equilibrium framework. Three case studies were analyzed by a step-by- step manner, covering San Francisco, Calif., Pittsburgh and Reading, PA. These case studies facilitate site specific verifications of the elasticities, the aggregate supply functions and the city classification scheme in terms of their operational feasibility in examining policy options. These urban scenarios serve as a reasonable cross-section of American cities for testing the applicability of our travel estimation procedures, since they represent not only the three most significant cells of the four-cell classification but also encompass a variety of transportation system implementations, including "capital intensive" heavy rail, "low cost" transit and the "basic" automobile system (see Figure 5-9). 148 Study Area Dimension I Population Size Dimension II Large Medium __________________________ ___________ Core-Concentrated Pittsburgh Reading, Pa. Multinucleated San Francisco Auto x x x Transit ("Low Cost") x Transit ("Capital Intensive") x FIGURE 5-9. COVERAGE OF THE CASE STUDIES 149 A Case Study of Spatial Transferability: Pittsburgh This first case study serves two purposes. The first and obvious one is to verify the forecasting steps of the demand approximation procedure (DAP). The second is to test the spatial transferability of the demand model parameters and the usefulness of the parameter-updating methodology outlined in the last section. "Spatial transferability" can be defined as the ability of the general parameters compiled within a certain cell to explain site-specific situations. This refers especially to cases in which the situation regarding travel behavior in the given urban area is exceptional compared to other urban areas in the same cell. Pittsburgh was chosen as the site for this case study since it provides a good example of the exceptionally slow system speed, which was prevalent in the base year 1958. Figure 5-10 demonstrates the plan of discussion. A forecast of 1980 aggregate travel demand for Pittsburgh will be made after the trip frequency and trip duration equations at base year (1958) levels are updated. As shown in the figure, the forecasts obtained using the demand approximation procedure will be compared with 1980 traditional estimates. The discrepancies between DAP forecasts and those obtained by traditional methods will be evaluated and discussed. For the sake of clarity, the detailed steps of this case study are documented in Appendix 5. A Case Study of Temporal Transferability: San Francisco The question of temporal transferability, whether the demand elasticities, the base condition equations and the city classification scheme are valid in some future year as in the "base year," is critical to the validation of the demand approximation procedure. In our second case study, we attempt to demonstrate the temporal stability of these elements, and, where stability is not guaranteed, the usefulness of updating procedures. At the same time, the question of spatial transferability is also addressed. Figure 5-11 illustrates the logic of our case study. First, the two base condition equations at base year (1965) levels are updated. A forecast of 1980 aggregate travel characteristics of the Bay Area is then made. These projections will be compared with the 1980 estimates made by traditional means. As shown in Figure 5-11, two estimates of the 1990 travel will be made using the forecasting parameters and following the demand approximation procedure. One of the 1990 forecasts is made by using the same base condition equations as updated in 1965. The alternate projection is made using new base condition equations, updated at 1980 levels to accurately represent actual conditions. For purposes of this update, the traditional forecasts of trip frequency and trip duration are assumed to be equivalent to the actual demand. 150 Click HERE for graphic. FIGURE 5-10. THE SPATIAL TRANSFERABILITY OF TRAVEL FORECASTING PARAMETERS IN PITTSBURGH 151 Click HERE for graphic. FIGURE 5-11. THE TEMPORAL STABILITY OF TRAVEL FORECASTING PARAMETERS IN SAN FRANCISCO 152 Temporal stability will be evaluated on the basis of time series comparisons of the forecasts. The step-by-step details of this case study are discussed in Appendix 6. A Case Study of Spatial and Temporal Transferability: Reading The previous two case studies in Pittsburgh and San Francisco have been used to verify the spatial and temporal transferability properties of the forecasting parameters. The current case study in Reading, Pa. is undertaken to demonstrate both of these properties. From the data availability point of view, Reading is an excellent site for verifying the demand approximation procedure. The logic of the case study in Reading can be illustrated in Figure 5-12. It is to be noted that pertinent data is available in Reading for four points in time: 1958, 1964, 1975 and 1990. Two major freeway improvements occurred between 1958 and 1964, and several other highway improvements took place during the 1964-75 period. The 1964 and 1975 actual traffic counts can be used to verify the 1964 and 1975 traffic prediction made by DAP, using the 1958 updated parameters. In this way, the spatial transferability of model parameters derived from other urban areas and the temporal transferability of parameters updated in Reading can be verified. It would be an ideal case if the forecasting parameters updated in 1958 could also be used to forecast the 1975 and 1990 demand, so that the stability of DAP equations could be further observed. Unfortunately, the 1958 study area only covers the central city area while the 1975 and 1990 study area includes the suburbs of Reading. The characteristics of travel forecast in these areas are by definition quite different. The 1964 study area, however, is quite comparable to the ones used in 1975 and 1990. The base condition equations have to be updated in 1964 to forecast the 1975 and 1990 traffic. Note that during the 1975-1990 period a great deal of highway improvements are also planned. The comparisons of the DAP forecast against: (a) actual traffic counts in 1964, (b) actual traffic counts and the forecast made by the traditional method in 1975, and (c) the forecast made by the traditional method in 1990 will indicate the trasferability of forecasting parameters in both time and space and the capability of DAP as a fast-response tool for demand forecasting. 153 Click HERE for graphic. FIGURE 5-12. EVALUATIONS OF DAP TRANSFERABILITY IN TIME AND SPACE 154 The step-by-step details of the Reading case study is illustrated in Appendix 7. Results These case studies examine carefully the mechanics of forecasting equilibrium city-wide traffic such as vehicle-miles-of-travel (VMT) and passenger-miles-of-travel (PMT) using the demand approximation procedure (DAP). Three case studies were conducted covering San Francisco, Pittsburgh, and Reading,- respectively. They facilitate site-specific verification of the accuracy of the generalized forecasting parameters and the updating procedures for these parameters. These studies indicate that most of the successful demand-forecasting models can be expressed in terms of a general set of forecasting parameters. A consistent way of applying them for estimating future travel is the supply/demand equilibrium framework of DAP. Built upon level-of-service elasticities, bivariate socioeconomic equations and the updating procedures, DAP is shown to be applicable to study areas of disparate size, urban structure and transportation system implementations. Spatial Transferability The spatial transferability of travel demand models is the ability of these models to predict travel behavior in locations other than the area for which the model was estimated. Previous studies dealt with models that were calibrated on data from one area and used to forecast travel in another area, where the data used for calibration and the unit-of- analysis it be household, zonal, or city-wide) in the new area consisted (whether of the same level of aggregation (Kannel and Heathington 1973). Spatial transferability, as used in DAP, refers to the way that trip frequency, trip duration, or elasticities obtained for certain cells in our city classification scheme can be transferrred to other urban areas in the same cell. In order to distinguish spatial transferability from another similar term, spatial stability, it is to be noted that the process of "transferability" includes updating or re-calibrating the set of parameters while stability refers to the direct use of a borrowed model without modification. In order to improve accuracy, it is often desirable to adjust the forecasting parameters tabulated within or across the different cells of 155 the classification scheme to be more site-specific, This would allow them to explain better the travel behavior in the urban area under consideration. Updating is not necessary all the time; in many cases, the stability of these parameters permits one to explain the travel behavior in the specific site with a sufficient degree of accuracy. The important question is: when should one consider updating? Here is a straight-forward answer: when the model is-unsuccessful in explaining the travel behavior in the base year. In this case, there is no reason to believe that it will be successful in explaining --ravel behavior in the future, and updating should, therefore, be considered. In Section B the various updating procedures have been reviewed. The differences among the various procedures were discussed mainly from the point of view of data requirements. The amount of data required by the updating procedure is a major criterion in selecting the procedure that is to be applied. The demand approximation procedure is a fast-response technique which intends to save time and money through a reduction in the amount of data and computation effort required for its application. It would be unreasonable, therefore, to pose high data requirements during the updating procedure. For the reasons mentioned above and others discussed in the case study appendices, an updating procedure involving the adjustment of the constant term was suggested. The constant term in a travel demand model accounts for factors which are not explicitly considered in the model. 'Since the need for updating in the DAP context arises when a general or overall model is unsuccessful in explaining the exceptional characteristics of the urban area under consideration, the constant term, which accounts for these extraneous factors, is the-parameter to be updated. It is to be noted that the suggested updating procedure has two additional advantages: (a) It uses aggregate data from the urban area level, making it directly compatible with the unit-of-analysis used in DAP. (b) It requires a minimum amount of computations and of data. The application of DAP for the large city of Pittsburgh indicates the success of the updating procedure. The city of Pittsburgh is an example of extreme conditions on the highway level-of-service, which are not 156 explained by the overall two-cell trip duration equation and should, therefore, be taken care of by the updating procedure. Using the forecasting parameters without an updating procedure has resulted (both in Pittsburgh and elsewhere) in a less accurate forecast when compared with traditional projections. In the case study for the medium city of Reading, both the trip frequency and trip duration equations needed to be updated. The necessity to update the trip frequency equation is particularly cogent for two reasons. First, for medium cities the trip frequency equation (instead of the trip duration equation in the Pittsburgh case) is a two- cell model. This implies that the equation is an overall model without the stratification by urban structure, which by definition is not as precise as single-cell models. Second, the variation regarding trip frequency is simply greater in medium cities as can be seen from observing the data on which the models were calibrated. In general, the good estimates obtained for the total number of trips and average trip duration for 1990 in Reading with respect to the actual traffic and the traditional forecast would not have been obtained without the updating procedure described above. Temporal Transferability The question of the temporal stability of the trip frequency and trip duration equations has been addressed in the case studies from two points of view. On the one hand, in the case of the medium city of Reading, Pa., DAP estimates have been compared with actual travel figures, using home interview survey data from two points in time. Also, in both the Reading and San Francisco Bay Area case studies, DAP forecasts have been compared with projections made by traditional means. Below, we will make our conclusions on the accuracy of the base- condition equations in estimating average trip duration and total person trips. In the Bay Area case study, only the trip-duration equation was found to require updating. This fact takes into account the unique level-of- service characteristics of San Francisco. After updating in the 1965 base year, a comparison between the 1980 forecast trip duration by traditional means (14.27 minutes) and by DAP (16.60 minutes) reveals a discrepancy of only 16.33 percent. This would certainly lend credence to the temporal stability of using a socioeconomic factor such as population to estimate mean trip duration. It should be noted, however, that the final 1980 DAP 157 estimate mentioned above does not reflect the actual value yielded by the trip-duration equation, but rather is the result of the DAP equilibrium analysis used to show the impact of the recommended transport system improvement plan. The actual direct output of the updated tripduration equation, corresponding to the hypothetical situation of no system improvement, is shown to be 15.4 minutes. The 16.60 minutes of average travel time is the figure corresponding to the same implementation of transportation improvements as the traditional forecasts. The twin DAP forecasts of the 1990 Bay Area travel time adds further credence to the assertion of temporal transferability. Where no update was made at 1980 levels (Figure 5-11), the 1990 forecast of 13.0 minutes is -8.84 percent different from the traditional estimate of 14.26 minutes. When the DAP trip duration regression equation is updated at 1980 levels to accurately reflect traditional projections (assumed to hypothetically represent actual conditions), the 1990 DAP forecast is changed to be 10.94 percent above traditional. In the Reading case study, temporal stability is illustrated by the comparison of DAP estimates with actual trip durations. After updating at the 1958 base year levrls, the 1964 projection of mean trip duration is 7.27 minutes by DAP. This compares reasonably well with the actual value obtained from a home interview survey, 7.65 minutes. The most encouraging result with respect to mean trip duration was obtained in the 1990 forecasts in Reading. The DAP projections of 8.6 minutes is within 2.27 percent of the traditional estimate of 8.8 minutes. It is apparent from the above evaluation that the assumption of temporal transferability with respect to average travel time is clearly acceptable. At first glance, the assertion of temporal stability of the trip frequency equation (in which parameters are used without updating) might appear to be disproved by both case studies. For example, the 1990 total person trips estimated by DAP (without updating) for the San Francisco Bay Area differ by as much as 15.27 percent from traditional methodologies. However, by the nature of the induced travel resulting from improved accessibility, as indicated by the slope of the demand curve and equilibrium analysis, the DAP estimate should be higher than that made by sequential means which typically treat trips as being perfectly inelastic. A closer 158 examination reveals, in addition, that the discrepancy between DAP and sequential forecasts are 7.28 percent with the 1980 update, which again speaks favorably of the updating procedure. In the Reading case study, after updating in 1958, the trip frequency equations yields a 1964 forecast within 2.0 percent of actual. The 1990 forecast also compares favorably with the DAP estimate although the latter is higher than the former by 7.20 percent (or 13.20 percent when the trip frequency equation is updated in 1975). This is again justifiable by the concept of induced demand, which is addressed only by DAP. In summary, while updating is recommended to ensure temporal trans- ferability (especially in the case of predicting average trip durations), both base condition equations appear to be temporally stable. Updating, on the other hand, would obviously improve on the accuracy of the forecast. Temporal and Spatial Transferability The spatial and temporal transferability discussion thus far suggests that the equations and parameters selected from a particular cell or across two cells of the city classification scheme need to be updated before they can be directly used for a particular city. The updating procedure is required to account for the temporal and spatial variations of unobserved variables, whether they be socioeconomic or level-of- service factors. Because DAP has been developed to be a fast-response technique, it obviously cannot take all variables related to travel demand into consideration. The updating procedure is embodied in DAP to account for any inadequacies in the explanatory power of some of the statistical relationships established. A simple updating procedure involving the adjustment of the intercepts in the trip frequency and duration equations (and possibly the slope of the demand curve) is put forth. With the updating procedure, for example, it appears that DAP can accurately forecast the 1964 actual traffic in Reading, Pa. In all of the three case studies, San Francisco, Pittsburgh, and Reading, the forecasts made by DAP equations and parameters are comparable to those made by traditional methods. The results of these three case studies indicate strongly that the parameters compiled in this document can be a powerful "quick turn-around" tool for the evaluation of urban transportation policy options. 159 D. Equilibration and Correlative Forecasting Thus far the demand/supply equilibration framework has been compared with the traditional forecasts and actual post-implementation traffic. It is necessary at this juncture to compare the DAP forecasts with the other urban area multimodal forecasts, which use a purely correlative- type estimation procedure. The first method is the Macro Urban Travel Demand Model (Koppelman 1972), which has been applied in the area of modal split. Another is the multimodal forecasts by elasticities alone (on an urban area level). By comparing the DAP modal split with the results of these approaches, one can verify the general applicability of our methodology. The two different modal split approaches, i.e., the one using elasticity alone and the macro travel demand models using regression analysis, have to be demonstrated and evaluated. As shown in Figure 5- 13, the evaluation includes a comparison between the modal split obtained by the existing procedure and that obtained from: (a) regression analysis and (b) the use of elasticities alone. The Pittsburgh Case The data pertinent to the modal split comparison for the city of Pittsburgh is given in Table 5-1. Using the regression approach detailed in Chapter III, one estimates the modal split for Pittsburgh in 1967 by the equation: % Transit = 1.587 + 0.00368 x (Transit Mileage) = 1.587 + 0.00368 x 1.968 = 8.83 %. According to the Pittsburgh Master Plan, the only proposed improvement to the transit system by 1980 is a relatively small 17 mile rapid rail transit system. This would raise the number of transit miles in the region to 1,985. This new figure is substituted into the regression equation: % Transit = 1.587 + 0.00368 x 1,985 = 8.89%. This compares with the 1980 transit modal split of 9.88 percent from DAP (and 13.10 percent from traditional methods). The application of modal split using elasticities alone is impossible since the average travel times* by auto and by transit are not available separately. 160 TABLE 5-1. PARAMETERS FOR MODAL SPLIT IN PITTSBURGH 1958 1980.1 DAP Item Transit Mileage 1,968 1,985 Person Trips by Transit 473,570 473,388 513,079 Person Trips by Auto 1,926,070 3,302,884 3,516,921 Total Person Trips 2,300,820 3,801,272 4,030,000 Number of Dwelling Units 470,000 570,000 Average Travel Time by Auto 23.1 N.A. Average Travel Time by Transit23.2 N.A. Auto ownership/Dwelling Unit 0.84 1.15 ___________________________ 1. When the entries are not obtained exogenously they are obtained from traditional forecasts. 2. The value is available only for 1967. Source: PATS (1961) 161 The San Francisco Case The data pertinent to the modal-split comparison for the city of San Francisco are given in Table 5-2. Since the transit mileage is not available, the regression analysis approach is not applicable. The elasticities method can be applied to measure the modal split in 1990, using the 1980 Bay Area data as base year input. Substituting this data in the formulation derived in Chapter III, one obtains: c d V 2.346 x 0.423 [1 + ( x 0.012 - ( x -1.000)] tf t t a where: V = the total number of trips made by transit in the forecast year t f c = the cross-elasticity showing the change in transit trips with t respect to a change in the auto travel time, and a d = the direct-elasticity representing the change in transit trips t with respect to a change in the transit travel time. The direct and cross-elasticities are obtained from the tabulation of disaggregate elasticities available to the research team (Chapter III, Section B). They are: c d = .37 = -.30. t t a Hence, the estimate of total transit trips in 1990 in the Bay Area is given by: V = 2,346,000 x 0.423 [1 + .37 (0.009) - .30 (-0.032)] = 1,005,188 t f The percentage of person trips by transit in 1990 using the elasticities method is, therefore: 1,005,188 % Transit = ------------------ 6.98%. 14,401,000 The percentage of person trips by transit according to traditional methodology, on the other hand, is: 961,000 % Transit = ---------------- = 6.67%. 14,401,000 This compares with the DAP forecast of 6.51 percent. 162 TABLE 5-2. PARAMETERS FOR MODAL SPLIT IN SAN FRANCISCO Item 1980 1990 1990 DAP Transit Mileage N.A. N.A. N.A. Person Trips by Transit 823,000 961,000 1,090,000 Person Trips by Auto 10,948,000 13,440,000 15,660,000 Total Person Trips 11,771,000 14,401,000 16,750,000 Number of Dwelling Units 1,944,000 2,346,000 Average Travel Time by Auto 13.00 min. 13.12 min. Average Travel Time by Transit 31.2 30.2 Auto Ownership/Dwelling Unit 1.40 (est.) 1.60 (est.) Transit Trips/Dwelling Unit 0.423 0.410 0.464 Source: BATSC (1969) 163 The equilibrium approach to modal split employed in the demand approximation procedure clearly provides better results in San Francisco than those obtained by using the elasticities alone and by the traditional method. The Reading Case The unavailability of certain data enables one to apply neither the regression method nor the method using cross elasticities for the city of Reading. The regression analysis method is not applicable due to the unavailability of "transit mileage," while the method based on elasticities requires travel times by transit and by auto which are not available. This lack of data combined with the fact that travel in Reading is predominantly by auto does not allow for meaningful comparison. Recommended Approach The limited comparison conducted in this section does not allow one to rank the three "simple" areawide forecast methods in a-conclusive way. Some observations, however, can be made in the Pittsburgh case. The regression analysis model was not successful in replicating the forecast obtained by the traditional methodology. The elasticity method, when applied to San Francisco, is not particularly successful. On the other hand, the equilibrium approach using DAP provides a better estimate of future modal split in both cases. The inaccuracy of the forecast by regression may result from temporal instability which can be traced back to the lack of a set of sound structural equations. On the other hand, the shortcoming of the elasticity approach is that it is based on the implicit assumption that only minor changes occur in the study area between the base and forecast year-rendering the methodology inoperable in other than a short term forecast. From the data requirement viewpoint, we can conclude that both the regression analysis method and the method using elasticities include variables or parameters which are often not available in the "real world" context, particularly for two points in time. This, in conjunction with their theoretical weaknesses, points toward the equilibrium approach as a more reliable and more problem-responsive technique (although further comparisons based on additional case studies will allow a more definitive statement to be made). 