Two-Stage Equilibrium Travel Demand Model for Sketch Planning
Abstract
This paper describes a two-stage equilibrium travel demand model. The unique feature of this model is that it takes time-of-day traffic counts instead of land use and demographic data as inputs to derive spatial and temporal travel demand patterns. The first stage of the model is a trip matrix estimator based on traffic count; the second stage is an elastic-demand network flow estimator, which recognizes latent demand shifts while performing mode split, time-of-day split, and traffic assignment in a multilevel equilibration. The main purpose of this paper is to describe model development, algorithm design, and software implementation experiences. An example application illustrates how the model is used to evaluate multiclass, multimode, and multiperiod network flow patterns for sketch planning purposes.
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References
1. Carroll J.D. Jr., and Bevis H. W. Predicting Local Travel in Urban Regions. Papers and Proceedings of the Regional Science Association, Vol. 3, No. 1, 1957, pp. 183–197.
2. Boyce D. E. Forecasting Travel on Congested Urban Transportation Networks: Review and Prospects for Network Equilibrium Models. Networks and Spatial Economics, Vol. 7, No. 2, 2007, pp. 99–128.
3. Sheffi Y., and Daganzo C. F. Computation of Equilibrium over Transportation Networks: The Case of Disaggregate Demand Models. Transportation Science, Vol. 14, No. 2, 1980, pp. 155–173.
4. Safwat K. N. A., and Magnanti T. L. A Combined Trip Generation, Trip Distribution, Mode Split, and Trip Assignment Model. Transportation Science, Vol. 18, No. 1, 1988, pp. 14–30.
5. Beckmann M., Magnanti C.B., and Winsten C. B. Studies in the Economics of Transportation. Yale University Press, New Haven, Conn., 1985.
6. Carey M. The Dual of the Traffic Assignment Problem with Elastic Demands. Transportation Research, Vol. 19B, No. 3, 1985, pp. 227–237.
7. Florian M., Nguyen S., and Ferland J. On the Combined Distribution-Assignment of Traffic. Transportation Science, Vol. 9, No. 1, 1975, pp. 43–53.
8. Evans S. P. Derivation and Analysis of Some Models for Combining Trip Distribution and Assignment. Transportation Research, Vol. 10, No. 1, 1976, pp. 37–57.
9. Erlander S. Efficient Population Behavior and the Simultaneous Choices of Origins, Destinations and Routes. Transportation Research, Vol. 24B, No. 5, 1990, pp. 363–373.
10. Lundgren J.T., and Patriksson M. The Combined Distribution and Stochastic Assignment Problem. Annals of Operations Research, Vol. 82, No. 1, 1998, pp. 309–329.
11. Florian M. A Traffic Equilibrium Model of Travel by Car and Public Transit Modes. Transportation Science, Vol. 11, No. 2, 1977, pp. 166–179.
12. Abdulaal M., and LeBlanc L. J. Methods for Combining Modal Split and Equilibrium Assignment Models. Transportation Science, Vol. 13, No. 4, 1979, pp. 292–314.
13. Fisk C., and Nguyen S. Existence and Uniqueness Properties of an Asymmetric Two-Mode Equilibrium Model. Transportation Science, Vol. 15, No. 4, 1981, pp. 318–328.
14. Aashtiani H.Z., and Magnanti T. L. Equilibria on a Congested Transportation Network. Journal of Algebraic and Discrete Methods, Vol. 2, No. 3, 1981, pp. 213–226.
15. Dafermos S. The General Multimodal Network Equilibrium Problem with Elastic Demand. Networks, Vol. 12, No. 1, 1982, pp. 57–72.
16. Florian M., and Spiess H. On Binary Mode Choice/Assignment Models. Transportation Science, Vol. 17, No. 1, 1983, pp. 32–47.
17. Fernandez E., De Cea J., Florian M., and Cabrera E. Network Equilibrium Models with Combined Modes. Transportation Science, Vol. 28, No. 3, 1994, pp. 182–192.
18. Cantarella G. E. A General Fixed-Point Approach to Multi-Mode Multi-User Equilibrium Assignment with Elastic Demand. Transportation Science, Vol. 31, No. 2, 1997, pp. 107–128.
19. Boyce D.E., and Bar-Gera H. Network Equilibrium Models of Travel Choices with Multiple Classes. In Regional Science in Economic Analysis (Lahr M.L. and Miller R. E., eds.), Elsevier Science, Oxford, United Kingdom, 2001, pp. 85–98.
20. Wu Z.X., and Lam W. H. K. Combined Modal Split and Stochastic Assignment Model for Congested Networks with Motorized and Non-motorized Transport Modes. In Transportation Research Record: Journal of the Transportation Research Board, No. 1831, Transportation Research Board of the National Academies, Washington, D.C., 2003, pp. 57–64.
