Abstract
Progress in formulating, solving and implementing models with multiple user classes that combine several travel choices into a single, consistent mathematical formulation is reviewed. Models in which the travel times and costs on the road network are link flow-dependent are considered; such models seek to represent congestion endogenously. The paper briefly summarizes the origins of this field in the 1950s and its evolution through the development of solution algorithms in the 1970s. The primary emphasis of the review is on the implementation and application of multiclass models. The paper concludes with a brief discussion of prospects for improved solution algorithms.
Similar content being viewed by others
References
Aashtiani, H.Z. and T.L. Magnanti. (1981). “Equilibria on a Congested Transportation Network.” SIAM Journal on Algebraic and Discrete Methods 2, 213–226.
Abdulaal, M. and L.J. LeBlanc. (1979). “Methods for Combining Modal Split and Equilibrium Assignment Models.” Transportation Science 13, 292–314.
Abrahamsson, T. and L. Lundqvist. (1999). “Formulation and Estimation of Combined Network Equilibrium Models with Applications to Stockholm.” Transportation Science 33, 80–100.
Altman, E. and L. Wynter. (2003). “Equilibrium, Games, and Pricing in Transportation and Telecommunications Networks.” Networks and Spatial Economics 4(1), 7–21.
Bar-Gera, H. (2002). “Origin-Based Algorithm for the Traffic Assignment Problem.” Transportation Science 36, 398–417.
Bar-Gera, H. and D. Boyce. (2003). “Origin-Based Algorithms for Combined Travel Forecasting Models.” Transportation Research 37B, 405–422.
Beckmann, M., C.B. McGuire, and C.B. Winsten. (1956). Studies in the Economics of Transportation. New Haven: Yale University Press.
Boyce, D.E. (1984). “Network Models in Transportation/Land Use Planning.” In M. Florian (ed.), Transportation Planning Models. Amsterdam: North-Holland, pp. 475–498.
Boyce, D.E. (1990). “Network Equilibrium Models of Urban Location and Travel Choices: A New Research Agenda.” In M. Chatterji and R.E. Kuenne (eds.), New Frontiers in Regional Science. New York: Macmillan, pp. 238–256.
Boyce, D. (1998). “Long-Term Advances in the State of the Art of Travel Forecasting Methods.” In P. Marcotte and S. Nguyen (eds.), Equilibrium and Advanced Transportation Modelling. Dordrecht: Kluwer, pp. 73–86.
Boyce, D. and H. Bar-Gera. (2001). “Network Equilibrium Models of Travel Choices with Multiple Classes.” In M.L. Lahr and R.E. Miller (eds.), Regional Science Perspectives in Economic Analysis. Amsterdam: Elsevier Science, pp. 85–98.
Boyce, D. and H. Bar-Gera. (2003). “Validation of Urban Travel Forecasting Models Combining Origin-Destination, Mode and Route Choices.” Journal of Regional Science 43, 517–540.
Boyce, D.E., K.S. Chon, Y.J. Lee, K.T. Lin, and L.J. LeBlanc. (1983). “Implementation and Computational Issues for Combined Models of Location, Destination, Mode and Route Choice.” Environment and Planning A 15, 1219–1230.
Boyce, D.E. and M.S. Daskin. (1997). “Urban Transportation.” In C. ReVelle and A. McGarity (eds.), Design and Operation of Civil and Environmental Engineering Systems. New York: Wiley, pp. 277–341.
Boyce, D.E., L.J. LeBlanc, and K.S. Chon. (1988). “Network Equilibrium Models of Urban Location and Travel Choices: A Retrospective Survey,” Journal of Regional Science 28, 159–183.
Boyce, D. and Y. Zhang. (1998). “Parameter Estimation for Combined Travel Choice Models.” In L. Lundqvist, L.-G. Mattsson and T.J. Kim (eds.), Network Infrastructure and the Urban Environment. Berlin: Springer, pp. 177–193.
Dafermos, S.C. (1972). “The Assignment Problem for Multiclass-User Transportation Networks,” Transportation Science 6, 73–87.
de Cea, J. and J.E. Fernandez. (2001). “ESTRAUS: A Simultaneous Equilibrium Model to Analyze and Evaluate Multimodal Urban Transportation Systems with Multiple User Classes,” In Proceedings of the Ninth World Conference on Transport Research. Seoul, Korea.
de Cea, J., J.E. Fernandez, V. Dekock, A. Soto, and T.L. Friesz. (2003). “ESTRAUS: A Computer Package for Solving Supply-Demand Equilibrium Problems on Multimodal Urban Transportation Networks with Multiple User Classes.” Presented at the Annual Meeting of the Transportation Research Board, Washington, D.C.