164 E. Generalization of the Forecasting Procedure Thus far a city-classification scheme has been established, and the conditions under which demand-forecasting parameters are transferable and stable within each cell of the classification as well as when they are transferable across the cells have been outlined. Furthermore, the classification scheme also groups cities corresponding to their prevalent type of transportation systems, e.g., heavy rail in large/core-concentrated cities and autos in multinucleated medium cities. Based on these findings, it can be stated that cities within each cell share common demand and supply characteristics, and detailed study of a representative city in each of the cells helps us to infer these characteristics among the cities in the cell via extrapolation or interpolation. The issue that still remains to be solved is: "Does the working data base of candidate urban areas upon which the above findings are built constitute an adequate sample to render statistically significant results?". Representativeness of the Data Base The applicability of the recommended regionwide fast-response travel forecasting procedure in each of the urban scenarios (e.g., large/core- concentrated with rapid rail, medium/multinucleated with bus transit only, etc.) depends to a large extent on the sufficiency of the coverage of each scenario by the data base. In this case, the data base is composed of this information (see Appendix 1): (a) Socioeconomic Data: Auto per household Urban population (b) Travel Data: Trip frequency per household Average trip duration (c) Travel Response Parameter: Demand elasticities. The first two categories of data allow us to classify cities into groups as well as estimating the base-condition travel before any proposed transportation system improvements. The last category of data provides the means for us to estimate the travel responses corresponding to the change in the level-of-service. In addition to this information, an extensive collection 165 of technical reports was compiled for various cities, from which our case study areas were selected (see Bibliography under "Site Demonstrations"). While formal presentation of the statistical representativeness of the data base, as well as the geographical distribution of the sources of data, is made in Appendix 1, a brief summary of the data sample for purposes of assessing the relative level of coverage of the various scenarios is presented here. One recalls that a small portion of the trip frequency and trip duration data was collected from "third-level" sources. The most significant amount of this information, however, was obtained from an extensive survey of many of the nation's cities. Questionnaires were mailed to numerous State Departments of Transportation, with the response far exceeding the expectations of the research team. A total of 29 states and the District of Columbia forwarded data for 143 cities. A few data points were eliminated because they represented two points in time for a single urban area. The survey data, when combined with our limited third level sample, yielded a total of 100 data points for fitting the trip-duration equation and 133 points for the trip-frequency equation, all for urban areas with a population greater than 50,000. Demand elasticity values were obtained. from third level sources for 23 cities. About 75 reports and other references were collected for possible use in the site demonstration of the research findings. From this extensive array of cities, 13 potential case study cities were selected. After careful analysis, Pittsburgh, San Francisco and Reading were chosen. In addition to representing three of the four classification cells, these three areas represented various urban transport options ranging from an extensive rapid rail implementation in the San Francisco Bay Area to the almost exclusive auto/highway system in Reading. Sufficiency of Coverage In order to examine the sample cities in terms of their coverage of all the cities in the U.S. one may use two criteria. One is to use the number of cities of each population class as a reference in which one examines whether the sample is representative of the cities in the cell. The other is to use the total population-of sample cities as a reference, in which, on an equity basis, one ensures that the U.S. population in each cell 166 are adequately represented. In this section, and in more detail in Appendix 1, both criteria are analyzed carefully to show they are indeed taken into account and our sampling frame and procedure are meaningful (Figure 5-14). The city observations used in our study are made up of three collections, which we call the "circumstantial sets": (a) Set one contains the data base for determining trip frequency/ duration. (b) Set two allows us to estimate demand elasticities. (c) The last set is a collection of cities where system improvements have been implemented or planned. The intersection of the three circumstantial sets (namely the common set) consists of cities used for all three statistical purposes. They represent the study areas where the forecast should be quite accurate (as borne out by the Pittsburgh case study). The coverage of the sample cities in the various circumstantial sets totals as high as 73 percent of all U.S. SMSAs for the number of cities with population less than 250,000. The sample sizes are selected in proportion to the actual distribution of all the U.S. cities. The coverage in general is, therefore, considered adequate to insure reliable and representative results. It is shown that the sample distribution of the combined set of cities closely follows the rank order of all SMSAs in the U.S., meaning that, when there are a large number of U.S. cities in a particular population group, the sample size is correspondingly large and vice versa. This is true not only in the case of number of cities but also the total population represented-a most gratifying finding indeed. The coverage of sample cities is also presented in proportion with respect to urban structure. For example, with respect to trip generation data, there are 59 percent of the sample cities in population group I (greater than 800,000) that belong to the multinucleated structure and 41 percent in the core-concentrated structure. This agrees well with the fifty/fifty split between the 2 categories for all the U.S. cities. F. Summary This chapter examines the step-by-step procedure of forecasting city- wide traffic such as vehicle-miles-of-travel and passenger-miles-of- travel 167 Click HERE for graphic. FIGURE 5-13. THE COMPARISON BETWEEN THREE "SIMPLE" METHODS OF AREAWIDE TRAVEL FORECASTING 168 Click HERE for graphic. FIGURE 5-14. RELATIONSHIP BETWEEN CIRCUMSTANTIAL SET AND COMMON SET 169 using a supply/demand equilibrium approach. Three case studies were conducted, covering San Francisco, Calif., Pittsburgh and Redding, Pa. These case studies facilitate site-specific verifications of the city classification scheme, the demand elasticities, and the aggregate supply functions in a consistent framework called the demand approximation procedure. These urban scenarios serve as a reasonable cross-section of American cities for testing the applicability of our travel estimation procedures, since they represent not only the three most significant cells of the four-cell classification but also encompass a variety of transportation system implementations, including "capital intensive" heavy rail, "low cost" transit and the "basic" automobile system. In as much as a set of generalized parameters are compiled in this research, several strategies are recommended in the chapter to insure that such parameters are applicable in specific sites. The tabulated parameters and formulas, whether they be elasticities, trip-frequency or trip duration equations, often need to be calibrated or updated before they can be applied. This is to take into consideration more accurately the peculiar socioeconomic and level-of-service pattern of the urban area under consideration. In this way any deficiency in the explanatory power of the generalized parameters can be overcome. In all of the three case studies the forecasts made by the equilibrium approach using the generalized parameters are comparable to those made by traditional methods, such as actual post-implementation traffic counts, the elasticity method and a correlative-type analysis. These results strongly indicate that the forecasting parameters compiled from over 70 percent of the U.S. cities in this research can be powerful, fast-response tools for the evaluation of urban transportation policy options. In order to guarantee spatial and temporal transferability of the tabulated parameters, however, a simple updating procedure, involving the adjustment of the bivariate equations and the slope of the demand curve segment, is recommended. Such an updating procedure serves to account for the temporal and spatial variations due to extraneous factors. 170 CHAPTER VI CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH Although the art of urban transportation planning is still in its embryonic stage, it is felt that the body of demand forecasting methods and models could have more impact on mission-oriented, policy-oriented functioning of the transportation profession, if "fast-response" forecasting techniques based on generalized model parameters such as elasticities can be developed. The argument is that while policy decisions have to be made typically under pressing deadlines, sophisticated demand-forecasting techniques require the process of data collection, calibration and sensitivity analysis, much of which entails a time span longer than what the real time decision and policy formulation can afford. In response to this challenge, the researchers have accomplished several tasks in our undertaking, among them two are more notable: (a) Urban areas were classified according to size (large vs. medium) and urban structure (multinucleated vs. core- concentrated). Such a taxonomy scheme facilitates subsequent analysis in two ways. First, it reflects the basic differences in travel pattern among different urban forms. Second, previous findings in urban passenger travel forecasting indicate that such a taxonomy is most meaningful for the tabulation of model parameters. A generic set of forecasting parameters for each group of cities which share similar demand responses to various levels-of-service and socioeconomic variables is deemed necessary. (b) The compilation of demand model parameters and procedures helps to shorten the "turnaround time" to perform forecasts. Since many of these parameters were calibrated repeatedly for a variety of urban areas over the last two or-three decades, a synthesis of these model calibration experiences will not only help us to understand the demand for travel better, but also reduce the replication of calibration efforts since parameters can be transferred from previous studies. 171 A. Research Results In the urban transportation planning profession two types of demand models are often used. They are respectively named "aggregate" and "disaggregate." Dependent on the types of model and data, demand fore- casting may have four different values: (a) Aggregate model and aggregate data, (b) Aggregate model and disaggregate data, (c) Disaggregate model and aggregate data, and (d) Disaggregate model and disaggregate data. To date, all demand model calibration parameters fall into the aforementioned categories. The main purpose of this study is to transform all of-these parameters into a useful form that will enrich the body of demand forecasting models and make these parameters more understandable and usable to urban transportation planners. The demand elasticity, for example, is one of those parameters, since it is directly related to the evaluation of alternative policies. "Model transferability," the fact that there exist a common set of parameters among models calibrated in different sites and time periods implies that operationally parameters estimated in one region can be applied to other areas. Identifying the conditions and procedures for the spatial and temporal transferabilities of model parameters is among the contributions of this research. Tabulated in this document is a general set of elasticities and the base conditions under which they are applicable. In order to ensure their transferability among cities, the tabulations are stratified by urban structure and urban size, resulting in a group of parameters for large/multinucleated cities, large/core-concentrated cities, medium/multinucleated and medium/ core-concentrated cities respectively. The following discussions will summarize our research results under six objectives we set for ourselves at the beginning of our endeavors. First, these objectives are reviewed briefly below (and graphically illustrated in Figure 6-1): (a) To identify a set of parameters which is common to many demand models (such as elasticities); 172 Click HERE for graphic. FIGURE 6-1. GENERALIZED DEMAND FORECASTING PARAMETERS BY POPULATION SIZE AND BY URBAN STRUCTURE 173 (b) To examine the structural differences (on a theoretical basis) among the various types of models and data used in order to support effort (a) above. (c) To use empirical studies as a means to verify theoretical results; (d) To observe and identify the spatial and temporal transferability properties of model parameters; (e) To generalize the calibrated parameters into a "generic" set for use in urban areas of similar travel characteristics; and (f) To demonstrate in a consistent procedure the use of these generalized parameters for quick evaluation of transportation policy options. City Classification The purpose of the city classification scheme is to capture similarities among urban areas with respect to their activity system and transportation services, both of which are manifested in terms of travel characteristics. These base travel conditions, represented by trip frequency and duration, are used as the major criteria for grouping cities. A rather interesting result of the city classification analysis, for example, is that, as far as base travel patterns are concerned, there is a sharp distinction between cities above 800,000 in population and those below. The analysis in Chapter II shows that stratifying cities into four classes (rather than treating them as a single group) helps to explain the variation in trip-making frequencies among cities by an additional 31 percent. Another 36 percent in the variation of trip duration can be explained by the recommended city classification scheme. The significant improvement over the statistical estimation on trip frequency and duration reported by other researchers, such as Koppelman (1972), can be mainly attributed to our urban area classification. Demand Elasticities Although the calibrated demand elasticities compiled by this study are limited to twelve sets of data from nine urban areas, we are able to use those data to aggregate four generic sets of elasticities according to 174 our city classification scheme. They consist of direct and cross- elasticities with respect to various components of level-of-service such as trip time and trip cost. In the spirit of keeping the urban areawide forecasting procedure simple, several steps are taken to aggregate these elasticities into more easy-to-use parameters: (a) First, the various components of level-of-service, such as time and cost, are collapsed into a single measure called impedance by valuating travel time. (b) Second, the various trip purposes, such as work and non-work and the various modes such as auto vs. transit, are aggregated in order to estimate the overall person-trips in an urban area. (c) Finally, one obtains an overall impedance elasticity, which reflects the areawide travel response to an improvement in the level-of-service of the transportation system. It is to be noted that the respective tables of elasticities are kept at the intermediate levels-of-aggregation, and they are fully documented in Chapter III. For example, one of these tables contains the impedance elasticities by mode (but with the trip purposes aggregated), so that the change of traffic volume of a particular mode corresponding to changes of level-of-service, such as travel time and cost of that particular mode and its competing modes, can be assessed directly. Such a series of "concensus" elasticity tabulations allows one to perform "first-cut" estimation on travel responses corresponding to transportation system improvements (or degradations). The use of elasticities calibrated by direct demand model, using zonal data as upper bounds for aggregation, allows us to check the numerical values of the aggregated elasticities. On the other hand, empirical demand elasticities (rather than calibrated elasticities) can serve as lower bounds. While this facilitates the aggregation-process a good deal, the researchers feel that the precise relationship between empirical, aggregate, and disaggregate model elasticities is yet to be uncovered. The readers are reminded also that the adjustment factors used for aggregation, often derived from one or two case studies, cannot be defended rigorously. These items may constitute good topics for future research. 175 Supply Function While demand elasticities by themselves can be used as a crude tool for short-term forecasting, a much more reliable estimate can be obtained using equilibrium analysis. Critical to the use of equilibrium analysis in traffic forecasting is the plotting of the supply function. When dealing with a quick-response, areawide forecasting procedure, such as that developed in this research, one must delineate the total system supply curve, encompassing all major multimodal services and facilities in the study area. The derivation of the aggregate supply curve in an urban area is no small task. It has been demonstrated that only the two end points on the aggregate curve can be determined accurately. They correspond to the places where the volume/capacity ratios are 0.00 and 1.00 respectively. Using these anchor points, the research team has developed a method for making a reasonable approximation of the slope and location of the system supply curve, encompassing both the highway and transit elements of the system. In addition to providing a means for reflecting the changes in the level-of-service-in an urban area resulting from some major change in the transport system, the aggregate supply function, when used in conjunction with the demand function, lends itself well to the evaluation of the impact on travel of policy decisions, such as alternative investment decisions among candidate cities. Limited examples of such applications were shown in Chapter V and Appendices 5, 6 and 7. B. Mission-Oriented Applications An objective of this research is to provide a policy-sensitive demandforecasting procedure. As part of the fiscal study performed by the State of Pennsylvania (PennDOT 1976), for example, Vehicle-Miles of Travel (VMT) must be estimated on a local and regional level in order to assist the state in the allocation of resources among various substate regions and localities. An exemplary application is in connection with the proposed turnback of some 13,000 mile s of local roads to municipalities. The proposal, when adopted, may require a reallocation of maintenance funds between counties and municipalities--a task which could be facilitated by an accurate determination of VMTs on a local level. 176 This is a typical example of the mission-oriented application of the results of this research on a statewide level. Many more on a national level can be cited. These analyses can be facilitated to a large extent by the major contribution of our research, which can be summarized once again: (a) A city classification scheme, (b) Tabulations of elasticities and base-condition equations according to the classification scheme, (c) A method to determine areawide supply functions, and (d) A step-by-step illustration of the process of transferring the generic parameters to specific sites for equilibrium traffic estimation. While previous sections have discussed these contributions quite adequately, the way they work together in traffic forecasting needs to be reviewed. In so doing we will bring out the merits (and demerits) of the research results in "real-world" applications. The three site- specific case studies in Pittsburgh, San Francisco and Reading, Pa. allow us to make some conclusive remarks on the relevance of our research to travel forecasting, particularly regarding the transferability of generic parameters, such as elasticities, to three cities which are rather disparate in both urban structure and size. Our equilibrium analysis shows that relatively accurate forecasts were obtained using the forecast parameters compiled in this research. Our forecasts on the number of person trips in Pittsburgh, for example, was obtained within five percent of that by the traditional urban transportation planning (UTP) process, at only a small fraction of the cost. A principal objective of our San Francisco Bay Area case study was an evaluation of the temporal stability of our parameter tabulations. It was found through the 1980 and 1990 forecasts that such stability properties are established, provided parameter updatings are performed. The Case study suggests, however, that our parameter tabulations are somewhat more applicable for less diversified urban structures than those found in the Bay area. This should not imply, however, that the procedure is not applicable in extremely multinucleated regions, but rather that more case studies need to be performed to make a proper assessment. 177 The case study of Reading, Pa. has verified the accuracy of the synthesized parameters adequately in two forecasts. One uses the actual 1964 traffic counts, and the other the 1975 traffic counts. The forecast using the demand approximation procedure (DAP) is two percent lower than the 1964 counts and six percent lower than the 1975 counts respectively. Both comparisons speak favorably for our research results. With these limited case studies, the usefulness of our compilations are illustrated. It is to be noted that these studies also show the stepby-step procedures in which the tabulated parameters can be used consistently for mission-oriented applications. C. Conclusions Over the years the body of urban travel demand-forecasting models has been steadily extended, corresponding to the intense efforts of research and practice in urban transportation planning. Numerous model calibrations have proved to be successful in various studies. However, compilations of these successful calibration parameters are scanty in the profession. This is attributed to three problem areas (also, refer to Figure 6-1): (a) Temporal Transferability. If a transportation planner wishes to adapt a set of "successful" demand model parameters from a previous study to his present scenario, the first question he would like to ask is: Are these parameters stable over time? Thus far, no satisfactory answer to the above questions have been provided. (b) Spatial Transferability. If the planner finds that these demand model parameters have been verified as temporally stable, then the next question that is raised, presumably by another planner in another city, is: Are those parameters transferable from that area to my own region? Again, few researchers have addressed the problem successfully. (c) Modeling Transferability. If there are several successful demand forecasts with various types of models and different levels of data, aggregation, the next problem the planners face is: Which set of parameters should I take? Very few guidelines (if any) have been provided to the confused planners. In many well-developed professions, rules and measurements have been developed and used as primary tools to deal with related problems. The 178 generalization of demand-forecasting model parameters performed in this research, albeit limited in nature, provides one of the few pioneering measurements for the transportation planning profession. With a general set of parameters, transportation planners can more effectively forecast the future travel demand and anticipate the implications of their policies and decisions. D. Extensions Given the usefulness of the parameters tabulated in this report, a more in-depth compilation of elasticities is proposed as a future as a future extension of this piece of research. Demand Elasticities Figure 6-1 indicates that cities are to be classified into four possible groups according to size and urban structure. In the current research, representative sets of demand elasticities in each cell have been compiled from a variety of model calibrations. These calibrations include rather disparate structural cover formulation and data aggregation levels. Theoretically, they encompass these four types: (a) Direct or simultaneous models using aggregate (zonal) data, (b) Direct or simultaneous models using disaggregate data, (c) Indirect or sequential models using aggregate data, and (d) Indirect or sequential models using disaggregate data. Accordingly, four types of demand elasticities can be obtained. They are .AA .AD so .DA and .DD respectively. In the literature search, it has been found that the parameters .DD calibrated by disaggregate models with disaggregate data are most stable both temporally and spatially.. However, it is not known quantitatively how much more stable they are compared to .AA.s. At the same time, it is expected that the magnitude of the elasticities share this relationship: .AA > .DA > .AD > .DD. The exact amount of difference among the various types of elasticities again is not known. A study is proposed to address these two issues. An objective of such a study would be to establish such a relationship by statistical and empirical approaches. 179 One of the results of the study is to find the precise numerical differences among these calibrated elasticities. The differences can be attributed to the model structures or the aggregation of data (or both)'. Another related result of the study is the relative stability of-these four types of elasticities. Along these lines, it is suggested that a more extensive elasticity data base be assembled in future extensions of this research, so that the aggregation of trip purposes and the transformation between direct demand elasticities and modal-split elasticities can be performed more accurately. It is also suggested that empirical elasticities should be transformed into logarithmic form, so that they can be more closely comparable to the point elasticities obtained from model calibrations. Parallel to this overall undertaking are the following related areas of investigation. City Classification The current research indicates that demand elasticities are best stratified according to city classifications. There are several approaches to city classification. In the current research, regression and linear goal programming are used to group cities. Another approach which was investigated but not adopted is cluster analysis. Among other considerations, this technique was not used because of the vast amount of effort which it entailed, placing it well beyond the scope of our current research. Where additional support is forthcoming, a parallel study of classifying cities via cluster analysis may supplement the results obtained from regression and linear goal programming. Remembering that, in this research, cities were classified as core- concentrated or multinucleated mainly on a judgmental basis, another area for further investigation is the development of a set of more well defined criteria for classifying cities according to their urban structure. A-set of criteria based on density and development patterns, if available, would result in a more adequate classification of cities into core-concentrated versus multinucleated categories. Supply Curves This study shows that a rigorous determination of future urban travel requires aggregating the transportation services and facilities 180 into a supply function. As previously discussed, the determination of the total system supply curve is not a straightforward process. While the recommended approach yields a reasonable approximation of the curve's orientation, possible extensions to this research concerning the derivation of the aggregate supply function include the development of a more accurate procedure for plotting the curve between the end points of the curve (other than plotting the "best fit" straight line). The more Precise specification of which types of facilities should properly be included in the highway classification scheme, and the generation of more distinct guidelines for the calibration of the base year highway curves should also be investigated. In short, a major flaw associated with the recommended procedure is that a good deal of judgment is-required of the user. The principal, objective of future research in this area should be oriented toward a reduction in the amount of this subjective input and the development of a more clear-cut procedure. The Integration and Verification Problem There remains the issue of putting all the demand elasticities, supply functions and city classification schemes together to perform a meaningful forecast and to show that the forecast is reasonably accurate. The current research points toward a demand/supply equilibrium approach named the demand approximation procedure (DAP). While the performance of such an approach was demonstrated positively in our case studies, several research extensions are suggested for further refinement. Since the thrust of this research is in areawide travel forecasting, the problem of study area definition is indeed critical to the successful use of the demand approximation procedure. The development of appropriate guidelines for the delineation of study areas, the types and sizes of facilities to be included in the analysis and a specific means for dealing with intrazonal versus interzonal trips might be considered as subjects of future research. There are a few other areas where further research is desirable. Perhaps the most significant one is the development of a more rigorous modal split procedure. The accuracy of the DAP forecast can probably be improved significantly via such a piece of research. 