Abstract
We consider a multi-class multi-mode variable demand network equilibrium model where the mode choice model is given by aggregate hierarchical logit structures and the destination choice is specified as a multi-proportional entropy type trip distribution model. The travel time of transit vehicles depends on the travel time of other vehicles using the road network. A variational inequality formulation captures all the model components in an integrated form. A solution algorithm, based on a Block Gauss-Seidel decomposition approach coupled with the method of successive averages results in an efficient algorithm which successively solves network equilibrium models with fixed demands and multi-dimensional trip distribution models. Numerical results obtained with an implementation of the model with the EMME/2 software package are presented based on data originating from the city of Santiago, Chile.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abrahamsson, T. and Lundqvist, L. (1999). “Formulation and Estimation of Combined Network Equilibrium Models with Applications to Stockholm,” Transportation Science, 33, 1, 80–100.
Beckmann, M., McGuire, C.B. and Winsten, C.B. (1956). Studies in the Economics of Transportation. New Haven, CT: Yale University Press.
Boyce, D. (1998). “Long-Term Advances in the State of the Art of Travel Forecasting Methods”, Equilibrium and Advanced Transportation Modeling, Edited by Marcotte, P. and Nguyen, S., Kluwer Acacemic Publishers.
Dafermos, S. (1980). “Traffic Equilibria and Variational Inequalities,” Transportation Science, 14, 42–54.
Dafermos, S. (1982). “Relaxation Algorithms for the General Asymmetric Traffic Equilibrium Problem,” Transportation Science, 16 (2), 231–240.
ESTRAUS, (1998). Internal report.
Evans, S.P. (1976). “Derivation and Analysis of Some Models for Combining Trip Distribution and Assignment,” Transportation Research, 10, 37–57.
Fernandez, E., De Cea, J., Florian, M. and Cabrera, E. (1994). “Network Equilibrium Models with Combined Modes,” Transportation Science, 3, 182–192.
Fisk, C.S. and Nguyen, S. (1982). “Solution Algorithms for Network Equilibrium Models with Asymmetric User Costs,” Transportation Science, 3, 361–381.
Fisk, C.S. and Boyce, D.E. (1983). “Alternative Variational Inequality Formulations of the Network Equilibrium-Travel Choice Problem,” Transportation Science, 4, 454–463.
Florian, M. (1977). “A Traffic Equilibrium Model of Travel by Car and Public Transit Modes,” Transportation Science, 2, 166–179.
Florian, M., Ferland, J. and Nguyen, S. (1975). “On the Combined Distributed-assignment of Traffic,” Transportation Science, 9, 45–53.
Florian, M. and Nguyen, S. (1978). “A Combined Trip Distribution Modal Split and Trip Assignment Model,” Transportation Research, 12, 241–246.
Florian, M. and Spiess, H. (1982). “The Convergence of Diagonalization Algorithms for Asymmetric Network Equilibrium Problems,” Transportation Research, 16B, 447–483.
Frank, M. and Wolfe, P. (1956). “An Algorithm for Quadratic Programming,” Naval Research Logistics Quarterly, 3, 95–110.
Friesz, T.L. (1981). “An Equivalent Optimization Problem for Combined Multi-class Distribution, Assignment and Modal Split which Obviates Symmetry Restrictions.” Transportation Research, 15B, 5, 361–369.
Garrett, M. and Wachs, M. (1996). Transportation Planning on Trail: The Clean Air Act and Travel Forecasting. Thousand Oaks, CA: Sage Publications.
Lam, W.H.K. and Hai-Jun, H. (1992). “A Combined Trip Distribution and Assignment Model for Multiple User Classes,” Transportation Research, 26B, 4, 275–287.
Oppenheim, N. (1995). Urban Travel Demand Modeling. A Wiley-Interscience Publication, John Wiley & Sons, Inc.
Ortuzar, J. de D. and Willumsen, L.G. (1996). Modeling Transport. John Wiley & Sons, Second Edition.
Pang, J.S. and Chan, D. (1982). “Iterative Methods for Variational and Complementarity Problems,” Mathematical Programming, 24, 284–313.
Safwat, K. and Magnanti, T. (1988). “A Combined Trip Generation, Trip Distribution, Modal Split, and Trip Assignment Model,” Transportation Science, 1, 14–30.
Safwat, K., Nabil, A. and Walton, C.M. (1988). “Computational Experience with an Application of a Simultaneous Transportation Equilibrium Model to Urban Travel in Austin, Texas,” Transportation Research, 22B, 6, 457–467.
Smith, M.J. (1979). “The Existence, Uniqueness and Stability of Traffic Equilibria,” Transportation Research, 13B, 289–294.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Florian, M., Wu, J.H., He, S. (2002). A Multi-Class Multi-Mode Variable Demand Network Equilibrium Model with Hierarchical Logit Structures. In: Gendreau, M., Marcotte, P. (eds) Transportation and Network Analysis: Current Trends. Applied Optimization, vol 63. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6871-8_8
Download citation
DOI: https://doi.org/10.1007/978-1-4757-6871-8_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-5212-7
Online ISBN: 978-1-4757-6871-8
eBook Packages: Springer Book Archive