Evans, S.P. (1976). “Derivation and Analysis of Some Models for Combining Trip Distribution and Assignment.” Transportation Research 10, 37–57.
Florian, M. (1977). A Traffic Equilibrium Model of Travel by Car and Public Transit Modes.” Transportation Science 11, 166–179.
Florian, M. and S. Nguyen. (1978). “A Combined Trip Distribution, Modal Split and Trip Assignment Model.” Transportation Research 12, 241–246.
Florian, M., J.H. Wu, and S. He. (2002). “A Multi-Class Multi-Mode Variable Demand Network Equilibrium Model with Hierarchical Logit Structures. In M. Gendreau and P. Marcotte (eds.), Transportation and Network Analysis: Current Trends. Dordrecht: Kluwer, pp. 119–133.
Frank, C. (1978). “A Study of Alternative Approaches to Combined Trip Distribution-Assignment Modeling.” Ph.D. Thesis, Regional Science, University of Pennsylvania, Philadelphia.
Friesz, T.L. (1981). “An Equivalent Optimization Problem for Combined Multiclass Distribution, Assignment and Modal Split which Obviates Symmetry Restrictions.” Transportation Research 15B, 361–369.
Lam, W.H.K. and H.-J. Huang. (1992a). “A Combined Trip Distribution and Assignment Model for Multiple User Classes.” Transportation Research 26B, 275–287.
Lam, W.H.K. and H.-J. Huang. (1992b). “Calibration of the Combined Trip Distribution and Assignment Model for Multiple User Classes.” Transportation Research 26B, 289–305.
Lam, W.H.K. and H.-J. Huang. (1994). “Comparison of Results of Two Models of Transportation Demand in Hong Kong: CDAM and a Version of MicroTRIPS.” Journal of Advanced Transportation 28, 107–126.
LeBlanc, L.J. and M. Abdulaal. (1982). “Combined Mode Split-Assignment and Distribution-Mode Split-Assignment with Multiple Groups of Travelers.” Transportation Science 16, 430–442.
LeBlanc, L.J. and K. Farhangian. (1981). “Efficient Algorithms for Solving Elastic Demand Traffic Assignment Problems and Mode-Split Assignment Problems.” Transportation Science 15, 306–317.
Murchland, J.D. (1970). “Road Network Traffic Distribution in Equilibrium.” Mathematical Models in the Social Sciences 8, Meisenheim am Glan, Germany: Anton Hain Verlag, pp. 145–183 (German translation).
Oppenheim, N. (1995). Urban Travel Demand Modeling, New York: Wiley.
Ortúzar, J.D. and L.G. Willumsen. (2001). Modelling Transport, 3rd ed. New York: Wiley.
Patriksson, M. (1994). The Traffic Assignment Problem: Models and Methods. Utrecht: VSP.
Patriksson, M. (2003). “Algorithms for Computing Traffic Equilibria.” Networks and Spatial Economics 4(1), 23–38.
Resource Systems Group, Inc. (1997). “Route 53 Alternatives Study, Lake County Model Description,” Environmental Law and Policy Center, Chicago.
Safwat, K.N.A. and T.L. Magnanti. (1988). “A Combined Trip Generation, Trip Distribution, Modal Split, and Trip Assignment Model,” Transportation Science 22, 14–30.
Sheffi, Y. (1985). Urban Transportation Networks. Englewood Cliffs: Prentice-Hall.
van Vliet, D., T. Bergman, and W.H. Scheltes. (1986) “Equilibrium Traffic Assignment with Multiple User Classes,” In Proceedings, PTRC Summer Annual Meeting. PTRC Education and Research Services Ltd, London, pp. 111–121.
Wardrop, J.G. (1952). “Some Theoretical Aspects of Road Traffic Research.” Proceedings of the Institution of Civil Engineers, Part II 1, 325–378.
Williams, H.C.W.L. (1977). “On the Formation of Travel Demand Models and Economic Evaluation Measures of User Benefit.” Environment and Planning A 9, 285–344.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Boyce, D., Bar-Gera, H. Multiclass Combined Models for Urban Travel Forecasting. Networks and Spatial Economics 4, 115–124 (2004). https://doi.org/10.1023/B:NETS.0000015659.39216.83
Issue Date:
DOI: https://doi.org/10.1023/B:NETS.0000015659.39216.83