181 Finally, it should be clear that due to the well known fallacies involved in the traditional method, it cannot be considered as an absolute reference for DAP's evaluation. More comparative analysis with actual post-implementation traffic counts is, therefore, recommended. Policy Alternative Analysis Generalized forecasting parameters such as those compiled in this research can be used in two different ways. One is to forecast the travel demand in terms of areawide travel figures such as passenger- miles-oftravel (PMT) or vehicle-miles-of-travel (VMT). The other is to analyze the cost/benefit relations of transportation capital investment. 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State Highway Department of Georgia, Division of Highway Planning in Cooperation with the U.S. Department of Commerce, Bureau of Public Roads: Atlanta, GA. __________ 1963. Atlanta Area Transportation Study, Truck Interview, Coding Procedure Manual. State Highway Department of Georgia, Division of Highway Planning in Cooperation with the U.S. Department of Commerce, Bureau of Public Roads: Atlanta, GA. __________ 1963. Atlanta Area Transportation Study, Truck-taxi Inter- view, District Supervisor's Manual. State Highway Department of Georgia, Division of Highway Planning in Cooperation with the U.S. Department of Commerce, Bureau of Public Roads: Atlanta, GA. __________ 1967. Atlanta Area Transportation Study, Existing Conditions Report. State Highway Department of Georgia, Division of Highway planning in Cooperation with the U.S. Department of Transportation, Federal Highway Administration, Bureau of Public Roads: Atlanta, GA. BART Office of Research. 1971. 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Highway Study: A Research Study of Traffic Patterns and Highway Needs for 1960 and 1980-85. Prepared in Cooperation with General Lane Planning Council: Eugene & Springfield, Oregon. Charles River Associates. 1967. A Model of Urban Passenger Travel Demand in the San Francisco Metropolitan Area. Prepared for Peat Marwick Livingston & Co.: Washington, D.C. __________ . 1968. An Evaluation of Free Transit Service. National Technical Information Service: Springfield, Virginia. __________ . 1971. Development of a Behavioral Urban Travel Demand Method. U.S. Department of Transportation, Federal Highway Administration: Washington, D.C. __________ . 1976. "Estimating the Effects of Urban Travel Policies." U.S. Department of Transportation: Washington, D.C. Chicago Area Transportation Study 1960. Sponsored by the State of Illi- nois, Cook County, and the City of Chicago in Cooperation with the U.S. Department of Commerce, Vols. I and II: Chicago, IL. 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Toledo Transit Analysis Toledo, OH. Gilman, W. C. and Voorhees A. M. & Associates, Inc. 1969. Traffic Revenue and Operating Costs. Washington Metropolitan Area Transit Authority: Washington, D.C. 194 Goldner, W. 1968. Projective Land Use Model (PLVM): A Model for the Spatial Allocation of Activities and Land Uses in A Metropolitan Region. Bay Area Transportation Study Commission: Berkeley, CA. Goldmuntz, L. A. 1974. "An Urban Overrun." Published in Personal Rapid Transit II. Minneapolis: University of Minnesota Press. Grefe, R. and Smart, R. 1975. "A History of the Key Decisions in the Development of Bay Area Rapid Transit." McDonald and Smart, Inc., prepared for the U.S. Department of Transportation: Washington, D.C. Hamer, A. M. 1976. The Selling of Rail Rapid Transit: A Critical Look at Urban Transportation Planning. Lexington, MA: Lexington, Books, D.C. Heath and Company. Hartgen, D. T. and Keck, C. A. 1976. "Forecasting Dial-A-Bus Ridership in Small Urban Areas." Transportation Research Board 563: 53-62. Holland, D. K. 1974. "A Review of Reports Related to the Effect of Fare and Service Changes in Metropolitan Public Transportation Systems." Prepared for U.S. Department of Transportation, Federal Highway Administration: Washington, D.C. Houston-Harris: County Transportation Study Office. 1971. Houston- Harris County Transportation Plan. Houston, TX. Howard, Needles, Tammen and Bergendoff. 1970, Feasibility Study for Bus Rapid Transit in the Shirley Highway Corridor Prepared for the Metropolitan Council of Governments: Washington, D.C. Kavak, F. C. and Demetsky, M. J. 1975. "Behavioral Modeling of Express Bus Fringe Parking Decisions." Transportation Research Record 534: 10- 23. Kemp, M. A. 1974. "Reduced Fare and Fare-Free Urban Transit Services-- Some Case Studies." Transport and Road Research Laboratory Report SR37: Crowthorne, Berkshire, England. Kollo, H. P. H. and Sullivan, E. C. 1969. Trip Generation Model Development. Bay Area Transportation Study Commission: Berkeley, CA. Lassow, W. 1968. "Effect of the Fare Increase of July 1966 on the Number of Passengers Carried on the New York City Transit System." Highway Research Record 213. Levinson, H. S. and Hoey, W. F. 1973. Bus Use of Highways: State of the Art. Wilbur Smith & Associates, National Cooperative Highway Research Program Report 143: Washington, D.C. McFadden, D. 1974. "The Measurement of Urban Travel Demand." Journal of Public Economics 3: 303-328. McGillivray, R. G. 1972. "Binary Choice of Urban Transport Mode in the San Francisco Bay Region." Econometrics. 40: 827-848. 195 McQueen, J. T., et al. 1975. "Evaluation of the Shirley Highway Express-Bus-on-Freeway Demonstration Project-Final Report." Prepared by the U.S. Department of Commerce, Analysis Division and the National Bureau of Standards for the U.S. Department of Transportation, Urban Mass Transportation Administration. Miller, J. H., et al. .1975. Shenango Valley Transit Development Program. Prepared for Shenango Valley Council of Governments, Report PTI 7520, The Pennsylvania Transportation Institute, University Park, PA. Miller, J. H., et al. 1976. DuBois Area Transit Development Program. Prepared for DuBois-Falls Creek-Sandy Township Joint Transportation Authority, Report PTI 7522, The Pennsylvania Transportation Institute: University Park, PA. Mullen, P. 1975. "Estimating the DP-and for Urban Bus Travel." Transportation 4: 231-252. Niagara Frontier Transportation Study. 1966. Conducted by a State Policy Committee, Financed by the State Department of Public Works and the U.S. Department of Commerce, Vol. II: Niagara Frontier, NY. North Carolina Department of Transportation, Division of Highways. 1974. Development of Travel Forecasting Models, Asheville Area Transportation Study. Report Nos. 1 & 2: Asheville, NC. __________ 1975. Report on the Development of Travel Forecasting Models, Greensboro Area Transportation Study. Technical Reports 1& 2: Greensboro, NC. __________ 1975. Report on the Origin-Destination Survey, High Point Urban Area Transportation Study. Technical Report I: High Point, NC. __________ . 1976. Gastonia Urban Area Transportation Study. Technical Reports 1 & 2: Gastonia, NC. Parody, T. C. 1977. An Analysis of Disaggregate Model Choice Models in Prediction. Presented at the 56th Annual Meeting, Highway Research Board: Washington, D.C. Parsons, Brinckerhoff, Hall and Macdonald, Engineers. 1955. Regional Rapid Transit. San Francisco Bay Area Transit Commission: San Francisco, CA. Parsons Brinckerhoff-Tudor-Bechtel. 1962. The Composite Report, Bay Area Rapid Transit. San Francisco Bay Area Rapid Transit District: San Francisco, CA. Peat, Marwick, Mitchell & Co. 1972. Implementation of the N-Dimensional Logit Model, Final Report. Comprehensive Planning Organization, San Diego County: San Diego, CA. 196 __________ 1974. A Review of Some Anticipated and Observed Impacts of the Bay Area Rapid Transit System (BART Impact Program). Prepared for the U.S. Department of Transportation and The U.S. Department of Housing and Urban Development: Washington, D.C. __________ . 1974. A Study of Public Transportation Improvements in Montgomery and Prince George Counties. Maryland. Prepared for Maryland National Capital Park and Planning Commission: Maryland. __________ . 1975. Analysis of BART's Energy Consumption for Interim System Operation (BART Impact Program). Prepared for U.S. Department of Transportation: Washington, D.C. __________ . 1976. Transportation and Travel Impact of BART: Interim Service Findings (BART Impact Program). Prepared for the U.S. Department of Transportation and The U.S. Department of Housing and Urban Development: Washington, D.C. Philadelphia, Urban Traffic and Transportation Board. 1956. Plan and Program 1955, Conclusions and Recommendations of the Board. Philadelphia, PA. Pittsburgh Area Transportation Study. 1961. Sponsored by the Commonwealth of Pennsylvania, in cooperation with the U.S. Department of Commerce, Vols. 1&2: Pittsburgh, PA. Pratsch, L. 1976. "Knoxville and Portland: Two Successful Commuter Polling Programs." Transportation Research Board Special Report 164: Washington, D.C. Pratt, R. H. and Associates, Inc. and DTM, Inc. 1976. Development and Calibration of Mode Choice Models for the Twin Cities Area. Twin Cities, MN. Pucher, J. and Rothenberg, J. 1976. "Pricing in Urban Transportation: A Survey of Empirical Evidence on the Elasticity of Travel Demand." Working Paper, M.I.T.: Cambridge, MA. Reading Area Transportation Study. 1972. Sponsored by the Commonwealth of Pennsylvania in Cooperation with the U.S. Department of Transportation and the U.S. Department of Housing, Vols. 2 & 3: Reading, PA. Reid, F. A. 1974. The Determinati on and Evaluation of Objective Access Times to Public Transit for Disaggregate Traveler Behavior Modeling. Prepared by the Metropolitan Transportation Commission for the U.S. Department of Transportation and the U.S. Department of Housing and Urban Development: Washington, D.C. San Francisco Metropolitan Transportation Commission. 1976. Impact of BART on Transportation and Travel-Interpretive Summary. Schultz, G. W. and Pratt, R. H. 1971. "Estimating Multimode Transit Use in a Corridor Analysis." Highway Research Record 369: 39-46. 197 Sherret, A. 1975. Immediate Travel Impact of Transbay BART (BART Impact Program). Peat, Marwick, Mitchell & Co., Prepared for the U.S. Department of Transportation: Washington, D.C. __________ . 1977. "BART's Operating Energy Consumption, Costs, and Revenues." Peat, Marwick, Mitchell and Co., Prepared for U.S. Department of Transportation: Washington, D.C. Simpson and Curtin, 1974. Modal Split Methodology for the Toledo Regional Area. Technical Re ports 6.3 & 6.31: Toledo OH. Wilbur Smith and Associates. 1959. Highway Planning Study for the St. Louis Metropolitan Area. Prepared for the Missouri State Highway Commission in Cooperation with the U.S. Department of Commerce, Vols. 1 & 2: St. Louis, MO. __________ 1959. Kansas City Metropolitan Area Origin and Destination Survey. Prepared for the State Highway Commissions of Kansas and Missouri in Cooperation with the U.S. Department of Commerce, Vols. 1 & 2: Kansas City, MO. __________ . 1961. Nashville Metropolitan Area Transportation Study: Origin Destination Survey. Nashville, TN. Sosslau, A. B., Heanue, K. E. and Balek, A. J. 1965. "Evaluation of a New Modal Split Procedure" Highway Research Record 88: 44-63. Southwestern Pennsylvania Regional Planning Commission. 1965. Regional Development Planning and Transportation Planning. Pittsburgh, PA. __________ . 1972. Development of Trip Distribution Models for the Southwestern Pennsylvania Region. Pittsburgh, PA. __________ . 1972. Modal Split Model for Southwestern Pennsylvania. Pittsburgh, PA. __________ 1972. Development of Trip Generation Models. Pittsburgh, PA. __________ 1973. Cycle I; Transportation Planning: A Report on the Conception and Evaluation of Initial Transit and Highway Alternatives. Pittsburgh, PA. Talvitie, A. P., 1971. "An Econometric Model for Downtown Work Trips." Ph.D. Dissertation, Northwestern University, Department of Civil Engineering, Evanston, IL. __________ 1973. "A Direct Demand Model for Downtown Work Trips." Transportation 2: 121-152. Texas Highway Department. 1960. Houston Metropolitan Area Transportation Study: Origin-Destination Survey. Houston, TX. 198 Train, K. 1976. "A Post-BART Model of Mode Choice: Some Specification Tests." Working Paper No. 7620, Urban Travel Demand Forecasting Project, University of California, Institute of Transportation Studies: Berkeley, CA. Tri-State Regional Planning Commission. 1976. Urban Densities for Public Transportation. Urban Mass Transportation Administration: Washington, D.C. Tucson Area Transportation Study: An Inventory Analysis of Existing Conditions. Sponsored by the city of Tucson-County of Pima-State of Arizona in Cooperation with the U.S. Department of Commerce. U.S. Department of Transportation (U.S. DOT). 1975. Intermodal Transportation Planning: Washington, D.C. Voorhees, A. M. & Associates and Burgwin & Martin Consulting Engineers. 1964. Fort Worth Metropolitan Area Transportation-Planning Study. Fort Worth, TX. Voorhees, A. M. 1959. "Estimating and Forecasting Travel for Baltimore by Use of a Mathematical Modal." Highway Research Board 224: 105-114. Voorhees, A. M. & Associates, Inc. 1967. Altoona Area Transportation Study Technical Report No. 5: Trip Generation and Gravity Model Calibration: Altoona, PA. Vuchic, V. R. and Stanger, M. R. 1973. Lindenwold Rail Line and Shirley Busway: A Comparison. Presented at the 52nd Annual Meeting of the Highway Research Board: Washington, D.C. Weiss, D. L. and Hartgen, D. T. 1976. "Revenue Ridership and Equity of Differential Time of Day Fares." New York Department of Transportation, Planning Research Unit: Albany, NY. Wiant, R. H. 1961. "A Simplified Method for Forecasting Urban Traffic." Highway Research Board 297: 128-145. Wichita-Sedgwick County Metropolitan Planning Department. 1964. Transportation Study for the Wichita-Sedgwick County Metropolitan Area. Vols. 1 & 2: Wichita, KS. Wigner, M. F. 1973. "Disaggregate Modal-Choice Models for Downtown Trips in the Chicago Region." Highway Research Record 446: 49-65. 199 APPENDIX 1: DESCRIPTION OF DATA BASE AND DATA TABULATIONS Of the rather large amount of data which was collected during this research effort, the most critical elements can be divided into three principal categories. The first two include information pertaining to average trip duration, frequency characteristics and demand elasticities respectively. The third group consists of an extensive collection of technical reports for possible use in case study demonstrations of the research findings. It is, of course, critical to the analysis to verify if the data collected constitutes a large enough sample to render statistically significant results. Further, it is desirable to review the geographical distribution of the cities contained in each sample to ensure that no unnecessary bias is introduced from the relative locations of the data points. The three categories of data are described and evaluated below. A. Description of the Survey Data Base In an effort to complete one of the most important elements of this research endeavor, the compilation of demand forecasting experiences, the researchers mailed a brief Demand Forecasting Data Questionnaire to transportation planners across the country. In an effort to consolidate mailing expenses and to encourage a more stable response, the research team decided to distribute these questionnaires to the appropriate members of the planning departments of several state departments of transportation. The information was solicited for each urban area over 50,000 population within the United States. As may be seen in Table A-1-1, a copy of the actual questionnaire, two basic types of information were requested. The most critical was aggregate level forecasting data, shown in Table A-1-1. In all, nine items were solicited which served primarily as input to the regression analysis and the development of the base-condition equations. In addition, planners were queried as to the availability of disaggregate level home survey data for possible use in the development of an updating technique. Response to the survey exceeded by far the expectations of the research team. Based on a list of home interview surveys and a quick assessment of 200 URBAN AREA ______________________________ TRAVEL DEMAND FORECASTING DATA QUESTIONNAIRE The following data items pertaining to urban transportation demand fore- casting are routinely inventoried during conduct of typical comprehensive regional planning studies. This information is of critical importance to a research project currently underway at the Pennsylvania Transportation Institute. The requested data fall into two categories; aggregate (areawide) level and household level. It would be most appreciated if you could supply as much of the following information as possible. All data should be at base year levels,.i.e., the year when home interview survey was conducted. Aggregate Level Data (Base Year) Base Year _______________ 1. Average Trip Duration: Work Trips _______________ minutes All Purposes Combined _______________ minutes 2. Total Daily Person Trips _______________ , by auto _______________ , by transit _______________ 3. Total Daily Auto Trips _______________ 4. Average Network Speed _______________ mph 5. Population of Study Area _______________ 6. Average Auto Ownership per Dwelling Unit _______________ 7. Number of Dwelling Units _______________ 8. Highway Mileage _______________ Linear Niles Lane Miles Freeway _______________ _______________ Arterial _______________ _______________ Local _______________ _______________ 9. Transit Mileage Linear Miles Route Miles (Linear Miles x Daily Frequency) Rail _______________ _______________ Bus _______________ _______________ TABLE A-1-1. TYPICAL SURVEY FORM 201 Disaggregate (Household) Level Data The following information is requested in the original raw, unadjusted, uncalibrated form-sample of the actual home interviews conducted. Available Yes No 1. Number of autos in household ( ) ( ) 2. Number of residents in household ( ) ( ) 3. Number of daily trips in household ( ) ( ) 4. If data is available in a form which can be forwarded directly, please do so. If computer tapes should be supplied for transfer of data, please indicate type. All data should be forwarded to: Mr. Jossef Perl Pennsylvania Transportation Institute Research Building B University Park, PA 16802 Thank you in advance for your kind cooperation in this important matter. TABLE A-1-1. TYPICAL SURVEY FORM (Continued) 202 the relative number of potential data points in each state, a total of 33 survey packages were mailed to 32 states and the District of Columbia, on December 10, 1976. A varying number of questionnaires were included in each package, depending on the estimated number of potential data points in a given state. In all, 170 survey forms were distributed. By February 28, 1977, a total of 29 states and the District of Columbia had responded, forwarding to the research team 143 completed questionnaires. This represented an excellent 90.9 percent return based on the number of states responding and a 84.1 percent return based on the number of questionnaires completed. Based on previous research findings, and supported by the data collected in the recent survey, the "cut-off" point between large and medium size cities in the classification scheme is 800,000. The survey results provide excellent coverage of both large and medium size urban areas, based both upon the number of cities in each group and the total population represented by each group. Figure A-1-1 indicates the relative sample size of each size classi- fication. Due to the rather large number of cities between 50,000 and 800,000, this classification was subdivided into two parts, corresponding to whether a city is above or below 250,000. This is done for statistical sampling analysis and should not be construed to represent a modification of the classification scheme. In addition, the comparison with United States totals should be taken to represent only an "order-of-magnitude" rather than an absolute relationship for two reasons. The population values for the U.S. cities are taken from 1970 census data, while the base year of the various transportation study data received ranged from 1960 to 1976. Secondly, the U.S. figures represent SMSA values, which are often slightly different from study area boundaries. Nevertheless, it would appear that the two basic comparisons, including the two base condition variables, trip duration and trip frequency, clearly indicate good statistical coverage. As can be seen from the data tabulations in Tables A-1-2 and A-1-3, trip duration information was available for 12 cities over 800,000 population, the lower limit for large cities in the recommended classification scheme.. Of these, seven were considered multinucleated in structure and five coreconcentrated. Of the 88 urban areas under 800,000 for which trip duration data was obtained, 16 were classified as multinucleated while the remaining 72 were considered core-concentrated. With respect 203 FIGURE A-1-1., SUMMARY OF SURVEY RESULTS COMPARED WITH U.S. TOTALS Population Survey Results Group Number/ Number and* ______________________________ PopulationPopulation in United States Trip % of Trip % of Duration U.S. Frequency U.S. Urban Areas Number 41 15 36.6 20 48.8 Over 800,000 Population87,713,997 33,881,164 38.6 43,583,757 49.7 Urban Areas Number 84 26 31.0 34 40.5 Between 250,000-800,000Population34,689,51411,108,140 32.0 15,495,279 44.7 Urban Areas Number 118 82 69.5 86 72.9 Between 50,000-250,000Population17,067,112 10,100,483 59.2 10,507,302 61.6 Total of All Number 243 123 50.6 140 57.6 Urban Areas over 50,000 Population139,470,62355,089,787 39.5 69,586,338 49.9 ___________________________ * U.S. Census, 1970 Statistics 204 to trip frequency data, 22 of the cities had a population over 800,000 of which 13 were multinucleated and nine were core-concentrated. Of the remaining 111 points, 30 were multinucleated and 72 were core- concentrated. As may be seen in Figure A-1-1 and the histograms in Figures A-1-2 and A-1-3, data relating to trip duration was slightly exceeded by trip frequency data, although neither element was included on all the questionnaires. Of the 243 SMSAs in the country, trip frequency data was furnished for 140, or 57.6 percent. The sample represented approximately 49.9 percent of the population residing in these areas. Trip duration data included 50.6 percent of the SMSAs and 39.5 percent of the population. The largest number of data points for both pieces of information involved the smallest population group, 50,000-250,000. Seventy-two percent of all SMSas in this category were represented in the trip-frequency data sample, and 69.5 percent by the trip-duration sample. The geographical representativeness of the sample is illustrated in Figures A-1-4 and A-1-5. For each basic data item, the bulk of the data points is shown to be in the eastern half of the nation. Being selective in the distribution of the questionnaires, the researchers did not sample much of the Rocky Mountain region, since only a few cities over 50,000 exist in those states. No response was received from the state of California where the bulk of the potential data points in the western states are located. Those locations in Figure A-1-4 and A-1-5 where two points are shown to be connected indicate they are located where travel data has been received for two points in time. The open circles refer to cities over 800,000, the solid circles to cities under 800,000. The travel demand-forecasting experiences compiled during the survey may represent the largest collection of such data in existence. When supplemented by the various other cities the research team has obtained from third level sources, the data base is shown to clearly represent travel characteristics of all types of cities, both statistically and geographically. A complete tabulation of all average trip duration and trip generation data is shown in Tables A-1-2 and A-1-3. Also attached here is Table A-1-4, containing the data base for the modal-split analysis performed in Chapter III. These lists include both survey responses and information obtained from third level sources, and, as such, represent our final working data base. 205 Click HERE for graphic. FIGURE A-1-2. HISTOGRAM OF NUMBER OF CITIES AND POPULATION--ALL U.S. SMSAs VERSUS SURVEY RESPONSE-TRIP DURATION (SHADED AREA SURVEY RESPONSE) 206 Click HERE for graphic. FIGURE A-1-3. HISTOGRAM OF NUMBER OF CITIES AND POPULATION--ALL U.S. SMSAs VERSUS SURVEY RESPONSE-TRIP FREQUENCY (SHADED AREA - SURVEY RESPONSE) 207 Click HERE for graphic. 208 Click HERE for graphic. 209 TABLE A-1-2. TRIP DURATION Year ofPopulation Work TripAverage Trip Urban Area Survey (000) Urban Duration Duration Structure (Min.) (Min.) Detroit, Mich. 1965 4041.81 Multinucleated 24.27 17.525 Philadelphia, Pa. 1960 4007.00 Multinucleated 19.60 11.9 Washington, D.C. 1968 2750.00 Core-Concentrated 25.00 N.A. St. Louis, Missouri 1965 2174.45 Core-Concentrated 20.20 15.80 Twin Cities, Minn. 1970 1874.38 Multinucleated 22.30 12.30 Dallas-Ft. Worth, Tex. 1964 1821.47 Multinucleated 14.14 9.43 Atlanta, Ga. 1970 1441.89 Core-Concentrated N.A. 17.50 Kansas City, Mo. 1970 1327.00 Multinucleated N.A, 14.90 Phoenix, Ariz. 1976 1220.00 Core-Concentrated 20.70 16.60 Denver, Col. 1971 1119.00 Core-Concentrated 18.62 15.11 Niagara Frontier, N.Y. 1973 1234.51 Multinucleated 21.00 18.80 San Antonio, Tex. 1969 825.84 Multinucleated 14.94 12.87 Louisville, Pa.