21. Florian M., and Nguyen S. A Combined Trip Distribution Modal Split and Trip Assignment Model. Transportation Research, Vol. 12, No. 4, 1978, pp. 241–246.
22. Sheffi Y., and Powell W. B. An Algorithm for the Equilibrium Assignment Problem with Random Link Times. Networks, Vol. 12, No. 2, 1982, pp. 191–207.
23. Lam W. H. K., and Huang H. J. A Combined Trip Distribution and Assignment Model for Multiple User Classes. Transportation Research, Vol. 26B, No. 4, 1992, pp. 275–287.
24. Lam W. H. K., and Huang H. J. Calibration of the Combined Trip Distribution and Assignment Model for Multiple User Classes. Transportation Research, Vol. 26B, No. 4, 1992, pp. 289–305.
25. Oppenheim N. Urban Travel Demand Modeling: From Individual Choices to General Equilibrium. John Wiley & Sons, New York, 1995.
26. Friesz T. L. An Equivalent Optimization Problem for Combined Multi-class Distribution, Assignment and Modal Split Which Obviates Symmetry Restrictions. Transportation Research, Vol. 15B, No. 5, 1981, pp. 361–369.
27. Boyce D.E., Chon K.S., Lee Y.J., and Lin K. T. Implementation and Computational Issues for Combined Models of Location, Destination, Mode, and Route Choice. Environment and Planning, Vol. 15A, No. 9, 1983, pp. 1219–1230.
28. Safwat K., Nabil A., and Walton C. M. Computational Experience with an Application of a Simultaneous Transportation Equilibrium Model to Urban Travel in Austin, Texas. Transportation Research, Vol. 22B, No. 6, 1988, pp. 457–467.
29. Slavin H. An Integrated, Dynamic Approach to Travel Demand Modeling. Transportation, Vol. 23, No. 3, 1996, pp. 313–350.
30. Abrahamsson T., and Lundqvist L. Formulation and Estimation of Combined Network Equilibrium Models with Applications to Stockholm. Transportation Science, Vol. 33, No. 1, 1999, pp. 80–100.
31. Boile M.P., and Spasovic L. N. An Implementation of the Mode-Split Traffic-Assignment Method. Computer-Aided Civil and Infrastructure Engineering, Vol. 15, No. 4, 2000, pp. 293–307.
32. Florian M., Wu J.H., and He S. A Multi-Class Multi-Mode Variable Demand Network Equilibrium Model with Hierarchical Logit Structures. In Transportation and Network Analysis: Current Trends (Gendreau M. and Marcotte P., eds.), Kluwer Academic Publishers, Dordrecht, Netherlands, 2002, pp. 119–133.
33. Bar-Gera H., and Boyce D. Origin-Based Algorithms for Combined Travel Forecasting Models. Transportation Research, Vol. 37B, No. 5, 2003, pp. 405–422.
34. Bar-Gera H., and Boyce D. Solving a Non-Convex Combined Travel Forecasting Model by the Method of Successive Averages with Constant Step Sizes. Transportation Research, Vol. 40B, No. 5, 2006, pp. 351–367.
35. Siegel J.D., De Cea J., Fernandez J.E., Rodriguez R.E., and Boyce D. Comparisons of Urban Travel Forecasts Prepared with the Sequential Procedure and a Combined Model. Networks and Spatial Economics, Vol. 6, No. 2, 2006, pp. 135–148.
36. Zhang T., Xie C., and Waller S. T. An Integrated Equilibrium Travel Demand Model with Nested Logit Structure: Fixed-Point Formulation and Stochastic Analysis. In Transportation Research Record: Journal of the Transportation Research Board, No. 2254, Transportation Research Board of the National Academies, Washington, D.C., 2011, pp. 79–96.
37. Boyce D.E., LeBlanc L.J., and Chon K. S. Network Equilibrium Models of Urban Location and Travel Choices: A Retrospective Survey. Journal of Regional Science, Vol. 28, No. 2, 1988, pp. 159–183.
38. Boyce D.E., and Bar-Gera H. Multiclass Combined Models for Urban Travel Forecasting. Networks and Spatial Economics, Vol. 4, No. 1, 2004, pp. 115–124.
39. Boyce D.E., Zhang Y.-F., and Lupa M. R. Introducing “Feedback” into Four-Step Travel Forecasting Procedure Versus Equilibrium Solution of Combined Model. In Transportation Research Record 1443, TRB, National Research Council, Washington, D.C., 1994, pp. 65–74.
40. Yang H., and Huang H. J. The Multi-Class, Multi-Criteria Traffic Network Equilibrium and System Optimum Problem. Transportation Research, Vol. 38B, No. 1, 2004, pp. 1–15.
41. Nguyen S. Estimation of an O-D Matrix from Network Data: A Network Equilibrium Approach. Publication No. 60. Centre de Recherché sur les Transports, Université de Montréal, Montreal, Quebec, Canada, 1977.