- 1964 751.88 Multinucleated 17.47 13.17 Portland, Oregon 1960 709.35 Core-Concentrated 19.50 16.30 Memphis, Tenn. 1964 656.60 Core-Concentrated 18.10 13.60 Norfolk-Portsmouth, Va. 1962 602.00 Multinucleated 13.00 10.68 Oklahoma City, Okla. 1965 563.90 Multinucleated 12.90 9.00 Birmingham, Ala. 1965 559.07 Core-Concentrated 31.59 24.39 Omaha-Council Bluffs, Iowa 1965 506.00 Multinucleated 12.52 10.60 Honolulu, Hawaii 1960 500.41 Core-Concentrated 20.50 16.00 Scranton-Wilkes Barre, Pa. 1964 453.20 Core-Concentrated 18.70 16.50 Richmond, Va. 1964 417.68 Multinucleated 12.10 9.21 Tulsa, Okla. 1964 363.87 Core-Concentrated 13.21 10.63 El Paso, Tex. 1970 362.79 Core-Concentrated 13.02 12.48 Nashville, Tenn. 1959 357.58 Core-Concentrated 16.38 13.04 Lehigh Valley, Pa. 1964 345.10 Multinucleated 7.76 6.53 Wichita, Kansas 1973 330.66 Core-Concentrated 14.61 11.83 Jefferson-Orange, Tex. 1963 314.71 Multinucleated 12.51 8.34 Mobile, Ala. 1966 279.68 Core-Concentrated 16.63 14.45 Peninsula, Va. 1964 277.75 Core-Concentrated 15.02 12.55 Spokane, Wash. 1965 270.00 Core-Concentrated 14.50 12.00 Columbus, Ga. 1965 269.00 Multinucleated 18.80 14.50 TABLE A-1-2. TRIP DURATION (Continued) Year ofPopulation Work TripAverage Trip Urban Area Survey (000) Urban Duration Duration Structure (Min.) (Min.) Des Moines, Iowa 1964 258.40 Core-Concentrated 13.80 11.20 Davenport, Iowa 1964 250.75 Multinucleated 16.02 13.02 Harrisburg, Pa. 1965 245.19 Core-Concentrated 12.24 10.03 Baton Rouge, La. 1965 245.08 Core-Concentrated 11.30 8.33 Tucson, Ariz. 1960 244.50 Core-Concentrated 13.14 10.26 Chattanooga, Tenn. 1960 242.00 Multinucleated 11.08 8.53 Shreveport, La. 1965 237.20 Core-Concentrated 10.84 8.47 Charleston, S.C. 1965 235.54 Core-Concentrated 16.04 12.68 Pensacola, Fla. 1970 230.29 Core-Concentrated 13.78 10.94- Austin, Tex. 1962 209.61 Core-Concentrated 9.46 7.19 Corpus Christi, Tex. 1963 196.09 Multinucleated 8.49 6.33 Columbia, S.C. 1965 195.97 Core-Concentrated 11.10 8.22 Greenville, S.C. 1965 184.37 Core-Concentrated 14.50 12.50 Greensboro, N.C. 1970 182.51 Core-Concentrated 10.04 8.29 Reading, Pa. 1964 178.27 Core-Concentrated 10.60 9.10 Colorado Springs, Col. 1964 172.50 Core-Concentrated 11.55 9.95 Montgomery, Ala. 1965 165.00 Core-Concentrated 11.65 10.07 Madison, Wis. 1962 162.24 Core-Concentrated 9.70 7.69 Duluth-Superior, Minn. 1964 160.24 Multinucleated 17.20 11.03 Amarillo, Tex. 1964 156.36 Core-Concentrated 11.76 7.88 Lubbock, Tex. 1964 152.78 Core-Concentrated 8.71 6.91 Roanoke, Va. 1965 151.86 Core-Concentrated 13.91 11.27 Steubenville, Ohio 1965 150.25 Core-Concentrated 16.30 15.60 Huntsville, Ala. 1964 133.97 Core-Concentrated 12.58 8.93 Topeka, Kansas 1965 132.81 Core-Concentrated 11.45 9.59 Waco, Tex. 1964 132.35 Core-Concentrated 9.68 7.50 Eugene, Ore. 1964 127.55 Core-Concentrated 13.50 11.50 Daytona Beach, Fla. 1972 126.56 Core-Concentrated 11.59 10.71 Tri-Cities, Va. 1972 125.24 Core-Concentrated 9.50 7.26 Cedar Rapids, Iowa 1965 124.11 Core-Concentrated 9.85 6.71 York, Pa. 1964 122.07 Core-Concentrated 9.23 8.05 Lexington, Ken. 1961 119.42 Core-Concentrated 9.06 7.57 Manchester, N.H. 1964 112.86 Core-Concentrated 8.90 7.20 TABLE A-1-2. TRIP DURATION (Continued) Year ofPopulation Work TripAverage Trip Urban Area Survey (000) Urban Duration Duration Structure (Min.) (Min.) Johnstown, Pa. 1965 110.35 Core-Concentrated 12.85 11.48 Spartanburg, S.C. 1968 110.59 Core-Concentrated 11.50 10.10 Gastonia, N.C. 1969 109.69 Multinucleated 6.60 6.42 Pueblo, Col. 1963 109.03 Core-Concentrated 12.80 11.27 Waterloo, Iowa 1964 108.84 Core-Concentrated 11.76 9.12 Lancaster, Pa. 1963 108.00 Core-Concentrated 9.25 8.15 Wichita Falls, Fex. 1964 107.70 Core-Concentrated 9.14 6.59 Sioux City, Iowa 1965 105.00 Core-Concentrated 12.66 11.25 Altoona, Pa. 1965 104.42 Core-Concentrated 11.15 10.19 Springf ield, Mo 1961 104.21 Multinucleated 8.40 7.60 Abilene, Tex. 1965 100.86 Core-Concentrated 16.21 4.87 Monroe, La. 1965 96.61 Core-Concentrated 9.16 7.33 Green Bay, Wis. 1960 96.41 Core-Concentrated 12.70 11.20 Albany, Ga. 1966 93.40 Core-Concentrated 10.14 9.56 Lake Charles, La, 1964 87.45 Core-Concentrated 8.84 7.54 Fargo-Moorhead, Min. 1963 80.48 Core-Concentrated 13.79 11.72 McAllen-Pharr, Tex. 1968 79.41 Multinucleated 5.14 5.21 Lafayette, La. 1965 78.94 Core-Concentrated 7.53 6.15 Bouder, Col. 1970 78.03 Core-Concentrated 11.38 9.87 Salem, Oregon 1962 77.13 Core-Concentrated 10.60 9.90 Alexandria, La. 1968 75.63 Core-Concentrated 9.25 8.10 Lawton, Okla. 1965 74.54 Core-Concentrated 9.62 8.92 Williamsport, Pa. 1969 73.79 Core-Concentrated 10.80 9.80 -Tuscaloosa, Ala. 1965 73.15 Core-Concentrated 13.05 11.73 Dubuque, Iowa 1965 70.68 Core-Concentrated 12.60 11.10 Harlington-San Benito, Tex. 1965 67.65 Multinucleated 5.72 4.77 Brownsville, Tex. 1970 65.02 Core-Concentrated 6.79 4.66 Tyler, Tex. 1964 64.51 Core-Concentrated 6.56 5.02 Laredo,Tex. 1964 64.31 Core-Concentrated 4.85 4.14 Texarkana, Tex.-Ark. 1965 64.28 Core-Concentrated 6.02 4.93 San Angelo, Tex 1964 63.44 Core-Concentrated 6.05 4.92 Sherman-Danison, Tex. 1968 62.12 Core-Concentrated 7.16 5.23 St. Cloud, Minn. 1970 60.64 Core-Concentrated 12.06 11.76 Bryan, Tex. 1970 57.00 Core-Concentrated 7.15 5.87 Gadsen, Ala. 1965 55.16 Core-Concentrated 11.12 6.29 TABLE A-1-3. TRIP FREQUENCY Car Average Year Popu- No. of Per No. of of lation Person Trips D.U. Persons Survey (000) Urban Structure per D.U. Per D.U. Chicago, III. 1956 5170 Multinucleated 5.96 0.80 3.10 Detroit, Mich. 1965 4042 Multinucleated 8.56 1.32 3.52 Philadelphia, Pa. 1960 4007 Multinucleated 6.26 0.84 3.08 Boston, Mass. 1963 3584 Multinucleated 7.33 0.98 3.30 Pittsburgh, Pa. 1967 2610 Core-Concentrated 5.67 1.08 3.30 St. Louis, Mo. 1965 2174 Core-Concentrated 6.58 1.20 3.44 Cleveland,Ohio 1963 2141 Multinucleated 7.39 1.28 3.16 Twin Cities, Minn. 1970 1874 Multinucleated 9.87 1.25 3.26 Dallas-Ft. Worth, Tex. 1964 1821 Multinucleated 8.96 1.24 3.09 Milwaukee, Wis.- 1963 1644 Core-Concentrated 7.05 1.12 3.41 Baltimore, Wis. 1963 1608 Core-Concentrated 5.56 0.92 3.34 Washington, D.C. 1955.1568 Core-Concentrated 5.05 0.81 3.01 Atlanta, Ga. 1970 1442 Core-Concentrated 8.88 1.46 3.24 Cincinnati, Ohio 1965 1392 Multinucleated 7.17 1.15 3.30 Seattle, Wash. 1962 1347 Multinucleated 5.32 1.09 Kansas City, MO. 1970 1327 Multinucleated 7.99 1.30 3.34 Niagara Frontier, N.Y. 1973 1234 Multinucleated 7.51 1.20 3.00 Phoenix, Ariz. 1976 1220 Core-Concentrated 7.70 1.70 2.61 Houston, Tex. 1960 1159 Core-Concentrated 7.31 1.12 Denver, Col. 1971 1119 Core-Concentrated 8.60 1.69 3.10 Kansas City, Mo. 1957 858 Multinucleated 6.69 0.95 3.07 San Antonio- Bexar County, Tex. 1969 826 Multinucleated 7.40 1.17 3.24 Louisville, Ken. 1964 751 Multinucleated 6.30 1.08 3.26 Genesee, N.Y. 1974 735 Multinucleated 8.03 1.31 3.14 Columbus, Ohio 1964 720 Multinucleated 7.66 1.06 2.89 Portland, Oregon 1960 709 Core-Concentrated 8.44 1.14 3.06 TABLE A-1-3 TRIP FREQUENCY (Continued) Car Average Year Popu- No. of Per No. of of lation Person Trips D.U. Persons Survey (000) Urban Structure per D.U. Per D.U. Atlanta, Ga. 1961 700 Core-Concentrated 5.41 0.97 3.04 Daytonn Ohio 1968 697 Core-Concentrated 10.38 1.32 3.09 Memphis, Tenn. 1964 657 Core-Concentrated 6.56 1.05 3.52 Norfolk, Va. 1962 602 Multinucleated 7.42 0.92 3.27 Oklahoma City, Okla. 1965 574 Multinucleated 9.51 1.27 3.17 Birmingham, Ala. 1965 559 Core-Concentrated 8.06 1.19 3.32 Akron, Ohio 1963 533 Core-Concentrated 8.57 1.14 3.20 Springfield, Mass. 1964 531 Multinucleated 7.05 1.00 3.13 Toledo, Ohio 1964 515 Multinucleated 9.57 1.07 2.93 Springfield, Ohio 1967 514 Core-Concentrated 10.53 1.33 3.26 Omaha-Council Bluffs, Iowa 1965 506 Multinucleated 11.00 1.26 3.30 Honolulu, Hawaii 1960 500 Core-Concentrated 8.35 .97 3.37 Scranton-Wilkes Barre, Pa. 1964 453 Core-Concentrated 8.05 .96 3.03 Richmond, Va. 1964 418 Multinucleated 7.57 1.07 3.25 Phoenix, Ariz. 1957 397 Core-Concentrated 6.88 1.05 3.01 Salt Lake City, Utah 1960 394 Core-Concentrated 9.00 1.22 3.51 Tulsa, Okla. 1964 364 Core-Concentrated 12.21 1.34 3.11 El Paso, Tex. 1970 363 Core-Concentrated 7.39 1.28 3.43 Nashville, Tenn. 1959 358 Core-Concentrated 7.52 .98 3.28 Lehigh Valley, Pa. 1964 345 Multinucleated 5.77 1.10 3.21 Canton, Ohio 1965 333 Core-Concentrated 10.40 1.21 3.11 Wichita, Kansas 1973 331 Core-Concentrated 12.56 1.66 2.96 Jefferson-Orange, Tex. 1963 315 Multinucleated 9.12 1.08 3.14 Mobile, Ala. 1966 280 Core-Concentrated 9.86 1.21 3.58 Peninsula, Va. 1964 277 Core-Concentrated 7.47 1.05 3.28 Spokane, Wash. 1965 270 Core-Concentrated 8.77 1.21 3.01 Columbus, Ga. 1965 269 Multinucleated 10.89 1.25 4.33 Des Moines, Iowa 1964 258 Core-Concentrated 13.02 1.32 3.17 Davenport, Iowa 1964 251 Multinucleated 10.66 1.16 3.21 TABLE A-1-3. TRIP FREQUENCY (Continued) Car Average Year Popu- No. of Per No. of of lation Person Trips D.U. Persons Survey (000) Urban Structure per D.U. Per D.U. Harrisburg, Pa. 1965 245 Core-Concentrated 7.26 1.05 2.87 Baton Rouge, La. 1965 245 Core-Concentrated 8.34 1.13 3.23 Tucson, Ariz. 1960 243 Core-Concentrated 7.58 1.20 3.20 Knoxville, Tenn. 1962 242 Core-Concentrated 8.08 1.04 3.22 Chattanooga, Tenn. 1969 242 Multinucleated 7.58 1.01 3.33 Shreveport, La. 1965 237 Core-Concentrated 9.55 1.15 3.40 Charleston, S.C. 1965 236 Core-Concentrated 8.28 1.01 3.24 Pensacola, Fla. 1970 230 Core-Concentrated 8.97 1.10 2.93 Little Rock, Ark. 1964 223 Core-Concentrated 9.89 1.10 3.20 Huntington, Ohio 1972 215 Core-Concentrated 9.09 1.10 3.18 Ft. Lauderdale, Fla. 1959 211 Core-Concentrated 3.63 .79 2.15 Austin, Tex. 1962 210 Core-Concentrated 8.05 1.10 2.95 Charlotte, S.C. 1958 202 Core-Concentrated 8.10 1.05 3.43 Corpus Christi, Tex. 1963 196 Multinucleated 7.80 1.04 3.30 Columbia, S.C. 1964 196 Core-Concentrated 8.63 1.12 3.17 Greenville, S.C. 1965 184 Core-Concentrated 9.52 1.40 3.28 Greensboro, N.C. 1970 182 Core-Concentrated 8.29 1.40 3.40 Erie, Pa. 1962 179 Core-Concentrated 6.25 1.00 3.20 Reading, Pa. 1964 178 Core-Concentrated 8.02 1.00 2.79 Colorado Springs, Col. 1964 173 Core-Concentrated 8.90 1.16 2.96 Madison, Wis. 1962 169 Multinucleated 7.08 1.05 3.14 Galveston County, Tex. 1964 168 Core-Concentrated 9.25 1.07 3.11 Montgomery, Ala. 1965 165 Core-Concentrated 10.5 1.16 3.86 Augusta, Ga. 1967 161 Core-Concentrated 8.60 1.10 3.05 Duluth-Superior, Minn. 1970 157 Multinucleated 8.23 1.01 2.91 Amarillo, Tex. 1964 156 Core-Concentrated 10.11 1.27 3.08 Lubbock, Tex. 1964 153 Core-Concentrated 9.08 1.27 3.15 Roanoke, Va. 1965 152 Core-Concentrated 7.78 1.22 3.25 Wheeling, Ohio 1965 148 Core-Concentrated 5.92 .87 2.93 Huntsville, Ala. 1964 139 Core-Concentrated 9.19 1.27 3.49 TABLE A-1-3. TRIP FREQUENCY (Continued) Car Average Year Popu- No. of Per No. of of lation Person Trips D.U. Persons Survey (000) Urban Structure per D.U. Per D.U. Topeka, Kansas 1965 133 Core-Concentrated 8.37 1.33 3.10 Waco, Tex. 1964 132 Core-Concentrated 7.41 1.07 2.83 Eugene, Ore. 1964 127 Core-Concentrated 10.89 1.29 3.16 Daytona, Fla. 1972 127 Core-Concentrated 14.60 1.27 2.49 Tri-Cities, Va. 1972 125 Core-Concentrated 9.31 1.17 3.03 Cedar Rapids, Iowa 1965 124 Core-Concentrated 15.06 1.24 3.03 Springfield, Ohio 1964 122 Core-Concentrated 8.52 1.09 2.93 York, Pa. 1964 122 Core-Concentrated 9.12 1.10 3.07 Lexington, La. 1961 119 Core-Concentrated 6.84 1.09 3.19 Manchester, N.H. 1964 113 Core-Concentrated 11.00 1.00 3.20 Johnstown, Pa. 1965 110 Core-Concentrated 10.50 .97 3.36 Gastonia, N.C. 1969 110 Multinucleated 8.94 1.34 3.38 Pueblo, Co. 1963 109 Core-Concentrated 11.15 1.72 3.58 Waterloo, Iowa 1964 109 Core-Concentrated 11.70 1.23 3.29 Wichita Falls, Tex. 1964 108 Core-Concentrated 10.28 1.16 3.03 Lancaster, Pa. 1963 108 Core-Concentrated 9.71 1.00 3.08 Sioux City, Iowa 1965 105 Core-Concentrated 9.81 1.09 3.20 Cumberland, N.J. 1972 104 Core-Concentrated 14.27 1.39 3.06 Altoona, Pa. 1965 104 Core-Concentrated 12.04 1.10 3.25 Springfield, Mo. 1961 104 Multinucleated 6.88 1.01 2.73 Abilene, Tex. 1965 101 Core-Concentrated 8.66 1.08 2.73 Mansfield, Ohio 1967 985 Core-Concentrated 12.72 1.29 3.16 Monroe, La. 1965 97 Core-Concentrated 9.58 1.05 3.21 Green Bay, Wis. 1960 96 Core-Concentrated 8.58 1.10 3.50 Albany, Ga. 1966 93 Core-Concentrated NA 1.09 3.51 Lake Charles, La. 1964 87 Core-Concentrated 11.06 1.04 2.96 Fargo-Moorhead, Minn. 1963 80 Core-Concentrated 9.89 1.00 2.79 McAllen-Pharr, Tex, 1968 79 Multinucleated 8.34 1.11 3.49 Lafayette, La. 1965 79 Core-Concentrated 8.76 1.66 3.44 TABLE A-1-3. TRIP FREQUENCY (Continued) Car Average Year Popu- No. of Per No. of of lation Person Trips D.U. Persons Survey (000) Urban Structure per D.U. Per D.U. Salem, Ore. 1962 77 Core-Concentrated 11.70 1.17 2.99 Alexandria, La. 1968 76 Core-Concentrated 9.52 1.08 3.06 Lawton, Okla. 1965 75 Core-Concentrated 7.02 1.07 3.08 Williamsport, Pa. 1969 73 Core-Concentrated 8.74 1.20 3.00 Rapid City, S.D. 1963 73 Core-Concentrated 7.41 1.14 3.15 Tuscaloosa, Ala. 1965 73 Core-Concentrated 11.79 1.04 3.22 High Point) N.C.1961 72 Core-Concentrated 7.30 1.34 3.65 Dubuque, Iowa 1965 71 Core-Concentrated 9.78 .94 3.14 Harlington-San Benito, Tex. 1965 68 Multinucleated 6.69 .87 3.29 LaCrosse Wis. 1966 66 Core-Concentrated 10.78 1.10 2.99 Brownsville, Tex. 1970 65 Core-Concentrated 7.50 1.10 3.63 Tyler, Tex. 1964 64 Core-Concentrated 9.83 1.19 2.95 Laredo, Tex. 1964 64 Core-Concentrated 8.30 .77 3.63 Texarkana, Tex.-Ark, 1965 64 Core-Concentrated 8.06 1.01 2.86 San Angelo, Tex'. 1964 63 Core-Concentrated 7.87 1.10 2.82 Sherman-Denison, Tex. 1968 62 Core-Concentrated 9.07 1.36 2.74 St* Cloud, Minn. 1970 61 Core-Concentrated 14.54 1.56 3.17 Owensboro, Ken. 1972 57 Core-Concentrated 13.13 1.20 2.90 Rochester, Minn. 1964 57 Core-Concentrated 11.40 1.15 3.17 Bryan-College Station, Tex, 1970 57 Core-Concentrated 8.09 1.44 2.76 Reno, Nev. 1958 55 Core-Concentrated 6.87 1.14 2.77 TABLE A-1-4. MODAL SPLIT DATA Total Total Auto Transit Highway City Pop. Structure Transit OwnershipMiles Miles (1) (2) (3) (4) (5) (6) (7) 1. Minneapolis-St. Paul, Minn. 1,874,308 multi. 3.2 1.25 550 3,135 2. Duluth-Sup., Minn. 460,242 Multi. 4.05 1.05 N.A. 421 3. Rochester, Minn. 57,485 Core 1.35 1.15 N.A. N.A. 4. Fargo, Minn. 80,476 Core 1.10 1.00 N.A. N.A. 5. St. Louis, Mo. 2,174,446 Core 4.2 1.20 1,334 1,364 6. Kansas City, Mo. 1,327,266 Multi. 1.97 1.30 1,054 1,072 7. Springfield, Mo. 104,209 Multi. 2.5 1.01 42 162 8. Columbia, Mo. 48,559 Core 0.47 73 28 104 9. Akron, Ohio 532,371 Core 2.4 1.14 190 575 10, Richmond, Va. 417,680 Multi 10.11 1.07 239 N.A. 11. Norfolk, Va. 602,000 multi 5.95 92 320 N.A. 12. Newport, Va. 277,150 Core 4.88 1.05 307 173 13. Petersburg, Va. 125,244 Core 1.79 1.17 N.A. 441 14. Roanoke, Va. 151,864 Core 4.38 1.22 N.A. 15. Atlanta, Ga. 1,441,881 Core 3.70 2,176 16. Denver, Co. 1,119,005 Core 1.46 1,088 1,094 1.83 1.69 N.A. N.A. 17. Boulder, Co. 78,031 Core 0.54 N.A. N.A. N.A. 18. Pueblo, Co. 109,031 Core 0.96 1.72 N.A. N.A. 19. Youngstown, Ohio 513,998 Core 0.96 1.33 314 207 20. Eugene, Ore. 12,755 Core 0.50 1.29 120 1,088 21. Portland, Ore. 709,350 Core 7.00* 1.14 410 185 22. Salem, Ore. 77,131 Core 3.00 1.17 80 367 23. Spokane, Wash. 270,000 Core 4.00 1.21 N.A. 76 TABLE A-1-4. MODAL SPLIT DATA (Continued) Total Total Auto Transit Highway City Pop. Structure Transit OwnershipMiles Miles (1) (2) (3) (4) (5) (6) (7) 24. Alexandria, La. 75,629 Core 1.63 1.08 N.A. 77 25. Baton Rouge, La. 245,076 Core 1.88 1.13 46 170 26. Lafayette, La. 78,940 Core 0.92 1.66 75 66 27. Lake Charles, La. 87,454 Core 1.05 1.04 136 77 28. Monroe, La. 96,608 Core 1.83 1.05 211 93 29. Shreveport, La. 237,202 Core 2.64 1.15 283 167 30. Greenville, S.C. 184,370 Core 2.06 1.4 117 238 31. Charleston, S.C. 235,537 multi. 3.00 1.01 375 340 32. Columbia, S.C. 195973 Core 3.01 1.12 19 212 33. Spartanburg, S.C. 110,592 Core 2.07 1.28 28 178 34. Birmingham, Ala. 559,074 Core 3.2 1.19 N.A. 770 35. Gadsen, Ala. 55,158 Core 2.3 1.27 82 163 36. Huntsville, Ala. 133,971 Core 0.9 1.27 162 37. Mobile, Ala. 279,683 Core 2.1 7.21 257 400 38. Montgomery, Ala. 165,000 Core 2.4 1.16 82 211 39. Tuscaloosa, Ala. 73,155 Core N/A 1.04 40. Oklahoma City, Okla; 563,900 multi. 0.55 1.27 N.A. N.A. 41. Tulsa, Okla. 363,876 Core 0.95 1.34 N.A. 288 42. Manchester, N.H. 112,861 Core 2.23 .988 633 N.A. 43. Dayton, Ohio 697,014 Core 3.6 1.32 600 44. Greensboro, N.C. 182,508 2.0 1.40 336 45. Phoenix, Ariz. 1,220,000 Core 0.6 1.70 1,003 177 46. Washington, D.C.. 2,750,000 Core 7.0 1.20 150 3,643 47. Honolulu, Hawaii 500,409 Core 10.7* 0.97 N.A. 9,796 48. Canton, Ohio 332,000 Core 1.5 1.21 N.A. 2,434 49. Columbus, Ohio 720,592 multi. 5.00 1.06 N.A. N.A. B. Description of the Elasticity Data Base Twenty-three cities are included in the sample of demand elasticities as shown in Table A-1-5. According to our city classification scheme, which defines cities with population greater than 800,000 as large and cities with population between 50,000 and 800,000 as medium" eight cities fall into the large/multinucleated class, seven cities in the large/ core-concentrated class, one in the medium/multinucleated class and seven in the medium/core-concentrated class. This distribution seems to have reasonable coverage among the four classification cells. The representativeness of the sample of demand elasticities can Also be observed from other points of view. In Figure A-1-6, the number of cities and the aggregate population in the elasticity sample are compared with that for the whole country. According to the size of population, cities contained in the table are classified into three groups. It is to be noted that this classification is used to verify the validity of the sample and has no relation to the urban classification scheme. Comparisons between all U.S. SMSAs and the sample are shown in Figure A-1-7. These tables indicate that the sample provides a reasonable coverage in both number of cities and total population in each class of cities. Another way to check the representativeness of the sample is geographic dispersion. Figure A-1-8 shows that the geographic distribution of the sample is widespread across the county. Its pattern is closely related to the population distribution in the United States. Overall, the sample of demand elasticities is representative of the number of cities, total population, and geographic space. C. Case Study Report Collection Over 75 reports and other references were collected for possible use in the site demonstration of the research findings. As may be seen in Figure A-1-9, the number of potential case study cities was reduced to 13. The elimination of numerous other urban areas was based on several criteria, the most significant of which were data availability and- transport options in existance or planned. Although case studies were performed in only three of these 13 cities, it is advantageous to list all references for each of the potential sites. These documents deal primarily with base year travel characteristics and socioeconomic data, a description of the traditional sequential forecasting 220 procedure employed and the forecast resulting from those procedures. In addition, in some cases reports concerning a specific major improvement (e.g., BART, Shirley Busway, etc.), are included in the collection. All of the reports listed below are, of course, included in the Bibliography where more complete reference information is available. Pittsburgh, PA (Large/Core-Concentrated PATS (1961) PATS (1963) SPRPC (1965) SPRPC (1972): Three Volumes SPRPC (1973) San Francisco-Oakland Bay Area (Large/Multinucleated) Simpson & Curtin (1967) Parsons, Brinckerhoff, Hall and McDonald (1955) BART Office of Research (1971) BART Office of Research (1972) BATSC (1969) and Supplements I and II Goldner (1968) Hamer (1976) SFMTC (1975) Sherret (1977) Sherret (1975) Grefe. and Smart (1975) Bay and Markowitz (1975) Peat, Marwick, Mitchell & Co. (1974) Peat, Marwick, Mitchell & Co. (1975) Two Volumes Peat, Marwick, Mitchell & Co. (1976) SFMTC (1976) Reid (1974) Cohn and Ellis (1975) Reading, PA (Medi /Core-Concentrated) PennDOT (1971) PennDOT (1972) PennDOT (1975) 221 Washington, D.C. (Large/Core-Concentrated Howard, Needles, Tammen and Bergendoff (1970) UMTA (1975) W. C. Gilman & Co. and Alan M. Voorhees & Associates (1969) Atlanta, GA (Large/Core-Concentrated) State Highway Department of Georgia (1962) State Highway Department of Georgia (1963) State Highway Department of Georgia (1965) State Highway Department of Georgia (1967) Houston, TX (Core-Concentrated) Texas Highway Department (1960) Texas Highway Department (1971) Nashville, TN (Medium/Core-Concentrated) Nashville Metropolitan Area Transportation Study (1959) Wilbur Smith and Associates (1961) Two Volumes Kansas City, MO-KS (Large/Multinucleated) Wilbur Smith and Associates (1959): Two Volumes St. Louis. MO (Large/Core-Concentrated) Wilbur Smith and Associates (1959): Two Volumes Wichita, KS (Medium/Core-Concentrated) Wichita-Sedgwick County Metropolitan Transportation Study Commission (1964): Three Volumes Reports and other pertinent information were requested but not received from the following urban areas: Denver, CO (Large/Core-Concentrated) Minneapolis-St. Paul, M (Large/Multinucleated) El Paso, TX (Medium/Multinucleated) 222 TABLE A-1-5. LIST OF CITIES OF CIRCUMSTANTIAL SET 2 (DEMAND ELASTICITIES) 1970 Population (000s) Urban Classification Geographic Area (Size/Structure) Central City SMSA Atlanta, Ga. L/C 497 1,390 Baltimore, Md. L/C 906 2,071 Boston, Mass. L/M 641 2,753 Chesapeake, Va. M/C 90 N.A. Chicago, III. L/M 3,367 6,975 Cincinnati, Ohio-Ky.-Ind. L/C 453 1,385 Detroit, Mich. L/M 1,511 4,200 Los Angeles-Long Beach, Calif. L/M 2,816* 7,036 Milwaukee, Wis. L/C 717 1,404 Minneapolis-St. Paul, Minn. L/M 744 1,814 New Bedford,-Mass. M/C 101 153 New York, NY L/C 7,895 11,572 Philadelphia, Pa.-N.J. L/M 1,949 4,810 Portland, Maine M/C 65 142 Richmo nd, Va. M/M 250 518 St. Louis, MID.-III. L/C 622 2,363 Salt Lake City, Utah M/C 176 558 San Diego, Calif. L/M 696 1,358 San Francisco-Oakland, Calif. L/M 716* 3,110 Springfield-Chicopee-Holyoke, Mass. M/C 164* 530 Tulsa, Okla. M/C 332 477 Washington, D.C. L/C 756 2,861 York, Pa. M/C 50 330 ___________________________ Population for main central city only. N.A. = Not Applicable Size: L Large city with SMSAs population of more than 800,000 M Medium city with SMSAs population 50,000-800,000. Structure: C = Core-Concentrated M = Multinucleated 223 Click HERE for graphic. 224 FIGURE A-1-9. POTENTIAL CASE STUDY CITIES Click HERE for graphic. FIGURE A-1-6. ELASTICITY DATA BASE COMPARED WITH U.S. TOTALS Population Group Number/ Number and* Cities Sample Population Population Included in as a in United States Elasticity % of U.S. Sample Urban Areas Number 4 15 36.6 Over 800,000 Population 87,713,997 55,110,000 62.8 Urban Areas Number 84 5 5.9 Between 250,000-800,000 Population 34,689,514 413,000 7.0 Urban Areas Number 118 3 2.5 Between 50,00-250,000 Populationa 17,067,112 385,000 2.3 Total of All Number 243 23 Urban Areas 9.5 Over 50,000 Population 130,470,623 57,908,000 44.4 * U.S. Census, 1970 Statistics 226 Click HERE for graphic. FIGURE A-1-7. HISTOGRAMS OF NUMBER OF CITIES AND POPULATION: ALL U.S. SMSAS SURVEY RESPONSE) VERSUS ELASTICITY DATA BASE (SHADED AREA) 227 APPENDIX 2: LINEAR GOAL PROGRAMMING The linear goal programming (LGP) calibration technique for the trip frequency and trip duration models was developed by Perl (forthcoming). LGP can be defined as "a systematic methodology for solving linear, multiple objective problems in which preemptive priorities and weights are associated with the objectives." (Ignizio 1976) Goal programming is used to establish a solution that comes as close as possible to the satisfaction of a set of stated goals, instead of optimizing a single objective as in linear programming. Every objective is provided on the left-hand-side with negative and positive deviations variables (n i and p i respectively). Each objective takes the form of: _ f (X) + n - p = b i - 1, 2. . . . k i i i i _ The LGP model minimizes an achievement function (a) which is an ordered vector of a dimension equal to the number of preemptive priorities within the problem. The specific LGP formulation for the calibration of our models is as follows: _ Find (X) = (X , X ) 0 1 So as to minimize: _ a = [n + p , n + p , . . . , n + p ] 1 1 2 2 k k such that: X h = X h + n - p = b 1 10 1 11 1 1 1 X h = X h + n - p = b 0 i0 1 i1 i i i X h = X h + n - p = b 0 k0 1 k1 k k k The vector of decision variables (X) consists of the model's coefficients. X = the intercept value of the bivariate equation 0 X = the independent variable coefficient in the equation 1 b = the observed value of the dependent variable in the ith i observation k = the number of observations on which the model is calibrated. 228 The observations of the independent variable are summarized by the matrix H. __ __ __ __ h h 1 h 10 11 11 H = h h 1 h kx2 i0 i1 i1 h h 1 h k0 k1 k1 __ __ __ __ where h is the value of the independent variable in the ith observation. i1 The reader who is familiar with linear programming may recall that the decision variables cannot take negative values, i.e., X.i > 0. In the calibration context, we cannot limit the values of the intercept and the model's coefficients to non-negative values. The above formulation should be transformed to account for all possible values of the intercept and the coefficients. This is achieved by replacing the variable X.i, which may take on any real values, with the difference between two non-negative variables. - < X < 0 - < X < 1 X = U - V 0 0 0 X = U - V 1 1 1 The final form of the model is: _ _ Find ( U, V) = (U , V , U , V ) 0 0 1 1 so as to minimize _ a = ( n + p , , n + p , , n + p ) 1 1 i i k k such that U - V + U h - Vh = n - p = b 0 0 1 11 11 1 1 1 U - V + U h - Vh = n - p = b 0 0 1 i1 i1 i i i U - V + U h - V = n - p = b 0 0 i k1 k1 k k k _ _ _ _ U, V, n, p, 0 229 The formulation discussed above enables us to obtain the linear curve which minimizes the deviation of the observed dependent variables from the values obtained from the model. This model minimizes the value of k r i=1 i instead of minimizing k 2 r i=1 i as is done by regression analysis, where r.i is the deviation of the dependent variable value obtained by the model (y^.i), from its observed value y.i. 230 APPENDIX 3: AREAWIDE SUPPLY AGGREGATION PROCEDURE A simple explanation of the recommended procedure for aggregating the supply functions of the various elements of the urban highway network has been presented in Chapter IV. A more rigorous mathematical derivation of the process is included here. It should be noted that this derivation is presented in terms of the unmodified CUTS (U.S. Department of Transportation 1974) classification scheme (rather than the modified one used in the text); however, the theoretical implications are equally applicable. Assume the number of locations in the urban area is i, the number of facility types is J, and the level of service at time t of the day is Z, the attributes of a detailed corridor is denoted as K.Z,t.ij The aggregation of detailed corridor attributes into composite forms can be shown as: Z,t Z,t {K } = {K ) by location, (A-3-1) ij i Z,t Z,t {K } = {K ) by facility, and {A-3-2) ij i Z,t Z,t Z,t Z,t {K } = {K ) = {K } = K overall. (A-3-3) ij ij i j j where in our context: i = CBD, Central Business District, FG, fringe, R, residential, or OBD, outlying business district; j = FW, freeway, EW, expressway, 2W-P, arterial, two-way with parking, 2W, arterial, two-way without parking, and 1W, arterial, one-way. Z = value of v/c, ranging from 0 to 1.0; and t = time of the day. Our objective is to aggregate corridor capacities (T-capacity and D- capacity) into an aggregate capacity (A-capacity) for an urban area. To perform the aggregation, a vector of lane-miles, consisting of the lane- miles for each corridor type i-j, ML.ij, is required. All the required data for aggregating supply curves over an urban area are shown in Table A-3-1. To 231 aggregate the freeway corridors, for example, one needs the data on the c apacities and mileages of the freeways at the central business district Z,t {K ; ML } CBD, FW CBD, FW at the fringe Z,t {K ; ML } FG, FW FG, FW and so on. A similar set of data is required if one wishes to aggregate all the roadway facilities at a geographic area within the city. Among the attributes represented in K.Z,t.ij are capacity and speed. The T-capacities and the corresponding speeds, for example, can be obtained from Figures 4-4, 4-5, and 4-6 in the text. The computational process involves the transformation of corridor point capacities (T- and/or D-capacity) to an areawide aggregate capacity (A-capacity), which can be expressed as follows: Z,t Z,t Z,t Z,t {K } {ML } -> {V } {ML } / {S } or {V } {ML }(A-3-4) ij ij ij ij ij ij ij __________________________ ___________________ vehicle-hours-of- vehicle-miles- travel of-travel where: K.Z,t.ij = measure of the hourly service volume V.Z,t.ij , under the travel speed S.Z,t.ij at time t of the day ML = lane-miles of corridor ij. ij Based on the aforementioned procedures one can compute A-capacity in terms of VMT or VHT and obtain the average system speed at different LOS combinations among corridors. If the average trip length for the urban area L is known, the service-volume and the average trip duration, , also can be obtained. This can be verified by the following equations. The aggregation can be performed via two approaches. It can either be aggregated according to type of facility first and location second or the other way around. The procedures to aggregate over the facilities are: Z,t V ML Daily VMT ti ij ij Z ---------- = -------------------------- = S (A-3-5) Daily VHT Z,t Z,t i V ML / S ti ij ij ij Daily VMT Z ----------- = V (A-3-6) L j L -Z ------- = t . (A-3-7) Z j S j 232 TABLE A-3-1. DATA REQUIREMENT FOR CORRIDOR AGGREGATION Click HERE for graphic. 