42. Turnquist M.A., and Gur Y. Estimation of Trip Tables from Observed Link Volumes. In Transportation Research Record 730, TRB, National Research Council, Washington, D.C., 1979, pp. 1–6.
43. LeBlanc L.J., and Farhangian K. Selection of a Trip Table Which Reproduces Observed Link Flows. Transportation Research, Vol. 16B, No. 2, 1982, pp. 83–88.
44. Fisk C. S. On Combining Maximum Entropy Trip Matrix Estimation with User Optimal Assignment. Transportation Research, Vol. 22B, No. 1, 1988, pp. 69–79.
45. Yang H., Sasaki T., Iida Y., and Asakura Y. Estimation of Origin–Destination Matrices from Link Traffic Counts on Congested Networks. Transportation Research, Vol. 26B, No. 6, 1992, pp. 417–434.
46. Chen A., Chootinan P., and Recker W. Norm Approximation Method for Handling Traffic Count Inconsistencies in Path Flow Estimator. Transportation Research, Vol. 43B, No. 8–9, 2009, pp. 852–872.
47. Nie Y., and Zhang H. M. A Relaxation Approach for Estimating Origin–Destination Trip Tables. Networks and Spatial Economics, Vol. 10, No. 1, 2010, pp. 147–172.
48. Yang H., Iida Y., and Sasaki T. The Equilibrium-Based Origin–Destination Matrix Estimation Problem. Transportation Research, Vol. 28B, No. 1, 1994, pp. 23–33.
49. Sherali H.D., Sivanandan R., and Hobeika A. G. A Linear Programming Approach for Synthesizing Origin–Destination Trip Tables from Link Traffic Volumes. Transportation Research, Vol. 28B, No. 3, 1994, pp. 213–233.
50. Nie Y., and Lee D.-H. Uncoupled Method for Equilibrium-Based Linear Path Flow Estimator for Origin–Destination Trip Matrices. In Transportation Research Record: Journal of the Transportation Research Board, No. 1783, Transportation Research Board of the National Academies, Washington, D.C., 2002, pp. 72–79.
51. Nie Y., Zhang H.M., and Recker W. W. Inferring Origin–Destination Trip Matrices with a Decoupled GLS Path Flow Estimator. Transportation Research, Vol. 39B, No. 6, 2005, pp. 497–518.
52. Xie C., Kockelman K.M., and Waller S. T. Maximum Entropy Method for Subnetwork Origin–Destination Trip Matrix Estimation. In Transportation Research Record: Journal of the Transportation Research Board, No. 2196, Transportation Research Board of the National Academies, Washington, D.C., 2010, pp. 111–119.
53. Xie C., Kockelman K.M., and Waller S. T. A Maximum Entropy-Least Squares Estimator for Elastic Origin–Destination Trip Matrix Estimation. Transportation Research, Vol. 45B, No. 9, 2011, pp. 1465–1482.
54. Frank M., and Wolfe P. An Algorithm for Quadratic Programming. Naval Research Logistics Quarterly, Vol. 3, No. 1–2, 1956, pp. 95–110.
55. Facchinei F., and Pang J. S. Finite-Dimensional Variational Inequalities and Complementarity Problems. Springer-Verlag, New York, 2003.
56. Patriksson M. A Unified Description of Iterative Algorithms for Traffic Equilibria. European Journal of Operational Research, Vol. 71, No. 2, 1993, pp. 154–176.
57. Fisk C., and Nguyen S. Solution Algorithms for Network Equilibrium Models with Asymmetric User Costs. Transportation Science, Vol. 16, No. 3, 1982, pp. 361–381.
58. Sheffi Y. Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods. Prentice-Hall, Englewood Cliffs, N.J., 1985.
59. Mouskos K.C., and Mahmassani H. S. Guidelines and Computational Results for Vector Processing of Network Assignment Codes on Supercomputers. In Transportation Research Record 1251, TRB, National Research Council, Washington, D.C., 1989, pp. 10–16.
60. Kockelman K.M., Xie C., Fagnant D.J., Thompson T., McDonald-Buller E., and Waller S. T. Comprehensive Evaluation of Transportation Projects: A Toolkit for Sketch Planning. Texas Department of Transportation Research Report 0-6235-1. Center for Transportation Research, University of Texas at Austin, 2010.
61. Xie C. Travel Demand Model for the Project Evaluation Toolkit: Program and Data Files. Center for Transportation Research, University of Texas at Austin, 2011.
62. Highway Capacity Manual 2010. Transportation Research Board of the National Academies, Washington, D.C., 2010.
63. Fagnant D. J. Highway Case Study Investigation and Sensitivity Testing Using the Project Evaluation Toolkit. MS thesis. University of Texas at Austin, 2011.
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Article first published online: January 1, 2012
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