233 Those for aggregation according to location, on the other hand, are: Z,t V ML Daily VMT tj ij ij Z ---------- = -------------------------- = S (A-3-8) Daily VHT Z,t Z,t i V ML / S tj ij ij ij Daily VMT Z ----------- = V (A-3-9) L i L -Z ------- = t . (A-3-10) Z i S i The aggregation over an urban area can then be performed: Z,t V ML Daily VMT tij ij ij Z Z Z ---------- = --------------------------- = S = S = S(A-3-11) Daily VHT Z,t Z,t j j i i V ML / S tij ij ij ij Daily VMT Z ----------- = V (A-3-12) L L -Z ------- = t . (A-3-13) Z S where V.Z is the daily service-volume and is the daily average trip duration when the A-capacity of the system is Z,t V ML in VMT and tij ij ij Z,t Z,t V ML / S in VHT. tij ij ij ij It should be noticed that the computed A-capacity should refer to the highway level-of-service "E" and is expressed in vehicles per day. It is also to be noted that in order to plot the daily supply function, proper adjustments from hourly account to daily account should be made if the input data is available only for a point of time of the day. For example, if the available information is collected during the peak hour, then the peak hour ratio (say 10 percent) could be used to adjust those peak hour data into daily account (ITE 1976). 234 If one applies the above computation steps for different levels-of- service (besides E), one may obtain a series of A-capacities and trip durations for the aggregate supply curve. Since the LOS of each corridor tends to vary according to flow conditions, the aggregate supply function is not unique for a given transportation network. However, those curves should share a common point when the system is completely empty or fully loaded, i.e., v/c ratio equals zero or unity. Thus, if we assign Z as v/c = 0 for all corridors of Table A-3-1, we can obtain t.-0 with V.0 = 0. On the other hand, if we assign Z as v/c = 1.0 for all corridors as contained in the same table, we may obtain i.-1.0 with V.1.0 equal to the maximum practical capacity of the system. In this way, the two extreme points of the curve are defined. 235 APPENDIX 4: BAYESIAN UPDATING The Bayesian statistician views the unknown parameter as a random variable generated by a distribution which summarizes his information about . He also thinks that this information should be brought into the estimate problem. An assumption is required concerning the distribution of the parameter when Bayesian theory is applied to linear statistical models such as linear regression (Raiffa and Schlaifer 1961) or to a non-linear model such as the logit model (Atherton and Ben-Akiva 1976). An appropriate assumption is that the model coefficients are distributed as a multivariate normal. In the Bayesian approach to statistics, the application of Bayes' theorem is an inferential procedure, and the resulting posterior distri- bution is an inferential statement about the uncertain quantity of interest. Bayes' theorem can be stated as follows: ~ ~ ~ P( = / = )P( = ) ~ ~ s i i P( = / = ) = ------------------------------------ (A-4-1) i s J ~ ~ ~ P( = / = )P( = ) j=1 s j j where: .s = The sample statistics which represent the new sample information ~ ~ P( = .s/ = .i) = the likelihood determined from the conditional distribution of .s given different values .1 . . . .j of . ~ ~ ~ P( = .i/ = .s) = the revised probability that = .i given the new sample information. Equation (A-4-1) makes it possible to revise probabilities concerning an uncertain-parameter ~ on the basis of sample information using prior information represented by the prior distribution of ~. The revised probability distribution is called "posterior distribution." 236 In the continuous case, Bayes' Theorem can be written as: f()f( /) s f(/ ) = ------------------------- (A-4-2) s f()f( /)d - s Having obtained the posterior distribution f(e/6 s ), one must find a single value (point estimation) ^ to estimate an unknown parameter . One important method for determining estimators is the method of maximum likelihood. This method finds the value of ~ that maximizes the likelihood function. For the sake of clarity, we will first present the Bayesian updating procedure for the univariate normal case. The discussion will be then generalized to the multivariate normal case. A. Univariate Normal Case The density of a normal distribution is given by: 1 - (X-) /2 f(X) = ---------- exp (A-4-3) 2 ~ ~ ~ If n random variables X.1 ,X.2 . . . X.n represent a random sample of size n from a normally distributed population with mean m and variance then the sample mean m~ is normally distributed with the following conditional mean and variance: ~ E (m/n, ) = , ~ V (m/n, = /n. If the prior distribution of the uncertain quantity ~ is a normal distribution, the posterior distribution will also be normal. The prior distribution of the mean ~ can be written as: 1 f'() = ------------- exp -(-m')/ 2' (A-4-4) 2 ' The posterior distribution of the mean given a sample information is given as: 1 f''() = ------------- exp -(-m'')/ 2'' (A-4-5) 2 '' 237 where: m' = the prior distribution mean, m = Sample information mean, m'' = the posterior distribution mean, /n = the variance of the sample information mean, n = the sample information size, ' = the variance of the prior mean, and '' = the variance of the posterior mean. The posterior variance and the posterior mean are obtained from: 1/'' = 1/' + n/ (A-4-6) (1/)m' + (m/)m m'' = ----------------------------- (A-4-7) 1/' + n/ where: = the variance of the data generating process or of the population in question. The prior distribution can be given in terms of the sample of size n' from the given population in the following form: ' N(m',/n'), (A-4-8) where: ' = /n'. The posterior mean and variance can be written as n'm' + nm m'' = --------------------- , and (A-4-9) n' + n '' = /n''. (A-4-10) where n'' = n' + n. 238 As ', the variance of the prior distribution decreases (i.e., more information is included in the prior distribution), the prior information is given more weight and vice versa. The same is true of the sample information. When the sample size increases, more information is included in the sample information, /n decreases and the sample mean is given more weight in obtaining the posterior mean. B. The Multivariate Normal Case To extend this to the multivariate normal case, consider the case of a linear model given as follows: Y = b + b X + b X . . . b X + (A-4-11) i 0 1 i1 2 i2 p-1 i,p-1 i E ( ) = 0 i where the unknown parameter that we wish to update (referred to as above) is the vector of coefficients b._ = (b.0 , b.1 . . . b.p-1). When this statistical model is expressed in matrix terms, we have: y 1 1 x x x 11 12 1,p-1 _ _ y = x = nx1 nxp y 1 x x x n n1 n2 n,p-1 b _ 0 1 b = b _ px1 1 = nx1 b p-1 n The updating procedure will be illustrated below for the special case of a regression model. It should be noted, however, that the same procedure can be applied for any model whose coefficients can be assumed to distribute as a multivariate normal. In matrix terms, the general linear regression model is _ _ _ _ _ Y = X b + . Consequently the random variable Y. has the following mean and variance: 239 _ _ _ _ E (Y) = X b, (A-4-12) _ (Y) = I. (A-4-13) where I is an identity matrix measuring n by p in dimension. Suppose that from A previous estimation, this model was obtained: _ _ _ Y = M b (A-4-14) 1 1 1 _ Using a sample we wish to update b.1, This consists of obtaining the maximum likelihood estimation (or the mean) of the posterior distribution which is the updated vector b._. Let _ _t _ _t_ N = X X N = X X 1 1 1 2 2 2 where: _ X = the matrix of the independent observation for the sample; and 2 _t _ X = transpose of X 2 2 _ _ From the definition of b.1 and b.2 in multiple regression, and through the substitution for N._.1and N._.2 above, _ _t_ -1_t -1_t_ b (X X ) X Y = N X Y (A-4-15) 1 1 1 1 1 1 1 1 _ _t_ -1_t _-1_t_ b (X X ) X Y = N X Y (A-4-16) 2 2 2 2 2 2 2 2 where: _ b.2 = the vector of coefficient obtained when the model is estimated on the sample only and _ Y.2 = the vector of dependent variables obtained from the sample. We further define: _ _ _ N = N + N . 1 2 The posterior mean (maximum likelihood estimator) of the parameter's distribution can then be written as: _ _ _-1 _ _ _ _ b = N (N b + N b ) (A-4-17) 1 1 2 2 _ _ Recalling that b is the posterior mean of the parameter's distribution, i.e., _ _ _ b = E(/Y), (A-4-18) we can verify that _ _ _ _ N = V(/Y) 1/. (A-4-19) 240 where: _ _ _ V(/Y) = the variance covariance matrix parameters. In conclusion, since both trip frequency and average travel time processes are stated as linear regression models, the updating procedure of these models can be adequately covered by the above discussion. The reader is reminded once again that the results indicated in (A-4-17) through (A-4-19) are general results for any linear statistical model _ _ _ _ Y = X b as long as the coefficient b is normally distributed. 1 1 1 1 C. Updating Demand Elasticities The updating of the elasticities, on the other hand, requires certain manipulations. The elasticities are usually derived from modal split models. If one defines V.m = number of patronage in mode m, and X = vector of the level-of-service such as travel costs and travel time, or socioeconomic variables such as income, the demand elasticity of mode m with respect to the variable X is Click HERE for graphic. 241 where; X.j = vector of the level-of-service, such as cost or time of node j where j = 1 . . . m, X.i = vector of socioeconomic variables for individuals for a given origin and destination, such as family income, auto ownership per residence, etc. where i = 1 . . . n, b.j, b.i = estimated vector of coefficients for the level-of-service and the socioeconomic variables respectively, and a = constant of restrained regression. The direct demand model can be transformed to the formulation: m m 1n Y = a' + b 1n X + b 1n X j=1 j j i=m+1 i i where a' = 1n a and 1n Y, 1n Xy, and 1n Xi are numerical functions of the observations; _ _ _ b.1 = b.1 . . . b.j . . . b.n and b.2 = b.n+1 . . . b.1 . . . b.n are the vectors of parameters given in the original model. The model is now expressed in a linear form and can be updated using the procedure described in Section B. Elasticities can be also derived from a multinomial logit model. Therefore, the updating of elasticities in this case consists of updating the logit model itself. The multinomial logit formulation itself is described in many references including Domencich and McFadden (1975), and is expressed as follows: p (i, A ) = exp ('X ) t it -------------------- exp ('X ) jA it t where: p(i,A.t) = the probability of behavioral unit t selecting alternative i from its choice set A.t. X.it = a vector of independent variables for alternative i and behavioral unit t, and ' = the vector of unknown parameters. 242 The Bayesian updating procedure of the multinomial logit model has been fully presented by Atherton and Ben-Akiva (1976). The vector of unknown parameters ') estimated using the maximum likelihood method has to be updated. The maximum likelihood method results in coefficient estimates that are asymptotically normally distributed. The vector of estimated parameters (') is a px1 vector of means as shown below: 1 . . ' = . . . p The variance of the distribution of ' is given by G.1 the pxp variance- covariance matrix. . . . 12 1p G = 2 p1 pp Before we can apply the Bayesian updating procedure, the following variables have to be defined. '.1 = the vector of mean values given by the prior distribution of ' '.s = the vector of mean values resulting from the sample G.1 = the variance-covariance matrix of the prior distribution G.s = the variance-covariance matrix resulting from the sample. We can now apply Bayes' theorem to obtain the vector of means of the posterior distribution--the updated vector of estimated parameters: -1 -1 ' = G (G ' + G ' ) 2 2 1 1 s s -1 -1 -1 G = (G + G ) 2 1 s 243 where: '.2 = vector of the mean values of estimated parameters given by the posterior distribution, and G.2 = the variance-covariance matrix of the posterior distribution. In order to update the prior knowledge of the coefficients with a sample information, the parameters of the sample distribution '.2 and G.2 are simply obtained from estimating the model specification on a small sample. For the prior distribution, '.1 would be given by values of the original coefficients, and G.1 would be given by the variance- covariance matrix of the original model. 244 APPENDIX 5: A CASE STUDY OF SPATIAL TRANSFERABILITY: PITTSBURGH A. Pittsburgh as a Core-Concentrated City Pittsburgh can be considered a milestone in the development of the transportation planning profession. The area covered by the 1958 study consisted of 1,120 square miles and contained about 1.5 million residents who owned and operated 393,000 autos and 112,000 trucks and taxis. In 1958 travelers in Pittsburgh were served by 19.7 miles of expressways,, 1,970 miles of arterial routes and some 2,467 miles of local streets and roads. As a result of the Pittsburgh Area Transportation Study (PATS 1960), recommended transportation improvement plan was developed which included total of 210 miles of limited access facilities, and in addition a 17 mile rapid rail transit system was proposed. Much of the base year data pertinent to the use of DAP was obtained from PATS for 1958. These variables are presented in Table A-5-1. The low average system speed in 1958 resulted from the lack of freeway-type facilities in the transportation system. This in turn results in an overall average trip duration of 23.1 minutes. Another exceptional variable was the average auto ownership rate of 0.811 autos per household, which was one of the lowest rates in the nation in 1958. Finally, Pittsburgh is identified as a large/coreconcentrated city, where a large portion of the activity is concentrated in the central business district referred to in PATS as the "Golden Triangle." B. Relationship Between Policy Options and Explanatory Variables A detailed description of the traditional methodology as used in the Pittsburgh Area Transportation Study (PATS) is out of the scope of this report. However, the elements of the 1980 forecast which are pertinent to the use of DAP are summarized in Table A-5-2. Looking at the percentage change column, one can observe the following changes in the socioeconomic and travel characteristics in Pittsburgh between 1958 and 1980--there will be 29.4 percent more people in the area and 58.4 percent more total daily person trips. Obviously, this means an increase in the trip rates per person or per dwelling unit. The above change is also reflected by the large increase in total vehicle-trips and total VMT. Extensive improvements were recommended in the freeway system, mainly on the 210 miles of limited access facilities. Such changes are projected to cause an increase in average system speed, and a decrease in 245 TABLE A-5-1. INVENTORY OF BASE YEAR VARIABLES Item 1958 Value Population 1,109,375 Dwelling Units 470,000 Autos Owned 395,321 autos Auto Ownership/D.U. 0.811 autos/D.U. Average Travel Length 5.2 miles Average System Speed 13.51 mph Average Trip Duration 23.1 minutes Internal Person Trips 2,399,820 Internal Person Trips by Auto 1,926,070 Internal Person Trips by Transit 173,750 Trips Per Dwelling Unit 5.1 Auto Occupancy Rate 1.50 Vehicle Trips 1,515,000 Person Miles of Travel 12,197,800 Person Miles of Travel by Auto 10,532,200 Person Miles of Travel by Transit 1,965,000 Vehicle Miles of Travel 8,897,280 Source: PATS (1961). 246 TABLE A-5-2. RESULTS OF TRADITIONAL FORECAST Item 1958 1980 % Change Population 1,169,375 1,902,185 29.4 Dwelling Units 470,000 570,000 21.3 Autos Per Dwelling Unit 0.84 1.15 25.5 Total Person Trips 2,399,820 3,801,272 58.4 Total Person Trips by Auto 1,926,070 3,302,884 71.5 Total Person Trips by Transit173,750 498,388 5.2 Total Vehicle Trips 1,575,000 2,645,000 74.6 Vehicle Miles of Travel 9,897,780 15,519,840 74.4 Passenger Miles of Travel 1,965,000 2,137,800 8.8 Average Trip Duration 23.1 16.4 -29.0 Average Trip Length 5.2 5.3 1.9 ___________________________ Source: PATS (1961). 247 average trip duration. Without those implementations, an increase in trip duration would have been predicted as a result of congestion effects. Another interesting value is the slight rise in transit trips. This is understandable in view of the very minor implementation recommended in the transit system compared to that recommended for the highway system. Finally, the increase of 25.5 percent in auto ownership can be considered as a result of changes in demographic and income characteristics (but one can actually suspect that such a change is also associated with the improvements in the highway system). The calibrated trip-frequency and trip-duration models for Pittsburgh are: _ _ (a) Y = 2.242 + 3.761 X, and _ (b) t = -10.54 + 3.616 1n P respectively. Substituting the values corresponding to the base year in Pittsburgh into our models one obtains: _ Y = 2.242 + 3.761 x 0.84 = 5.04 trips/D.U. _ t = -10.54 + 3.616 1n 1169 = 15.1 minutes. C. Transferability The actual value of trips per dwelling unit for the base year in Pittsburgh is 5.4, and it is assumed that the trip frequency process is explained adequately by the original model and no updating of the trip frequency model is required. The actual value of trip duration for the base year is 23.1 minutes, and the estimated value by-the model can be seen to be considerably lower than actual. Updating of the trip duration model therefore should be considered. The main reasons for updating are the exceptional conditions in Pittsburgh's transportation system in 1958. The lack of freeway type facilities, for example, resulted in exceptionally low average travel speed and high trip duration. The updating of the constant term is performed as follows: _ t = 23.1 = a + 3.616 1n 1169, u where a is the updated constant term for the city of Pittsburgh: u a = 23.1 - 3.616 1n 1169 = -2.44. u The updated model for the city of Pittsburgh is: _ t = -2.44 + 3.616 1n P. 248 Correspondingly, the total number of person trips in the base year is: V = 5.40 x 470,000 = 2,538,000 person trips. In order to incorporate both time and cost considerations in tripmaking, the total impedance per trip in 1958 is calculated as shown in Table A- 5-3. To obtain a single impedance value representing both travel by auto and transit, the impedances for the different modes are weighted by their relative modal splits. In Pittsburgh, for example, base year modal split is as follows: 1958 Value Percent Auto Trips 1,926,070 83.7 Transit Trips 473,750 16.3 Total Trips 2,399,820 100 Weighting the transit and auto impedance values by the relative modal split one obtains: Percent x Percent Impedance Impedance Auto 83.7 $1.300 1.088 Transit 16.3 $1.328 0.216 Weighted Impedance 1.304 D. Composite Elasticity The next step is to obtain the composite elasticity for Pittsburgh according to the procedure outlined in Appendix 10. In order to approximate the composite elasticity, the modal elasticities are combined through the weighting procedure in Table A-5-4, giving rise to a value of -0.473. Theoretically the cross elasticities for the city of Pittsburgh should have been included for modal-split purposes, but they were not available to the research team. This case study will use the demand approximation procedure to determine the future year modal split. Substituting n = 0.473, V = 2,399,820 and I = 1.304 in the slope equation in Chapter V, Section A, one obtains the slope of the demand curve for the base year: 0.473 x 2,399,820 S = ----------------------- = 180,407 trips/dollar of change in 1.304 impedance. 249 TABLE A-5-3. TOTAL IMPEDANCE IN TERMS OF TRAVEL COSTS (1958) Fixed Costs (Per Trip) Auto Transit Operating Cost $0.328 $0.250 ($0.063/mile) Parking 0.100 Tolls ----- Total $0.428 $ .250 Cost per person $0.305 $ .250 (1.4 person/car) Cost of Travel Time Auto Transit In Vehicle Time 23.1 minutes 16.8 minutes In Vehicle Time Cost Rate$0.048/minutes $0.043 In Vehicle Time Cost $0.993 $0.722 Out of Vehicle Time ----- 6.4 Out of Vehicle Time Cost Rate ----- $0.057 Out of Vehicle Time Cost ----- $0.365 Total Travel Time Cost $0.993 $1.078 Total Cost (Impedance) $1.300 $1.328 ____________________ 1. The values for "In Vehicle Time Cost Rate," "Out of Vehicle Time Cost Rate" and "Operating Cost Per Mile" were obtained by Atherton and Ben-Akiva (1976) for the city of Washington and were normalized to the city of Pittsburgh. 250 TABLE A-5-4. AGGREGATING BASE YEAR DEMAND ELASTICITIES (1) Valuation of Percent of Auto the Trip Portion the-Total Trip Percent x Elasticity In Vehicle Time $0.485 0.482 0.482 x -.27 = -0.13 Travel Cost 0.521 0.518 0.518 x -.52 = -0.27 Total Impedance $1.006 100 -0.40 Transit Linehaul Time $0.34 43-3 0.413 x -.66 = -0.272 Excess Time 0.273 33.2 0.332 x -1.04 = -0.345 Travel Cost 0.210 25.5 0.255 x -.22 = -0.056 Total Impedance $0.823 100 -0.673 (Transit Trips) (transit ) + (Auto Trips) (auto) = --------------------------------------------------------- 1958 Total Trips 473,750 (-0.673) + 1,926,070 x (-0.40) = -------------------------------------------- = 0.473 (2) 2, 399,820 ___________________________ 1. The elasticities before weighting were obtained from Atherton & Ben-Akiva (1976). 2. Notice this is an approximate rather than a precise form of the elasticity. Savings in data and computational requirements are achieved through such an approximation (see Appendix 10). 251 E. Design Year Demand Curve After plotting the base year demand curve, one proceeds with the 1980 forecasts. From the base condition equations, the number of trips made in 1980 can be estimated: _ _ Y = 2.242 + 2.761 X = 2.242 + 3.761 x 1.15 = 6.657, with _ _ V = nY = 3,743,275 person trips. The average trip duration is obtained using the updated model: _ t = -21.44 + 3.616 In 1,902 18 = 24.86 minutes. This trip time, when combined with the trip cost according to the procedure outlined in Chapter V, Section A, yields an impedance of 1.40 dollars. The slope of the design year demand curve can now be obtained: 0.473 x 3.743, 275 S = ------------------------- = 1,168,436 trips/dollar of change in 1.40 impedance. In deriving the above slope, the base year composite elasticity was applied at the base conditions where no transportation improvement is made (see Chapter V, Section A). As an approximation, no substantial change in modal splits is also assumed (which is justifiable since no improvement is made in the transportation system). Such an assumption, while simplifying the calculations, also allows an accurate forecast to be made. Ideally, in deriving the composite elasticity for the future year, the impedance elasticity by mode has to be weighted according to the future year modal split. In order to deal with this problem, an iterative procedure has been suggested. The first iteration starts with deriving the composite elasticity using the base year modal split. After performing the forecast,, one obtains a new value of modal split. In the second iteration, the new modal share values are used to derive a new value for the-composite elasticity, etc. However, it has been found that under any realistic conditions, there is no need to perform the iterative procedure. The changes in the composite elasticity between two successive iterations is infinitesimal and cannot be detected by our graphical procedure. The revised overall elasticity for the city of Pittsburgh is: 252 revised = 0.09427 x (-.673) + 0.90573 x (-.40) = .4257. This represents only .047 in the overall elasticity which results in a change of only 2.5 percent in the slope of the future year demand curve. With this small amount of divergence, it is impossible to detect any change in the estimated number of total daily person trips within the range of interest. F. Supply Curve A detailed description of plotting the base year supply curve was presented in Chapter IV. Following this procedure, an inventory of the 1958 highway system in Pittsburgh (referred to as the "G" network) is shown in Figure A-5-3. The major street system provides 16,321,000 vehicle miles of absolute capacity. The number of person trips at the maximum end point of the highway supply curve is calculated as follows: 16,231,000 Maximum Person Trips = --------------- x 1.4 = 4.369,885 trips. 5.2 The average system speed is 14.9 MPH under saturated system and 27.3 MPH under free flow conditions as shown in Figures A-5-4 and A-5-5. The average trip duration of these end points is, respectively: 5.2 x 60 T = ------------- = 11.4 minutes or $0.796 impedance, and 0 27.3 5.2 x 60 T = ------------- = 20.9 minutes or $1.204 impedance. 1 14.9 In Chapter 4, two ways of plotting the aggregate supply curve were discussed. In the Pittsburgh case, a large portion of the urban highway travel takes place on local streets not included in the highway aggregation. Therefore, the straight-line approximation of the aggregate supply curve derived using regression is shifted to intersect point "C"--the actual auto impedance/ volume point. A graphical presentation of DAP for the base year is given in Figure A-5-6. Since point A = 2,395,820 person trips, D = 2,361,736 and point C 1,926,070, the number of choice transit trips equals: 2,399,820 - 2,361,736 = 38,084. 253 FIGURE A-5-3. CLASSIFICATION OF THE BASE YEAR (1958) PITTSBURGH HIGHWAY SYSTEM Type of Facility Expressway Arterial Collector Total Location 1.0 38.6 9.6 49.2 Central (6) (4) (2) Business [8,000] [6,000] [4,000] District 48,000 926,400 76,800 8.5 108.1 36.1 152.7 (6) (2) (2) Fringe [10,000] [8,000] [5,500] 510,000 1,729,600 397,100 8.0 351.1 351.1 710.2 (4) (2) (2) Residential [11,000] [8,000] [5,500] 352,000 5,617,600 3,862,100 2.0 140.4 35.0 177.4 Outlying (4) (2) (2) Business [10,000] [8,000] [5,500] District 80,000 2,246,400 385,000 19.5 638.2 431.8 1089.5 Total 990,000 10,520,000 4,721,000 16,231,000 ___________________________ Key 0.0 Linear Miles of This Type of Highway (0) Estimated Average Number of Lanes [00,000] Estimated Daily T-Capacity 000,000 Per Lane Estimated-A-Capacity in Terms of VMT 254 FIGURE A-5-4. AN EXTREME POINT ON THE BASE YEAR SUPPLY CURVE; V/C RATIO = 1.00 Type of Facility Expressway Arterial Collector Total Location Central 48,000 926,400 76,800 1,051,200 Business (31) (12) (12) District [1,548] [77,200] [6,400] Fringe 510,000 1,729,600 397,100 2,636,700 (32) (15) (15) [153,937] [115,307] [26,473] Residential 352,000 5,617,600 3,862,100 9,831,700 (38) (15) (15) [9,263] [374,507] [257,473] Outlying 80,000 2,246,400 385,000 2,711,400 Business (31) (13) (13) District [2,581] [172,8001 [29,615] 990,000 10,520,000 4,721,000 16,231,000 Total [29,329] [739,814 [319,961] [1,089,104] ___________________________ Aggregate System Speed 16,231,000 ------------ = 14.9 MPH 000 Absolute A-Capacity in 1,089,104 Terms of VMT (00) Average Speed [000] Absolute A-Capacity in Source:U.S. DOT (1974) Terms of VHT PATS (1961) 255 FIGURE A-5-5. AN EXTREME POINT ON THE BASE YEAR SUPPLY CURVE; V/C RATIO = 0.00 Type of Facility Expressway Arterial Collector Total Location Central 48,000 926,400, 76,800 1,051,200 Business (37) (19.5) (17) District [1,297] [47,508] [4,518] Fringe 510,000 1,729,600 397,100 2,636,700 (44) (27) (25) [11,591] [64,059] [15,884] Residential 352,000 5,617,600 3,862,100 9,831,700 (47) (30) (28) [7,489] [?87,253] [137,932] Outlying 80,000 2,246,400 385,000 2,711,400 Business (37) (23) (22) District [2,162] [97,669] (17,500] Total 990,000 10,520,000 4,721,000 16,231,000 [22,539] [396,489] [175,834] [594,862] ___________________________ Aggregate System Speed 16,231,000 000 Absolute A-Capacity in ----------------- = 27.3 Terms of VMT 594,862 (00) Average Speed Source:U.S. DOT (1974) [000] Absolute A-Capacity in PATS (1961) Terms of VHT 256 Click HERE for graphic. FIGURE A-5-6. GRAPHICAL REPRESENTATION OF DAP ANALYSIS IN PITTSBURGH (1958) 257 The number of captive transit trips is given by: 2,361,736 1,926,070 = 435,666. G. Equilibrium Analysis The new freeways in the 1980 highway system would add nearly 9,000,000 vehicle miles of capacity to the system permitting a total of 25,153,000 vehicle miles at complete saturation as shown in Figure A-5- 8. The predicted average system speed is 31.4 MPH under free flow conditions and 18.7 MPHunder saturated system as shown in Figures A-5-9 and A-5-10. The maximum number of auto person trips in the forecast year is given by: 25,153,000 --------------- x 1.4 = 6,771,961 person trips. 5.2 The end points of the future highway system can be determined by calculating the trip durations: _ 5.2 x 60 T = --------- x 9.94 minutes = $0.733 Impedance 0 3.14 _ 5.2 x 60 T = --------- x 16.7 minutes= $1.024 Impedance. 1.0 18.7 It is estimated that the improvement in the transit system will result in an additional capacity of 130,000 person daily trips. This is calculated from the projected number of patrons in 1980, estimated at approximately 98,000 (PATS 1961), and an average systems load factor of .75: 98,000 --------- = 130,667 131,000. 0.75 H. Forecast A graphical representation of DAP analysis for the forecast year 1980 is shown in Figure A-5-7. The total estimated daily person trips in the design year represented by point "F" is approximately 4,000,000. Point "E" representing the equilibrium point for highway traffic shows 3,940,910 trips. Thus, the number of choice transit trips: 4,000,000 - 3,940,910 = 59,090. 258 Click HERE for graphic. FIGURE A-5-7. GRAPHICAL REPRESENTATION OF DAP ANALYSIS IN PITTSBURGH (1980) 259 FIGURE A-5-8. CLASSIFICATION OF THE DESIGN YEAR (1980) PITTSBURGH HIGHWAY SYSTEM Type of Facility Expressway Arterial Collector Total Location Central 16.1 38.6 9.6 64.3 Business (6) (4) (2) District [8,000] [6,000] [4,000] 772,800 926,400 76,800 Fringe 45.4 108.1 36.1 189.6 (6) (2) (2) [10,000] [8,000] [5,500] 2,724,000, 1,729,600 397,100 Residential 118.8 351.1 351.1 821.0 (4) (2) (2) [11,000] [8,000] [5,500] 5,227,200 5,617,600 3,862,100 Outlying 29.7 140.4 35.0 205.1 Business (4) (2) (2) District [10,000] [8,000] [5,500] 1,188,000 2,246,400 385,000 Total 210.0 638.2 431.8 1280.0 9,912,000 10,520,000 4,721,000 25,153,000 ___________________________ Key 0.0 Linear Miles of This Type of Highway. (0) Estimated Average Number of Lanes [00,000] Estimated Daily T-Capacity 000,000 Per Lane Estimated A-Capacity in Terms of VMT 260 FIGURE A-5-9. AN EXTREME POINT ON THE DESIGN YEAR (1980) SUPPLY CURVE; V/C RATIO = 0.00 Type of Facility Expressway Arterial Collector Total Location Central 772,800 926,400 76,800 1,776,000 Business (37) (19.5) (17) District [20,886] [47,508] [4,518] Fringe 2,724,000 1,729,600 397,100 4,850,700 (44) (27) (25) [64,059] [64,059] [15,884] Residential 5,227,200 5,617,600 3,862,100 14,706,900 (47) (30) (28) [111,217] [187,253] [137,932] Outlying 1,188,000 2,246,400 385,000. 3,819,400 Business. (37) (23) (22) District [32,108] [97,669] (17,500] Total 9,912,000 10,520,000 4,721,000 25,153,000 [228,270] [396,489] [175,634] [800,593] ___________________________ Aggregate System Speed 25,153,000 000 Absolute A-Capacity in ------------------ = 31.4 MPH Terms of VMT 800,593 (00) Average Speed [000] Absolute A-Capacity in Source: U.S. DOT (1974) Terms of VHT PATS (1961) 261 FIGURE A-5-10. AN EXTREME POINT ON THE DESIGN YEAR (1980) SUPPLY CURVE; V/C RATIO = 1.00 Type of Facility Expressway Arterial Collector Total Location Central 772,800 926,400 76,800 1,776,000 Business (31) (12) (12) District [24,929] [77,200] [6,400] Fringe 2,724,000 1,729,600 397,100 4,850,700 (32) (15) (15) [85,125] [115,307] [26,473] Residential 5,227,200 5,617,600 3,862,100 14,706,900 (38) (15) (15) [137,558] [374,507] [257,473] Outlying 1,188,000 2,246,400 385,000 3,819,400 Business (31) (13) (13) District [38,3231 [172,800] [29,615] 9,912,000 10,520.000 4,721,000 25,153,000 Total [285,935] [739,814] [319/,961] [1,345,710 ___________________________ Aggregate System Speed 25,153,000 ------------- = 18.7 MPH 000 Absolute A-Capacity in 1,345,710 Terms of VMT (00) Average Speed Source: U.S. DOT (1974) [000] Absolute A-Capacity in PATS (1961) Terms of VHT 262 The design year captive transit trips are given by: 0.84 1980 Captive trips = -------- = 318,000. 1.15 The total number of 1980 transit trips is: 59,090 + 318,004 = 377,094. The number of auto person trips is then: 4,000,000 - 377,094 = 3,622,906. The number of auto trips is obtained using an auto occupancy rate of1.40 (PATS 1961): 3,622,906 ------------ = 2,587,770. 1.4 With a constant average trip length of 5.2 miles, the estimated VMT is given by: 2,587,790 x 5.2 = 13,456,508. The passenger miles of travel is: 377,094 x 5.2 = 1,960,088. The base year value of travel time per minute is given by: $1.01 ----------- = $0.04 dollars per minute. 23.1 The value of travel time in the design year is: 1.19 - 0.305 x 0.91 - 0.25 x 0.09 = $0.89. The average trip duration in the future year is: $0.89 ---------- = 22.20. 0.04 I. An Assessment Before the accuracy of our parameter tabulations and the performance of the demand approximation procedure are assessed, it should be kept in mind that the approach is a "quick-turnaround" technique which intends to supply aggregate forecasts of regionwide travel, as opposed to the traditional methods which normally deal with travel demand on the zonal or link levels. DAP is not suggested for replacement of the traditional methods when the subareal or link level type detailed studies are required. Rather, it is a convenient tool for such policy analysis as the allocation of transportation resources on a nationwide or statewide scale. 263 For the time being, DAP is evaluated through a comparison with the traditional forecast. Toward this end, the two sets of forecasts are summarized. Taking the results shown in Table A-5-5 as a whole, one can notice that there is higher agreement between DAP and the traditional forecasts regarding travel by auto, than regarding the items associated with travel by transit. There is a large discrepancy between the total number of person trips by transit obtained using DAP and the value obtained using traditional methods. This can be partially attributed to DAP's crude manner of estimating the increase in transit capacity. Another significant dis- crepancy is found between average trip durations. This can be attributed mainly to the way by which the impedance associated with the DAP forecast at point "F" (see Figure A-5-7) is converted back to average trip duration. It-should be clear that the success of DAP is evaluated only with respect to the forecast obtained by traditional methods. Since there are some well-known fallacies involved in the traditional forecasting, consistency between the forecasts obtained by DAP and by traditional means cannot be considered as an absolute proof of the accuracy of DAP. However, the high level of agreement between the DAP forecast and the traditional forecast with respect to auto trips shows that as far as areawide travel forecasting is concerned, substantial cost savings can be achieved using the results of this research (rather than the VTP process). An ultimate evaluation of the updating success is not feasible since it would require a situation where no change occurs in the transportation system, and the values obtained from the updated model could have been compared to the actual value. However, if the measure is again the magnitude of the difference between the forecasts obtained by DAP versus those obtained from the traditional method, it is obvious that without the updating less of an agreement between the two forecasts would have resulted. 264 TABLE A-5-5. COMPARISON OF FORECASTS BY TRADITIONAL AND DAP METHODS Traditional DAP Percent Item Forecast Forecast Difference Total Person Trips 3,801,272 4,000,000 5.00 Total Person Trips by Auto 3,302,884 3,622,906 10.00 Total Person Trips by Transit 498,388 377,094 24.00 Total Auto Vehicle Trips 2,645,000 2,587,790 2.00 Average Trip Duration 16.4 22.20 25.00 Passenger Miles of Travel 2,137,800 1,960,088 8.00 Vehicle Miles of Travel 15,519,840 13,456,508 13.00 ___________________________ Source: PATS (1961) 265 APPENDIX 6: A CASE STUDY OF TEMPORAL TRANSFERABILITY: SAN FRANCISCO A. The Bay Area as a Large/Multinucleated City The city of San Francisco, home to over three-quarters of a million people in the study base year, 1965, is one of the most densely developed communities in the country. its concentrated urban core, a CBD dominated by industrial, commercial, and financial interests, suggests a classification label of "large/core-concentrated" according to our city classification if only the city of San Francisco itself is concerned. As shown in Figure A-6-1, however, this study region includes nine counties, at least three major cities, and a 1965 population of over 4.4 million. Well defined CBDs may be found in San Francisco, Oakland, and San Jose, with other major employment and commercial centers scattered throughout the region. Considering the Bay Area as a whole, one must classify the metropolis as a large/multinucleated city. In addition to its classic multinucleated structure, the San Francisco Bay Area was selected as one of our case study regions because of the recent implementation of a large rapid rail transit system, BART. One of the principal motivations behind this demonstration is an assessment of the capabilities of DAP with respect to forecasting the impact of various transportation policy decisions, in this case a "capital intensive" system. The massive increase in transit service in the Bay Area, for instance, constitutes a scenario in which the application of an aggregate analysis tool such as DAP would be appropriate. An inventory of pertinent base year travel data is presented in Table A-6-1. This information was compiled from a complete home interview, roadside interview, and truck-taxi survey conducted in 1965. Notice that two values of average trip length, trip duration, and number of person trips are given. Because of the rather large size of many of the outlying zones (see Figure A-6-1), a relatively large portion of the total person trips are intrazonal. In order to be able to compare DAP with traditional forecasts on a common denominator, we will concern ourselves only with interzonal trips. Our trip general equations will yield an estimate of total person trips, from which the appropriate number of intrazonal trips will be subtracted before conducting our equilibrium analysis. Trip duration data will be updated to reflect interzonal values. 266 Click HERE for graphic. FIGURE A-6-1. THE NINE-COUNTY SAN FRANCISCO BAY AREA STUDY AREA SOURCE: BATSC (1969). 267 TABLE A-6-1. INVENTORY OF PERTINENT BASE YEAR VARIABLES 1965 Value 1965 Value Item (Interzonal Trips Only)(Total Person Trips) Population 4,403,334 Dwelling Units 1,404,146 Autos Owned 1,713,000 Auto Ownership/D.U. 1.22 Average Trip Length 8.59 6.61 (est.) Average Trip Duration 14.00 11.27 Average System Speed 36.8 Internal Person Trips* 7,265,000 10,378,000 Auto 6,684,000 9,768,000 Transit 581,000 610,000 Trips per Dwelling Unit 5.17 7.39 Auto Occupancy Rate 1.45 Vehicle Trips 4,603,000 Vehicle Miles of Travel 39,573,000 ___________________________ *Excludes School Trips. Source: BATSC (1969). 268 TABLE A-6-2. PARAMETERS AND RESULTS OF TRADITIONAL FORECAST Item 1965 1980 1990 Population 4,403,334 6,157,800 7,477,100 Dwelling Units 1,040,146 1,944,400 (est.) 2,346,100 Autos per Dwelling Unit 1.22 1.40 (est.) 1.60 (est.) Total Interzonal Person Trips7,265,000 11,771,000 14,401,000 Auto 6,684,000 10,948,000 13,440,000 Transit 581,000 823,000 961,000 Total Vehicle Trips 4,603,000 8,003,000 9,818,000 Vehicle Miles of Travel 39,573,000 73,415,000 95,727,000 Average Trip Duration 14.71 14.27 14.26 Average Trip Length 8.59 9.17 9.75 ___________________________ Note: All travel characteristics in terms of interzonal trips only (excludes school trips). Source: BATSC (1969). 269 B. Forecasts by Traditional Means The "traditional" procedures employed by the Bay Area Transportation Study Commission (1969) are those typically used in most studies, involving the sequential steps of trip generation, distribution, modal split, and network assignment. Certain elements of the 1980 and 1990 travel forecasts made by the above methods are of interest in the verification of the temporal stability of our parameter tabulations; they are shown in Table A-6-2. The first three items in this tabulation are socioeconomic variables such as demographic and income characteristics, which are input rather than Output of the traditional transportation forecasting procedures. Likewise, they serve as input to the demand approximation procedure. The remaining items in Table A-6-2 are those aggregate level forecasts which will be directly comparable to those from DAP. The total number of daily interzonal person trips made in the Bay Area is expected to increase from 7,265,000 in 1965 to 11,771,000 in 1980 to 14,401,000 in 1990. With the implementation of the BART system, transit usage is shown to grow from 581,000 interzonal trips in 1965 to 961,000 in 1990. The total number of daily transit trips, including intrazonal movements, is forecasted to exceed a million in 1990. Even with the substantial increase in the transit trip forecast, the modal split in terms of percent transit usage, is actually expected to decline from 8.0 in 1965, to 7.0 in 1980 and 6.7 in 1990. It should be noted that the total future demand is taken to be perfectly inelastic under traditional forecasting practices. This assumes that the number of trips and travel patterns is unaffected by level-of-service improvements in the urban area. Such an assumption sidesteps the issue of supply-demand equilibrium. The use of DAP in making areawide travel forecasts may prove to be more accurate than traditional techniques in this regard, since one of the basic principles of DAP is equilibrium analysis. C. Base Year Calibration of the Demand Approximation Procedure Since the demand approximation procedure has been thoroughly detailed previously in this report, for the sake of brevity, only the most critical elements of the analysis, including numerical calculations, will be included in this case study. The actual analysis included all required calculations, etc., for each of the three forecasts made in demonstrating DAP in the Bay Area. 270 Updating Base Condition Equations The following base condition equations apply for the San Francisco Bay Area, a large/multinucleated urban area: _ Average Trip Duration: t = -10.54 + 3.618 1n P where P = study area population in thousands. _ Number of Trips Per Household: Y = 2.831 + 4.117 FE where R = the number of autos per household. If a homogeneous travel behavior among the households in the Bay Area is assumed, the total number of trips in the urban area may be given by: _ V = ny where n = the number of households in the study area. Using the parameter values shown in Tables A-6-1 and A-6-2, one can make the DAP estimates of base year trip duration and frequency correspondingly: _ t = -10.54 + 3.618 (8.39) = 19.8 _ Y = 2.831 + 4.117 (1.22) = 7.85 _ V = 7.85 x 1,404,146 = 11,027,797. The DAP forecast of trips per household and total number of study area person trips is shown to be quite accurate. As might be expected, the estimate of trip duration is somewhat different from the actual values for both total person trips and interzonal trips. The updating procedure described in Chapter V is used to adjust the trip duration to reflect the conditions specific to the group of large/multinucleated cities such as San Francisco. Since we are primarily concerned with interzonal trips, this adjustment will be made in the following manner. We equate the average trip duration t to the actual base year figure observed in the Bay Area and adjust the constant term a in the equation: _ t = a + 3.618 1n P = a + 3.618 1n 4,403 = 14.71; thus a = 14.71 3.618 1n 4,403 = -15.65. The trip duration equation for the San Francisco Bay Area is updated to be: _ t = -15.63 + 3.618 1n P. 271 TABLE A-6-3. TOTAL IMPEDANCE IN TERMS OF TRAVEL COSTS (1965) Total Costs* (Per Trip) Auto Transit Operating Cost (@ $0.088/mile) $0.756 $0.210 Parking 0.100 -- Tolls 0.015 -- TOTAL $0.871 TOTAL $0.210 Cost Per Person (@ 1.4 Persons/Car) $0.622 $0.210 Cost of Travel Time Auto Transit In Vehicle Time 14.0 minutes 16.5 minutes In Vehicle Time Cost Rate$0.021/minute $0.021/minute In Vehicle Time Cost $0.294 $0.346 Out-of-Vehicle Time -- 6.4 minutes Out-of-Vehicle Time Cost Rate -- $0.041/minute Out-of-Vehicle Time Cost -- $0.261 Total Travel Time Cost $0.294 $0.607 Total Cost (Impedance) $0.916 $0.817 ___________________________ *Assumes constant average trip length of 8.59 miles. Source: BATSC (1969) Simpson & Curtin (1967). 272 Impedance Having updated the basic equations to reflect actual base year condi- tions, one calculates the impedance of the typical 1965 trip (both by auto and by transit) (see Table A-6-3). The total cost per person-trip is shown to be $0.622 by auto and $0.210 by transit, using the base year average trip length of 8.59 miles. As a parallel calculation, the trip-duration characteristics are assigned cost figures based on assumed values of travel time. According to McFadden (1974) the value of in-vehicle time in San Francisco was approximately $1.23 per hour ($0.021 per minute) while the value of excess was $2.46 per hour ($0.041 per minute). Based on these values, total travel time costs of $0.294 for auto and $0.607 for transit are obtained, yielding a total impedance of $0.916 for auto and $0.817 for transit. To perform the aggregate analysis, a single impedance value, repre- senting both actual transit and highway travel, is calculated for the base year by weighting the transit and auto impedance values at the relative modal split. Percent of Total Trips Impedance Auto .92 x $0.916 = $0.843 Transit .08 x 0.817 = 0.065 Weighted Impedance $0.908 Demand Curve With this impedance value and the number of interzonal trips now known in the base year, we can locate point "A" in Figure A-6-2. The base year demand curve is then drawn through point A with the slope determined by the demand elasticity. Note that, while good data on elasticities is available for the San Francisco area, it is stratified by mode and portion of trip (e.g., linehaul time, excess time, cost, etc.). An aggregation procedure (involving the assignment of weights to individual portions of a trip) is used to approximate the composite elasticity, shown to be -0.554 in Table A-6-4. This yields a demand curve slope of 0.554 (7,265,000) S = ------------------------ = 4,432,610 4,433,000 trips/dollar. .908 273 Aggregate Supply Curve The final element of the base year DAP calibration is the plotting of the aggregate system supply curve. Three different networks were included in the original "Bay Area Transportation Report" (BATSC 1969). The 1965 highway system, referred to as the "G" Network, is shown in Figure A-6-3. This network was dominated by an extensive system of arterial highways with two main freeway corridors on each side of the Bay. A total of 3,248 miles of major highways made up this base year network (Figure A-6-4). In all, more than 15,000 miles of streets and highways existed in the study area in 1965, although only those facilities serving major portions of the interzonal traffic flow were included in the "G" Network. Of the 3,248 miles, 429 were classified as freeway, 2,625 as arterial, and 194 as collectors. The system provided an absolute capacity, referred to as "A-Capacity," of 74,338,000 daily vehicle miles of travel. Recall that uniform loading of the various cells of the highway classification scheme must occur at points of extreme loading--V/C = 0.00 and V/C 1.00. The average speeds for the "G" network are shown to be 36.3 MPH under free flow conditions and 20.5 MPH under the saturated system. Assuming the average trip length is constant, the average trip duration at these end points may be easily calculated by: _ 8.59 x 60 T = -------------- = 14.2 minutes = $0.910 Impedance 0.0 36.3 _ 8.59 x 60 T = -------------- = 25.1 minutes = $1.149 Impedance. 1.0 20.5 To determine the number of interzonal person trips at the maximum end point, we employ the following equation: Maximum "A-Capacity" Person = -------_------- x Auto Occupancy Rate Trips L 74,338,000 = ------------ x 1.45 - 12,548,323 = 12,550,000 trips. 8.59 These two end points are denoted by G.0 and G.m, respectively, in Figure A-6-2. Notice that one other point which should theoretically lie on the base year supply curve is known, the actual 1965 volume/ impedance for the auto (highway) mode only, point "C" in the figure. By using regression analysis, the slope of the best straight line through these three points may be determined. This is referred to as the 1965 274 TABLE A-6-4. AGGREGATION OF BASE YEAR DEMAND ELASTICITIES.1 Auto Value Percent X Elasticity In Vehicle Time $0.294 32.1 X -0.15 = -0.0484 Travel Cost 0.622 67.9 X -0.77 = -0.5228 Total Impedance $0.916 100.0 -0.5710 Transit Linehaul Time $0.334 40.9 x -0.46 = -0.1881 Excess Time 0.273 33.4 x -0.17 = -0.0568 Travel Cost (Fare) 0.210 25.7 x -0.45 = -0.1156 Total Impedance $0.817 100.0 = -0.3605 (Transit trips) (n ) + (auto trips) (n ) transit auto = -------------------------------------------------------- 1965 (Total trips) (581,000) (-0.3605) + (6,684,000) (-0.5710) = ----------------------------------------------- 7,265,000 = -0.554 ___________________________ 1. The aggregation procedure is described in Chapter III and Appendix 10. Source: McFadden (1974). 275 Click HERE for graphic. 276 FIGURE A-6-4. CLASSIFICATION OF THE 1965 BAY AREA HIGHWAY SYSTEM Type of Facility Expressway Arterial Collector Total Location Central Business District 12 150 19 1811 (6) (4) (2) [8,000] [6,000] [4,000] 576,000 3,600,000 152,000 Fringe 40 400 100 540 (6) (3) (2) [10,000] [8,000] [5,500] 2,400,000 9,600,000 1,100,000 Residential 347 1,825 75 2,247 (5) (2) (2) [11,000] [8,000] [5,500] 19,085,000 29,200,000 825,000 Outlying 30 250 280 Business (6) (3) District [10,000] [8,000] 1,800,000 6,000,000] TOTAL 429 2,625 194 3,248 23,861,000 48,400,000 2,077,000 74,338,000 ___________________________ KEY Source: BATSC (1969) 0.00 Linear Miles of This U.S. DOT (1974) Type of Highway (0) Estimated Average Number of Lanes [00,000] Estimated Daily T-Capacity Per Lane 000,000 Estimated Daily A-Capacity in Terms of VMT 277 highway supply curve. By the nature of the supply-demand equilibrium, the actual overall supply curve, including transit capacity, must pass through point "A," the actual base year total trip characteristics. This shift may be considered a reflection of the additional capacity afforded by the base year transit system. Equilibrium Note that the estimated 1965 highway supply curve intersects the demand curve at point B. From the points A and C, we can approximate the total number of transit trips by taking the difference between the ordi- nates of points C and A: Transit Trips = 7,265,000 - 6,684,000 = 581,000 trips. With the inclusion of point B, the total transit trips can be broken down into "captive" versus "choice" riders. Thus by taking the difference between the ordinates of point B and point A, we obtain the estimated volume of "choice" transit trips: "Choice" Transit Trips = 7,265,000 - 6,900,000 = 365,000 trips. "Captive" transit trips, on the other hand, can be obtained from the ordinate difference between B and C: "Captive" Transit Trips = 6,900,000 - 6,684,000 = 216,000 trips. This completes the base year calibration of several basic DAP elements, including trip duration, demand elasticity and the aggregate supply curve. Now DAP forecasts of Bay Area travel in 1980 and 1990 can be made. D. Bay Area Forecasts by the Demand Approximation Procedure The first step in making the 1980 forecast by the demand approximation procedure is to locate the estimated demand-curve segment for that year. This is accomplished by using the updated-base condition trip frequency and trip duration equations to locate a point on that curve and then determining its slope by using the composite elasticity at that point. Using input data which may be found in Table A-6-2, we obtain the following estimates of trip volume and average trip duration: Trips Per Household: Y = 2.831 + 4.117 (1.40) = 8.59 trips/household Total Regional Person Trips: V = 8.59 x 1,944,440 = 16,711,720 trips 278 Total Interzonal Person Trips: V = 16,711,729 x 0.70 = 11,698,210 trips where 0.70 is the base year interzonal trips, expressed as a percent of total trips. Trip Duration _ t = -15.65 + 3.618 1n (6,158) _ t = 15.92 minutes Since a new future year trip length estimate is available in this case from previous studies, it will be substituted for the base year value at this point in the analysis. As such, a new impedance value must be calculated. Since the modal split in the future year is not known at this point, the base year modal split value will be used to weigh the impedance. By combining all modes, we obtain an aggregate value of $0.0696 per mile and $0.0214 per minute. The new estimate of trip length (9.17 miles) is used to calculate the impedance of $0.969. Two estimates of 1990 travel characteristics will be made for purposes of assessing temporal transferability. The twin estimates of trip duration reflect the case where no further updating takes place and the case where the duration equation is updated to reflect 1980 base conditions. Since no actual data is available for 1980, however, it is assumed (for purposes of the current analysis) that the average trip duration estimated by traditional forecasting methods accurately represents actual conditions. Correspondingly, the temporal updating procedure is performed on the 1965 equation using "actual" 1980 data: _ t = a + 2.168 1n P = a + 31.57 = 14.27 therefore a = -17.30 and the updated equation is _ t = -17.30 + 3.618 1n P. The 1990 estimate of average trip duration is then: _ t = -17.30 + 3.618 (8,920) = 15.61 minutes. The 1990 estimated trip length of 9.75 miles is used to calculate the impedance at $1.003. Notice that without the 1980 updating the estimate would be: _ t = -15.65 + 3.618 1n (8,920) = 17.26 minutes $1.038 impedance. 279 Given the fact that the trip-frequency equation is temporally stable, no updating is deemed necessary. The trip frequency estimate will therein be the same in each case and is given by: Trips per household: _ Y = 2.831 + 4.117 (1.60) = 9.42 trips/household. Total regional person trips: V = 9.42 x 2,346,100 = 22,096,039. Total interzonal person trips: V = 22,096,039 x .70 = 15,467,227 trips. Demand Curves The implementation of an extensive rapid rail transit system in the Bay Area between 1965 and 1980 results in a change in the elasticity according to McFadden (1974). The elasticity values are updated accordingly in Table A-6-5 and a final estimate of -0.9288 is obtained. From this value the slopes of the 1980 and twin 1990 demand curves are obtained below: 1980 -0.9288 (11,698,210) --------------------- = 11,212,897 11,213,000 trips/dollar .969 1990 (with 1980 Update) -0.9288 (15,467,227) --------------------- = 14,322,991 14,323,000 trips/dollar 1.003 1990 (Without 1980 Update) -0.9288 (15,467,227) ---------------------- = 13,840,038 13,840,000 trips/dollar. 1.038 The resultant demand curves for 1980 and 1990, with or without the 1980 update of the trip duration equation, are shown in Figure A-6-5. Notice that the above approach assumes that there will be no change in modal split of Bay Area travel between 1965 and 1980 and 1990. This appears to be an erroneous assumption, especially in the light of the large scale transit improvements in this study area. A more accurate, iterative approach has been investigated by the research team and tested in the current case study: Step 1. Use base year modal split and determine overall demand elasticity. 280 TABLE A-6-5. AGGREGATION OF DEMAND ELASTICITIES FOR 1980 and 1990 (POST BART) Auto Value Percent x Elasticity In-Vehicle Time $0.294 32.1 x -0.59 = -.1894 Travel Cost 0.622 67.9 x -1.15 = -.7803 Total $0.916 100.0 -.9702 Transit Linehaul Time $0.334 40.9 x -0.30 -0.1227 Excess Time 0.273 33.4 x -0.70 -0.2338 Travel Cost (Fare)0.210 25.1 x -0.38 -0.0954 Total $0.817 100.0 -0.4519 (581,000) (0.4519) + (6,684,000) (0.9702) = ----------------------------------------------- 1980 or 1990 7,265,000 = -0.9288 ___________________________ Source: McFadden (1974) Note: Since no better estimate of modal split is available for 1980 and 1990, the 1965 value is assumed for purposes of weighting the elasticities. 281 Step 2. Determine the slope of the demand curve and perform the equilibration to forecast future trips. Step 3. Determine future year modal split using procedure outlined later in this appendix. Step 4. Substitute these new modal split values into the weighting formula to determine a revised overall elasticity and repeat steps two to four until the values of the overall elasticity and the modal split stabilize. It has been found, however, that under most realistic conditions, there is actually no reason to perform these lengthy iterations, especially in light of the fast-response nature of DAP. As may be seen in Table A-6-6 later in this appendix, the DAP estimate of 1980 modal split is 90.5 percent auto and 9.5 percent transit. This compares with a base year value of 8.0 percent transit and 92.0 percent auto. Substituting these into the original weighting formula, we obtain a revised estimate of overall elasticity: revised = (.4519) (.095) + (9.9702) (.905) revised = .9210. This represents a change of only .0078 in the overall elasticity. After recalculating the slope of the demand curve, using this new value, it is found that it is impossible to detect any change in the estimated number of daily person trips or modal split values. The error associated with approximating equilibrium graphically is certainly larger than the error introduced by initially assuming a constant modal split. Aggregate Supply Curves The equilibrium analysis is to be employed to estimate the impact of the implementation of the recommended highway and, in particular, transit improvement programs. To facilitate this, of course, the aggregate system supply curves must be plotted for each future year. Figure A-6-6 shows the assumed 1980 highway system, referred to as the "X" network. The most notable change in this network is the construction of over 400 miles of freeway, more than doubling the amount existing in 1965. Much of this freeway construction is assumed to have replaced some arterial routes, so the net effect is a slight loss of arterial mileage. Overall, the "X" 282 network provides an estimated 94,013,000 vehicle miles of capacity, as may be seen in Figure A-6-7. Using the new estimate of the 1980 mean trip length of 9.17 miles, the maximum number of auto person trips which may be accommodated by the new network is calculated to be 14,865,000 per day. The average system speeds are found to be 40.9 MPH at totally free flow conditions (V/C = 0.00) and 22.7 MPH at system saturation (V/C = 1.00). This yields trip duration estimates at the end points of the curves equal to 13.5 minutes and 24.2 minutes, which may be converted to impedance values of $0.947 and $1.172 respectively. These points are shown in Figure A-6-8. The 1980 highway supply curve is adjusted by shifting the lower end point approximately $0.037 to the left and the upper end point $0.042 to the left as suggested by the regression calibration performed in the base year 1965. The calibrated total 1980 supply curve before the installation of BART is obtained by shifting the highway curve the same vertical distance as in the base year--corresponding to the pre-BART transit capacity. It is then necessary to vertically add the capacity provided by the implementation of the BART system, resulting in an estimated 1980 total system supply curve, which is shown to intersect with the 1980 demand curve at point F. Equilibrium Just as in the 1965 case, the amount of total person trips and the amount of "choice" transit trips may be graphically determined. Since the total number of trips, point "E" is approximately 11,450,000 and Point E is located at 10,550,000 trips, the number of "choice" transit trips is 11,450,000 - 10,550,000 = 900,000 trips. A straightforward method of estimating "captive" trips has been developed in previous sections of this report. Namely, the ratio of 1980 "captive" trips to 1965 "captive" trips is inversely related to the ratio of 1980 auto ownership and 1965 auto ownership. Therefore: 1965 Auto Ownership 1980 Captive Trips = 1965 Captive Trips x -------------------- 1980 Auto Ownership 1.22 = 216,000 x -------- 188,000. 1.40 The total number of 1980 transit trips is then the sum of captive and choice trips: 900,000 + 188,000 = 1,088,000 trips. 283 The number of auto person trips is obtained by subtracting transit trips from the total: 11,450,000 - 1,088,000 = 10,362,000 trips. The number of auto trips is determined simply by dividing the number of auto person trips by the auto occupancy rate, 1.45: 10,362,000 ------------------ = 7,146,000 trips. 1.45 With an assumed average trip length of 9.17 miles, the estimated 1980 VMT is given by: 7,146,000 x 9.17 = 65,528,820. An estimate of the 1980 average trip duration may be obtained directly from the impedance shown to be $0.990 at equilibrium in 1980. Subtracting that element of the impedance which is attributable to travel cost, $0.629, the amount attributable to the value of the traveler's time is $0.361. The aggregate value of this time, combining all modes, is $0.0217 per minute. The trip duration is therefore given by: $0.361 ------------- = 16.6 minutes. $0.0217 This completes the DAP forecast for 1980. An identical procedure was followed in making a pair of projections of 1990 Bay Area travel, one corresponding to the case where the basic trip duration equation was updated to reflect "actual" 1980 conditions and one where no such update was made. While none of the calculations are included here, the results of these forecasts are presented in Table A-6-6. For the convenience of the reader, the assumed 1990 highway network, highway classification and the DAP equilibrium analysis are presented in Figures A-6-9, A-6-10, and A-6-11 respectively. E. An Assessment The principal objective of this case study is to evaluate the temporal stability of the tabulated parameters using the demand approximation procedure. In the absence of any actual post implementation data (at least at the present time), DAP forecasts at two future points in time have been made and compared with those obtained by traditional methods. Results of both DAP and sequential forecasts with respect to six aggregate level variables are included in Table A-6-6. 284 Most elements of the 1980 DAP forecast appear to be somewhat below the traditional projection. However, it should be noted that the DAP estimate of the total interzonal person trips is within 2.73 percent of the traditional forecast, which is hardly a significant discrepancy when one considers that neither forecasting approach has been validated by actual data in the year 1980. The most substantial disagreement occurs with respect to the projection of transit trips, or more specifically, the estimated modal split. The DAP forecast of the percentage of transit trips exceeds the traditional estimate by nearly 36 percent. As might be expected, the resultant number of auto person trips, auto vehicle trips and vehicle-miles-of-travel are somewhat lower than traditional projections while DAP forecasts of transit trips is considerably larger. Similarly the DAP estimate of mean trip duration is 16.33 percent higher than traditional, with this error partially attributable to the higher number of transit trips, which are typically longer in duration than auto trips, although usually of a somewhat lower overall impedance. Two DAP forecasts were made in 1990. The reader will recall that earlier in this section a 1980 intermediate update of the trip duration was made under the postulation that 1980 traditional forecasts were equivalent to actual conditions. This update is shown to have a favorable impact on the forecasts of most variables and an unfavorable effect on others. For example, the total number of interzonal person trips differs from traditional by 12.14 percent with the 1980 update and by 16.31 percent without. The number of auto person trips is within 11.61 percent of traditional with the update and 16.65 percent without. On the other hand, DAP forecasts of transit trips and average trip duration are closer to traditional estimates without the update. Before an actual assessment of the temporal stability is made, two important factors must be taken into consideration. Since we are comparing forecast to forecast, and not forecast to actual, the discrepancy between forecasts should be interpreted as just that, and not as percent error. Further, since the demand approximation procedure includes equilibrium analysis, and as such permits latent or induced demand to materialize, the number of trips should exceed the inelastic traditional estimates. It is quite reasonable, therefore, that the trip frequency related elements of the forecast are consistently higher under the demand approximation 285 Click HERE for graphic. 286 Click HERE for graphic. FIGURE A-6-5. FUTURE YEAR BAY AREA DEMAND CURVES 287 Click HERE for graphic. 288 FIGURE A-6-10. CLASSIFICATION OF THE 1990 BAY AREA HIGHWAY SYSTEM Type of Facility Expressway Arterial Collector Total Location Central 20 150 11 181 Business (7) (4) (2) District [8,000] [6,000] [4,000] 1,120,000 3,600,000 152,000 Fringe 80 400 100 580 (6) (3) (2) [10,000] [8,000] [5,500] 4,800,000 9,600,000 1,100,000 Residential 1221 1295 75 2,591 (5) (2) (2) [11,000] [8,000] [5,500] 67,155,000 20,720,000 825,000 Outlying 65 250 315 Business (6) (3) District [11,000] [8,000] 4,290,000 6,000,000 TOTAL 1,386 2,095 194 3,675 77,365,000 39,920,000 2,077,000 119,362,000 ___________________________ Source: BATSC (1969) 0.00 Linear Miles of This U.S. DOT (1974) Type of Highway (0) Estimated Average Number of Lanes [00,000] Estimated Daily T-Capacity Per Lane 1,000,000 Estimated Daily A-Capacity in Terms of VMT 289 Click HERE for graphic. FIGURE A-6-11. GRAPHICAL REPRESENTATION OF DAP IN MAKING 1990 FORECASTS (WITH AND WITHOUT UPDATE) 290 procedure. Discrepancies between traditional projections and the estimate made by DAP, assuming a 1980 update of the trip duration equation, range from 5.37 percent for total vehicle trips and VMT to 19.67 percent for transit trips. Without the 1980 update, percent differences range from -2.40 for the transit modal share to 16.65 for auto person trips. Trip duration estimates made by DAP in 1990 are lower than traditional forecasts. The fact that some of the 1990 estimates are more consistent with traditional forecasts when the DAP duration was updated in 1980 should be viewed with caution. The equations were updated to reflect 1980 traditional forecasts, not actual values, hence, no absolute conclusions can be drawn--even though most of the results speak favorably of updating. In summary, the demonstration of the quick-turnaround, regionwide aggregate forecasting procedure (DAP) in the San Francisco Bay Area is shown to be somewhat less consistent with traditional forecasts than case studies performed for Pittsburgh and Reading, Pennsylvania. The major reason for this is the extremely multinucleated structure of the Bay Area. For purposes of comparison with traditional forecasts, our DAP analysis used the same nine-county study area employed by the Bay Area Transportation Study Commission in its endeavor. The study area included significant amounts of what would have to be considered rural or intercity travel. The results of this demonstration suggest that the demand approximation procedure is somewhat more accurate for less diversified urban areas. This should not imply that the procedure is not applicable in multinucleated regions, but rather that the study area to be investigated should be appropriately delineated to make the analysis meaningful. Regarding temporal transferability, the trip frequency portion of the DAP projection is shown to be temporally stable, in spite of the fact that travel forecasts are somewhat higher than traditional estimates in 1990. This is due to the elasticities of demand and the equilibrium approach utilized rather than a lack of temporal transferability. There are fluctuating levels of consistency concerning the average trip duration estimates. For example, the 1980 DAP estimate is 16.33 percent above the traditional estimate, and the 1990 estimates are 10.94 percent (updated) and 8.84 percent (not updated) below the traditional estimate. Therefore, it can be surmised that the temporal stability as viewed by this element of the analysis is somewhat less certain. 291 TABLE A-6-6. COMPARISON OF DAP ESTIMATES WITH TRADITIONAL FORECASTS 1980 1990 _____________________ ______________________ DAP (With DAP (Without Item Traditional* DAP % Diff. Traditional* 1980 Update) % Diff. 1980 Update)% Diff. Total Inter- zonal Person Trips 11,771,000 11,450,000 -2.73 14,401,000 16,150,000 12.14 16,750,000 16.31 Auto 10,948,000 10,362,000 -5.35 13,440,000 15,000,000 11.61 15,660,000 16.65 Transit 823,000 1,088,000 32.20 961,000 1,150,000 19.67 1,090,000 13.42 Percent Transit 6.99 9.50 35.91 6.67 7.12 6.76 6.51 -2.40 Total Vehicle Trips 8,003,000 7,146,000 -10.71 9,818,000 10,345,000 5.37 10,800,000 10.00 Vehicle-Miles of-Travel 73,415,000 65,529,000 -10.74 95,727,000 100,864,000 5.37 105,300,000 10.00 Average Trip Duration 14.27 16.6 16.33 14.26 12.7 -10.94 13.0 -8.84 ___________________________ Source: BATSC (1969). Click HERE for graphic. FIGURE A-6-2. CALIBRATION OF DAP IN THE-BASE YEAR (1965). 293 FIGURE A-6-7. CLASSIFICATION OF THE 1980 BAY AREA HIGHWAY SYSTEM Type of Facility Expressway Arterial Collector Total Location Central Business18 150 19 187 District (7) (4) (2) [8,000] [6,000] [4,000] 1,008,000 3,600,000 152,000 Fringe 67 400 100 567 (6) (3) (2) [10,000] [8,000] [5,500] 4,020,000 9,600,000 1,100,000 Residential 724 1,545 75 2,344 (5) (2) (2) [11,000] [8,000] [5,500] 39,820,000 24,720,000 825,000 Outlying Business District 48 250 298 (6) (3) [11,000] [8,000] 3,168,000 6,000,000 TOTAL 857 2,345 194 3,396 48,016,000 43,920,000 2,077,000 94,013,000 ___________________________ KEY Source: BATSC (1969) U.S. DOT (1974) 0.00 Linear Miles of This Type of Highway (0) Estimated Average Number of Lanes [00,000] Estimated Daily T-Capacity Per Lane 000,000 Estimated Daily A-Capacity in Terms of VMT 294 Click HERE for graphic. FIGURE A-6-8. GRAPHICAL REPRESENTATION OF DAP IN MAKING 1980 FORECAST. 295 APPENDIX 7: A CASE STUDY OF SPATIAL AND TEMPORAL TRANSFERABILITY: READING, PENNSYLVANIA A. Reading, Pa. As a Core-Concentrated Medium City Reading, Pennsylvania is a medium, core-concentrated city located about 40 miles northwest of Philadelphia. The study area was 25 square miles in 1958 and expanded to cover 84 square miles in 1964 (see Figure A-7-1). The 1958 study area had a population of 141,600 in 1958 and 139,100 in 1964. The population of the extended study area in 1964 was 178,275 and was predicted to grow to 191,774 by 1975 and 206,136 in 1990. Two extensive home interview surveys were made: one in 1958 before the construction of two freeways, and the other in 1964 after completion of the freeways (Figure A-7-1). Table A-7-1 shows that from 1958 to 1964 the population within the 25 square mile study area declined 1.8 percent, but the number of dwelling units increased 0.8 percent. This means that persons per dwelling unit have been declining during the 1958-64 period, On the other hand, during the same period, the trip demand has increased considerably. This is due to the increase of car ownership as well as to the increase of person trips per household. For example, the total vehicle trips increased 32.9 percent; total person trips, 20.6 percent; and VMT, 49.1 percent. It is apparent that from 1958 to 1964 the automobile occupancy rate was declining. People-in Reading also made longer trips in 1964 than in 1958 (2.46 miles per trip in 1958 and 2.76 miles per trip in 1964)--a fact that DAP has to reckon with given the usual assumption about a constant trip length. The average trip duration increased 2.1 percent correspondingly. Table A-7-1 shows that, as predicted by traditional methods, travel demand will continue to increase from 1964 to 1990. The increase of demand may be traceable in part to the recommended highway improvements as shown in Figure A-7-2. The traditional projection also indicates that despite the positive change of socioeconomic variables such as popu lation, number of dwelling units, car ownership, and number of trips per household, the average of trip duration will be reduced 3.3 percent from 1964 to 1990. It assumes that the recommended highway improvements will provide higher levels-of-service in 1990. Finally, it should be noted that all values related to demand as contain ed in Table A-7 I were adjusted to account for interzonal traffic volumes. 296 Click HERE for graphic. FIGURE A-7-1. STUDY AREAS OF READING, PENNSYLVANIA 297 TABLE A-7-1. TRAVEL DATA FOR READING, PENNSYLVANIA, 1958, 1964, and 1990 Click HERE for graphic. ___________________________ NA = Data not available or not applicable. * The 1958 total person trips are estimated with the ratio of total person trips/total vehicle trips equal to 1.3. ** Average trip duration according to 1958 system. Source: Reading Area Transportation Study (1971 and 1975) and Alan M. Voorhees and Associates (1970. B. Relationship Between Policy Options and Explanatory Variables The selection of a study area in this report is based not only on data availability, urban/regional structure and size of population, but also on the mode-orientation of the transportation system. One of the case study options is to observe only the auto travel demand in a medium-coreconcentrated city. Since auto trips in Reading account for more than 93 percent of overall trips, it has been selected as a study area (Reading Area Transportation Study 1964). As has been indicated, during the 1958-64 period there were two new highway improvements in the Reading area. It is expected that the construction of the new transportation facility will improve the level- of-service and encourage people to use the transportation facilities more often. Shown in Figure A-7-2 are the recommended highway improvements for Reading up to 1990. Certain portions of highways, as recommended, have been completed or are under construction. All recommended highway improvements will be considered in the development of the 1990 supply curve. C. Spatial and Temporal Transferability The case study of Reading, Pa. examines the predictive accuracy and ability of the parameter tabulations through the demand approximation procedure (DAP). Reading is an ideal site for testing both spatial and temporal transferability. Reading has a four-point data base corresponding to 1958, 1964, 1975, and 1990. The 1964 data can be used as a temporal pivot point. It can update the parameters and verify the DAP forecast by comparing it with the 1975 actual traffic count and the forecast made by the traditional method on the one hand, and by comparing it with the 1990 forecasted traffic volume on the other. D. Data Preparation Based on the size and urban structure of Reading (which is a medium- sized, core-concentrated city), the proper base-condition equations and parameters from DAP can be selected. They are shown as follows: Average Trip Duration Equation: _ t - 03.748 + 2.134 1n P 299 Click HERE for graphic. 300 FIGURE A-7-3. INVENTORY OF HIGHWAY SYSTEM; READING PENNSYLVANIA, 1964, 1975 and 1990. Type of Facility Expressway Arterial Collector Total Location General (4) (4) (2) 15.0 Business 0.0 6.0 10.0 16.0 District 0.0 6.0 10.0 16.0 1.0 7.0 10.0 18.0 (4) (3) (2) 49.0 Fringe 4.0 10.0 35.0 49.0 4.0 10.0 35.0 49.0 6.0 12.3 35.0 53.3 Residential (4) (2) (2) 8.4 18.5 97.0 123.9 10.8 26.0 92.5 129.3 44.3 22.5 97.0 163.8 (4) (3) (2) Outlying 1.0 19.3 8.0 28.3 Business 1.0 19.3 8.0 28.3 District 3.0 19.3 8.0 30.3 Total 13.4 53.8 150.0 217.2 15.8 61.3 145.5 222.6 54.3 61.1 150.0 265.4 ___________________________ Note: Assumes 10% Peak Hour Factor and Level-of- Key Service E (Absolute Capacity). (0) Estimated Average No. of Lanes *Arterials are assumed to be most accurate-0.0 1964 Linear Miles ly represented by the "Two-Way Without Park0.0 1975 of this type ing CUTS Classification--half with signal 0.0 1990 of highway. progression, half without. ** Collectors are assumed to be most accurately represented by the "Two-Way With Parking CUTS Classification--with no progression. SOURCE: U.S. DOT (1974) PennDOT (1971) 301 where: _ t = average trip duration in minutes, and P = study area population in thousands of persons. Average Trip Frequency Equation: _ _ Y - 1.262 + 6.591 X where: _ Y = average number of daily trips per dwelling unit, and _ X = average auto ownership per dwelling unit. Demand Elasticities A set of demand elasticities is extracted from the medium/core- concentrated cell of the tabulation (which came from New Bedford, Mass.). Although the geographical locations of Reading (an interior city) and New Bedford (a port city) are different, both share similar urban size and urban structure. In 1970 the former had a population of 88,000 in central city and 296,000 in SMSA; while the latter had a population of 101,000 in central city and 153,000 in SMSA. Demand elasticities, which are calibrated by a 1963 New Bedford sample (Atherton and Ben-Akiva 1976) were tabulated in Chapter III and selected for use in-the 1964 Reading study. The data have been further transformed from work trip to overall trip elasticities. It should be borne in mind that since this case study is to demonstrate the application of the generic parameters to only auto demand forecasting, the cross-elasticities will not be used. Values of Travel Time The value of time, which is necessary for the aggregation procedure, is obtainable from New Bedford through its set of modal-split elasticities: linehaul time equal to 27 percent and excess time equal to 65 percent of the hourly earning rate. When these figures are transferred to Reading, the values of linehaul tim e and excess time are $0.46/hour, $1.02/hour for 1958 and $.69/hour, $1.52/hour for 1964 respectively. Supply Curve The data for deriving aggregate supply curve is the classification of various components of the highway system by their functional classes and their location within the urban area. Figure A-7-3 shows that the existing base year and recommended forecast year Reading networks are divided into three composite categories: expressways, arterials, and collectors. These roadway 302 types are further differentiated by their location within the central business district, fringe, residential or outlying business district. As discussed in Chapter IV, the derivation of an aggregate supply curve over an entire urban area is a difficult task. There are two principal factors which prohibit an absolute specification of the curve using the simple procedure devised during the conduct of. this piece of research. First., average trip lengths tend to change over time as population increases, reflecting changes in the travel patterns within the urban area. Second, as overall travel increases, the distribution of trips between the different types of highway facilities can occur in an infinte number of ways, which means that the aggregate supply curve can only be interpreted as the average performance function of the transportation system. Both of these difficulties are reflected in the intricacies involved in determining the aggregate supply curve. At this point we will use the base year trip length, and attempt to plot an aggregate supply curve under base year conditions. E. 1964 Forecast by Updating 1958 Conditions To forecast the areawide travel for 1964, one begins with updating the generic parameters using the 1958 data. Average Trip Duration According to the se lected trip duration equation, average trip duration in 1958 can be computed as: _ t = -3.748 + 2.134 x 4.953 = 6.83 minutes. Comparing the forecasted value of 6.83 minutes with the observed value of 7.49 minutes, one can see that the equation has underestimated the average trip duration for Reading in 1958. The equation may be updated by adjusting the constant of the equation, which represents unobserved factors not explained by the bivariate equation. When the observed trip duration of 7.49 minutes is used to adjust the constant term of the average trip duration equation, the updated equation becomes: _ t = -3.08 + 2.134 1n P. This equation can be further verified by the 1964 Reading data which covers the 1958 study area (refer to Table A-7-1): 303 _ t = -3.08 + 2.134 1n P = 7.45. Since the inventory of the highway system for the 1958 study area cannot be obtained, the base year supply curve cannot be determined. To overcome this problem, the average trip duration forecasted by DAP will be adjusted according to the effect of highway improvement. As shown in Table A-7-1, the level of highway improvements in 1964 was about 2.4 percent. The value oft after being adjusted by 2.4 percent becomes 7.27 minutes. Trip Frequency Equation To examine the transferability of the trip frequency equation, we start with the 1958 and 1964 data. In 1958 the auto ownership was .86 cars per dwelling unit. The average number of daily trips per dwelling unit is estimated from this figure via the trip frequency equation: _ Y = 1.262 + 6.591 x .86 = 6.93. Correspondingly, the total person trips amounts to 6.93 x 47,597 = 329,847, which is double that of the actual trips made at that time, indicating the necessity for updating. To make the cross-cell equation more site-specific it is updated to be: _ _ Y = -2.581 + 6.591 X. The updated equation shows a trip frequency of 4.01 trips per dwelling unit, which sums up to be: 4.01 x 47,965 192,244 trips over the study area. Since only the predominant mode is analyzed in the current case study, the auto trips are obtained from the above figure using the reported modal split of .927 192,244 x .927 = 178,210 trips. Trip Impedance Since both time and cost are components of the level-of-service, an exact demand forecasting procedure must consider all the time and cost factors associated with a trip. Toward this end, the linehaul time, excess time and cost of an average trip will be aggregated into a "trip impedance" (in dollar value). This aggregation involves summarizing all operating expenses to trip-makers for auto use. The cost per person per trip is shown as $0.17, while the total trip time is valued at $0.06, adding up to the total impedance of $0.230. 304 Demand Curve The first part of this study is to verify the temporal transferability of DAP parameters against the 1964 actual traffic counts. Toward this end, the impedance elasticity of demand according to an aggregation procedure must be derived. The aggregation involves combining the time and cost elasticities by weights: n x (trip cost) + n (excess time) + n x (linehaul time) cost excess impedance linehaul impedance = -------------------------------------------------------------------- ------ total trip impedance -0.22 (0.17) -0.35 (0.0) -0.15 (0.05) = ---------------------------------------- 0.23 -0.0477 = ------------------ = 0.20. .23 Since only the auto mode is involved, this impedance elasticity is also the composite elasticity. Using the elasticity n, one can determine the slope of the 1964 demand curve in Reading. Substituting = 0.20, V = 178,210 and I = 0.23, the resulting slope is: -0.20 (178,210) S = ---------------------- = 154,965 nt 155,000 trips/dollar. 0.23 With this slope of the demand segment, the induced demand corresponding to change of LOS can be forecasted. The change of impedance from 1958 to 1964 was $0.005 (corresponding to a 2.5 percent LOS improvment in the highway system). The induced demand computed in this manner is: V = 155,000 x 0.005 = 775 trips. The total forecasted trips for 1964 by DAP = 178,210 + 775 = 179,000 trips. The results of DAP are tabulated with the actual traffic counts as follows: Total Trips Average Trip Duration Actual 182,700 7.65 Forecasted 179,000 7.27 Difference 3,700 (2.0%) 0.38 (4.97%) Comparing the DAP forecasts with the actual counts, it shows that a simplified version of DAP (without the supply curves) can forecast the Reading traffic for 1964 with a high degree of accuracy. Since the elasticities are estimates from New Bedford from a different time period, these results suggest that the generic parameters are transferable both temporally and spatially. 305 F. 1975 and 1990 Forecast by Updating 1964 DAP Relationships To forecast the demand for the 1975 and 1990 study area of 84 square miles, one begins with the updat ing of parameters using the 1964 data. Trip Duration In updating average trip duration we use the 1964 population of 178,275, that is: _ t = 3.748 + 2.134 1n 178.3 = 3.748 + 2.134 x 5,183 = 7.3 minutes. The average trip duration was 9.1 minutes, therefore the equation is updated as: _ t = -1.948 + 2.134 1n P. With this modified average trip duration equation one can predict the 1975 trip duration with population of 191,774: _ t = -1.948 + 2.134 x 5.256 = 9.3. 75 It is expected that the average trip duration will be 9.3 minutes without highway improvements. Similarly, the updated trip duration equation can be used to forecast the 1990 trip duration with population of 206,136: _ t = -1.948 + 2.134 x 5.329 = 9.4. 90 When the highway system remains constant, the average trip duration is expected to change from 9.1 minutes in 1964 to 9.3 minutes in 1975 and 9.4 minutes in 1990. Trip Frequency Based on the 1964 auto ownership of 1.0 autos per dwelling unit, the number of trips per dwelling unit can be computed by: _ _ Y = 1.262 + 6.591 X = 7.853. With 7.853 trips per dwelling unit, the total number of trips made in 1964 can be estimated as 7.853 x 68,820 = 501,178. The actual auto trips in 1964 was 348,000. Considering that the auto modal split is 92.7 percent, the total trips in 1964 was 375,400. Therefore, the equation is updated to be: _ Y = -1.136 + 6.591 X. 306 Using the above equation and 1.1 autos/dwelling unit for 1975, 1.3 autos/dwelling unit for 1990, the number of trips per dwelling unit for 1975 and 1990 are forecasted to be: _ Y = -1.136 + 6.591 x 1.1 = 6.114 75 _ Y = -1.136 + 6.591 x 1.3 = 7.432. 90 With the number of trips/dwelling unit = 6.114 and the number of dwelling units = 68,820 for 1975 and the number of trips/dwelling unit = 7.428 and the number of dwelling units = 75,443 for 1990, we obtain 397,000 auto trips for 1975 and 528,750 auto trips for 1990, as resulting from changes in socioeconomic variables only. It is noted that the auto modal share is 93.7 percent for 1975 and 94.3 percent for 1990. Supply Curve The next step of DAP is to derive travel impedance so that supply curves for base year and forecast years can be developed. As demonstrated in previous case studies, a supply curve is determined by three points: the point denoting the current traffic and service values, the point corresponding to V/C = 0.00 and the point with V/C = 1.0. To find both end points of a supply curve we need to compute T-capacity and average network speeds with the following equations: , A-capacity (VMT) T - capacity = ----------------- Avg. Trip Length A-capacity in terms of VMT Average Network Speed = --------------------------- A-capacity in terms of VHT Average Trip Length Average Trip Duration = ----------------------- Average Network Speed With the data shown in Table A-7-2 the supply curves can now be developed. At point V/C = 1.0, there are 1,000,000 trips in 1964, 1,044,000 in 1975, and 1,500,000 trips in 1990. We can plot points G.m and G.0 on Figure A-7-4 respectively. With the service volume 348,000 trips and impedance $0.426, point E.1 can be located in the same figure. Since all points G.0, G.m , and E.1 are approximately on the straight line, a supply curve f.64 (.) with a "best-fit" straight line can be drawn. For the 1975 supply curve f.75 (.) and 1990 supply curve f.90 (.), points G.m and G.0 are simply connected. Similar to the 1964 supply curve, the 1975 and 1990 curves will pass the actual equilibrium point. 307 TABLE A-7-2. DATA BASE OF SUPPLY CURVES 1964 1975 1990 A-capacity (VMT) V/C = 0.0 3,359,800 3,508,900 5,247,600 V/C = 1.0 3,359,800 3,508,900 5,247,600 A-capacity (VHT) V/C = 0.0 121,648 125,552 164,927 V/C = 1.0 210,000 217,095 267,231 Average Trip Length (miles) 3.36 3.36 3.36 T-capacity (No. of Daily Trips) V/C = 0.0 0 0 0 V/C = 1.0 1,000,000 1,044,000 1,562,000 Estimated Service Volume 348,000 397,000 528,460 Average System Speed (Miles/Hr) V/C = 0.0 27.6 28.0 31.8 V/C = 1.0 16.0 16.2 19.6 Average Trip Duration (minutes) V/C = 0.0 7.3 7.2 6.3 V/C = 1.0 12.6 12.4 10.3 Service Value (1964 System) 9.1 9.3 9.4 Impedance (1964 Dollar Values) V/C = 0.0 $0.426 $0.426 $0.424 V/C = 1.0 0.484 0.483 0.457 Service Value (1964 System) 0.446 0.447 0.447 Cost Per Person 0.341 Cost of Travel Time 0.105 308 Demand Curve Before the induced demand can be predicted the demand curve must be plotted. The demand curve can be derived from the impedance elasticity which takes into consideration both travel time and travel cost: -0.25 (0.105) 0.59 (0.00) -0.32 (0.34) = ------------------------------------------------- 0.446 = -0.302, Given = -0.302, V = 348,000 and I = 0.446, the slope of the demand curve segment for 1964 is, therefore: -.302 (348,000) S = ---------------------- = 235,641 236,000 trips/impedance. 64 0.446 The demand curve segment .64 (.) through the equilibrium point E.1 is sketched in Figure A-7-4. According to the trip frequency equation, the passenger travel for Reading is 397,000 auto trips in 1975 and will be 528,750 in 1990. These travel figures are forecasted with the assumption that the highway system remains the same during the 1964-1990 period. Therefore, one can locate the equilibrium points E.2 and E.4 on the supply curve f.64 (.) with V equals 397,000 and 528,750 respectively. Through these two points one can draw the 1975 and 1990 demand curves .75 and .90 according to these slopes (see Figure A-7-4): -.302 (397,000) S = ---------------- = -207,024 75 .449 -267,000 trips/impedance -.302 (528,750) S = ----------------- = -347,895 90 .459 -348,000 trips/impedance. The predicted demand is 397,300 trips for 1975 and 536,000 trips for 1990. When the trip frequency equation is updated by 1975 data, the 1990 forecast will be 566,000 trips. A comparison of the final forecasts with those estimated by the frequency evaluation shows that the induced demand corresponding to highway improvements is 260 trips for 1975 and 7,700 trips (or 8,000 trips by using 1975 updated DAP) for 1990. The 309 Click HERE for graphic. FIGURE A-7-4. CALIBRATION OF DAP IN 1964 AND 1990 310 TABLE A-7-3. COMPARISON OF FORECASTS WITH ACTUAL TRAFFIC COUNT Click HERE for graphic. ___________________________ NA = Data not available or not applicable. * The vehicle occupancy and average trip length are 1. 045 persons/vehicle and 4.03 miles. These figures are derived from the 1975 forecast made by traditional methods. ** Numbers in parentheses are based on the 1975 updated DAP. 311 impedance forecasted for 1990, on the other hand, is $0.437. When thisimpedance is converted to travel time, the average trip duration will be 8.6 minutes. The comparison of forecasts made between DAP and traditional methods and the actual traffic counts are in Table A-7-3, which indicates a mixed result. For the 1975 forecast the DAP has underestimated 60 percent while the traditional method overestimated 2.3 percent. For the 1990 trip demand the DAP forecasts were 7.2 percent higher than the forecast made by traditional methods. On the other hand, for average trip duration the DAP forecast is 0.2 minutes lower than that of the traditional method. Some of these differences are due to the assumption of constant trip length during the 1964-1975 and 1964-1990 periods. From this comparison, it seems that the traditional method has underestimated the demand for 1990 in the Reading case. However, since these figures are comparable, in general, the spatial and temporal transferability of DAP is therein demonstrated by this case study. G. An Assessment In this case study, it has been found that the "cell-specific" base- condition equation of average trip duration, which was developed in accordance with the city classification scheme, can forecast travel time with a high degree of accuracy. In the case where the development of a supply curve according to system improvement is impossible, the use of trip duration to estimate the improvement in the change in the level-of- service is suggested. This is illustrated in the 1958-1964 forecast. The application of the cross-cell trip-frequency equation to the 1958 and 1964 study area has overestimated the auto travel in both cases. However, as shown in the 1958 observation after the constant term of the base-condition equation was updated to become site-specific, the equation could forecast the 1964 demand with accuracy. This indicates that-while cross-cell frequency equation appears too general, the site- specific update renders it transferable. The demand elasticity is shown to be transferable temporally and spatially. There is one reason for the updating of demand slope with respect to travel impedance and volume. It is to account for the differences between the base condition under which the elasticity was calibrated and that 312 where it is applied. with the updating of the demand parameters, DAP can effectively forecast the 1964 demand from the 1958 data base. Using the trip frequency equation and the slope of the demand curve as updated in 1964, the researchers made the 1975 and 1990 demand forecasts for Reading, where the base data of the number of dwelling units and number of autos per dwelling unit used in DAP are the same as those used in the traditional approach. The results show that in 1975 the traffic forecasted by DAP is 6 percent lower than the actual traffic counts. While comparing forecasts made by DAP with those made by the traditional method, it shows that the volume of trips forecasted by DAP is 8.8 percent lower in 1975, but 7.2 percent higher in 1990. By using the parameters as updated in 1975, the difference between the two forecasts is 13.2 percent. This case study verifies the spatial and temporal transferability of the tabulated parameters through the use of DAP. It also demonstrates the applicability of DAP as a tool for demand forecasting. Although the parameters are primarily compiled for "quick-turnaround" analysis, this case study shows that their use in demand forecasting does not only save a great deal of time and money, but also results in an accurate forecast. 313 APPENDIX 8: HOUSEHOLD, ZONAL, VS. AREAWIDE ELASTICITIES Demand elasticities can be classified as zonal or household according to the type of demand model from which they are calibrated. Zonal elasticities are generally obtained from direct demand models, while household elasticities are derived from disaggregate demand models. Many of the direct demand models were calibrated on aggregate zonal- level data. These models implicitly assume that intrazonal travel behavior is homogeneous, while in actuality, there is possibly more variation of travel behavior (particularly in terms of modal choice) within zones than between zones. The use of aggregate zone-to-zone data fails to extract a good deal of the variational information from the constituent observations that usually are obtained to generate the zonal aggregates. On the other hand, the disaggregate models, which use individual trips (or household trips) as the unit of analysis, are able to tap an extremely rich source of variation. The current study recognizes that differences exist between elasticities derived from the direct-demand models and elasticities calibrated by disaggregate models. Moreover, since the thrust of this study is to forecast areawide travel, areawide elasticity and its relationship to household and zonal elasticities will also be discussed. A. Household Elasticities Household elasticities are usually derived from logit models of the following form: R X e m mt P(m,t) = ------------- j = 1, 2, . . . m, . . . n (A-8-1) n R X j=1 j jt e where: P(m,t) = probability of mode m being taken by subject (or household) t, X.mt = vector of level-of-service and socioeconomic characteristics of mode m for subject (or household) t, and R.j = estimated vector of coefficients for the level-of- service and socioeconomic variables. 314 Elasticities can be shown to be: (m, X , t) = [1-P(m,t)]R X (A-8-2) m x mt where: (m, X.m, t) = elasticity for mode m with respect to attribute X.m for subject (or household) t for a given destination and given that a trip will be made, R.x = estimated coefficient for level-of-service X, and X.mt = level-of-service vector of mode m, by subject (or household) t for a given destination. B. Areawide Elasticities There are mathematical relationships between household and areawide elasticities. Recall that the elasticity for subject (or household) t is (according to Equation A-8-1): (m,X ,t) = [1-P(m,t)]R X m x mt The demand elasticity aggregated over N subjects in an urban area is correspondingly: N P(m,t)[1-P(m,t)]R X t=1 x mt (m, X ) = ----------------------------- (A-8-3) N P(m,t) t=1 The above equation can also be derived in a different way (Warner 1962). _ Let us define P.m as the average market share of mode m for an urban area with a population N, that is: _ 1 N P = --- P(m,t). (A-8-4) m N t=1 _ We proceed to differentiate P.m with respect to X.m Click HERE for graphic. 315 Click HERE for graphic. 316 R X 1 r _ _ x mk = --- N P(m,k)[1-P(m,k)] -------- (A-8-9) N k=1 k _ P m The reader is reminded once again that the above relationship is obtained based on the assumption of homogeneous households within a zone. D. A Comparison For the k.th zone, one can compute the difference between the approximation of (A-8-9) and the theoretical definition for elasticity (Equation A-8-7), and show that the result is: R X N x mk k ------ { N P(m,k)[1-P(m,k)] - P(m,k,t)[1-P(m,k,t)] } _ k t=1 NP m R X N x mk k = ------- { [P(m,k,t) ] - N [P(m,k] _ t=1 k NP m R X x mk = ------- N . (A-8-10) _ k k NP m where .k is the variance of P(m,k,t) in zone k. The difference between an elasticity derived from an aggregate model (such as a zonal direct- demand model) and a disaggregate model (such as a household logit model) for the k.th zone is therefore: R X x mk = ------- N . (A-8-11) _ k k NP m If is defined as the maximum .k over the zones k = 1, 2, 3 . . . ,r (hence .k ), the inaccuracy of an elasticity estimated from a zonal model is bounded by the inequality N r k ---- R X ---- R X (A-8-12) k=1 _ k x mk _ x mk NP P m _ Since is the squared deviation of P(m,t)s from P.m over the study area, and both P(m,t) and P._.m are between 0 and 1, it seems that should be very small. However, in a case study using a 1965 data sample from Chicago, Warner (1962, p. 65) found that was about .04. 317 What can one say about the estimation error associated with an "average" elasticity for an urban area? To answer this question a comparison can be made between the estimated value according to (A-8-7) and the following estimation which has been corrected by (A-8-12). _ (m, X ) = [(1-P ) - ---] R X . (A-8-13) m m _ x m P m _ Using values of P = .824 and = .04 from Warner's experiment in Chicago, one obtains (m,X ) of (A-8-7) = .176 R X , and m x m (m, X ) of (A-8-13) = .127 R X . m x m The ratio between the two values is: .176 R X direct estimation x m ------------------------ = -------------------- = 1.386. corrected estimation .127 R X x m This shows that the elasticity could be overestimated by as much as 40 percent by an areawide average figure (which assumes homogenous travel behavior among all users in the area). Similarly, a zonal elasticity (which assumes homogeneous travel behaviors among the users in a zone), can overestimate actual elasticities by the ratio of _ _ 1 - P - / P m k m ----------------------- 1 (A-8-14) _ _ 1 - P - / P m k m even after corrections are made on the estimated value according to (A- 8-13). Example values of this ratio were not obtainable however. 318 APPENDIX 9: DEMAND ELASTICITIES VS. MODAL-SPLIT ELASTICITIES Although the concept of elasticity has been applied to the transportation profession for years, our knowledge about the subject is still quite limited. For example, the nature of and difference between two types of elasticities, demand elasticities and modal-split elasticities, are not clearly defined. Demand elasticities are often referred to as those calibrated by direct-demand models using zonal data, while modal-split elasticities are generally referred to as those calibrated by disaggregate models using household data. Are both types of elasticities the same? The answer to this question is yes. Both Domencich and McFadden (1975) share this point of view. It also can be illustrated as follows. A. Examples Take a zonal-level direct-demand model: V = a + b 1n X + c 1n X + d 1n Y (A-9-1) m m n where V = number of zonal trips of mode m m X = level-of-service attribute of mode m m X = level-of-service attribute of a competing mode n n Y = socioeconomic attribute of travelers a,b,c,d = calibration parameters. It can be shown that the demand elasticity implied by this form of equation is: Click HERE for graphic. A modal-split model can be obtained from the direct-demand model of (A- 9-1) by dividing the equation by a given number of total person trips, V: V 1n X 1n X m a m m 1n V P = ----- ----- + b ----- + c ------- + d ---------- (A-9-3) m V V V V V where P is the probability that a traveler will choose mode m. m 319 From such a model, the modal-split elasticity is computed to be: Click HERE for graphic. Comparing the elasticities obtained from direct-demand and modal- split models, one finds that they are identical. Take a household-level disaggregate modal-choice model such as the logit model: R X m mt P(m,t) = ------------ j = 1, 2, . . . ,m, . . ., n: (A-9-7) R X n j jt e J=1 where P(m,t) = probability of mode m being taken by individual t for a given origin and destination; X.mt = vector of level-of-service of mode m and socioeconomic attributes for individual t for a given origin and destination; R.j = vector of calibrated coefficients for the attributes in X.j and, i = index for the modes. The modal-split elasticity with respect to individual t can be computed from the above equation as: (m, X , t) = [1-P(m,t)] R X (A-9-8) m m mt On the other hand, the demand of mode m in a particular market segment with a given population Z is: 320 Click HERE for graphic. 321 Similarly, for a disaggregate modal-split model: Click HERE for graphic. Similar results can be derived for cross elasticities. It is shown, therefore, that the elasticities computed from a general demand model and a modal-split model are equivalent structurally and mathematically. This result allows us to compile a consistent set of elasticities from a variety of calibrations, including direct-demand and logit models. 322 APPENDIX 10: AGGREGATION OF ELASTICITIES The aggregation of elasticities can be divided into several steps. First, the stratification according to trip purposes such as work and nonwork is removed through aggregation. Second, the time and cost elas- ticities are aggregated into an impedance elasticity (by mode), where impedance is the linear combination of time and cost. Finally, these impedance elasticities by mode are again collapsed into a single number called "composite elasticity," which refers to the person-trip travel volume across all the modes. While the first two aggregation procedures are quite adequately explained in Chapter III, the results of the aggregation are often cited for the last step without detailed explanation in the text. This appendix is written to furnish the actual mathematical deviations of the composite elasticities. The development of composite elasticity is to collapse impedance elasticities by mode into a single number (without modal stratification). Since the induced demand of a particular mode, i, is affected by the change of level-of-service of its own and that of its competing modes, the computation of total demand response for mode i has to take both direct and cross demand response into account. Thus: ii ij ji V = V + V - V i not = j (A-10-1) where V.ii is the direct demand response of mode i, V.ij is the demand gain from mode J due to the improvement of its own LOS and V.ji is the demand loss to mode J due to the improvement of LOS in mode J. According to equation (A-10-1), the overall demand response of modes i and j, V, is: i j V = V + V ii jj (A-10-2) = V + V It is to be noted in the above equation that in the aggregation of overall demand, the traffic diversion among modes cancel out. Substituting the definition of elasticity V = (I/I) V in (A-10- 2) for the auto versus transit case, one obtains: A T I A I A T I T ---- V = ------ V + ------ V , (A-10-3) I A T I I 323 where I is the weighted average of the modal impedances, with the modal share serving as weights: A A T T I = I MS + I MS (A-10-4) Combining the above two equations, one obtains: A A A T T T R MS + R MS = ------------------------------ (A-10-5) R A A A T T T where R = I / I , R = I /I and R = I/I. As verified in the case studies (Appendices 5, 6, and 7), the equation can be approximated by: A A T T = MS + MS (A-10-6) A T which implies that R R R. If a more rigorous approach is to be followed, an iterative application of equations (A-10-6) and (A-10-5) is suggested. First, n is approximated by (A-10-6). Second, the demand approximation procedure is applied, resulting in a first approximation of R.A, R.T, and R. Third, these first approximations are substituted into (A-10-5). The process is repeated until a consistent is obtained. 324 U.S. GOVERNMENT PRINTING OFFICE: 1979 630-771/2668 1-3 Click HERE for graphic. Click HERE for graphic. .
