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Equilibria for Networks with Lower Semicontinuous Costs: With an Application to Congestion Pricing

Author

Listed:
  • David Bernstein

    (Department of Civil Engineering and Operations Research, Princeton University, Princeton, New Jersey 08544)

  • Tony E. Smith

    (Department of Regional Science, University of Pennsylvania, Philadelphia, Pennsylvania 19104)

Abstract

Network equilibrium models traditionally rely on the assumption of continuous travel cost functions. However, there are times when this assumption is not appropriate. For example, some proposed congestion pricing schemes make use of discontinuous step-function tolls. Hence, the purpose of this paper is to explore the existence of network equilibria in the presence of discontinuities. In particular it is shown that when such costs are at least lower semicontinuous, a behaviorally meaningful notion of user equilibrium can still be defined which reduces to Wardrop equilibrium in the continuous case. In addition, it is shown that such equilibria are guaranteed to exist under fairly general conditions. Finally, these results are applied to construct a class of lower semicontinuous congestion pricing schemes which ensure the existence of such equilibria.

Suggested Citation

  • David Bernstein & Tony E. Smith, 1994. "Equilibria for Networks with Lower Semicontinuous Costs: With an Application to Congestion Pricing," Transportation Science, INFORMS, vol. 28(3), pages 221-235, August.
    • Handle: RePEc:inm:ortrsc:v:28:y:1994:i:3:p:221-235
    DOI: 10.1287/trsc.28.3.221
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    Cited by:

    1. Robin Lindsey, 2004. "Existence, Uniqueness, and Trip Cost Function Properties of User Equilibrium in the Bottleneck Model with Multiple User Classes," Transportation Science, INFORMS, vol. 38(3), pages 293-314, August.
    2. Wen-Long Jin, 2015. "Advances in Dynamic Traffic Assgmnt: TAC," Networks and Spatial Economics, Springer, vol. 15(3), pages 617-634, September.
    3. Lo, H. & Hickman, M. & Walstad, M., 1996. "An Evaluation Taxonomy For Congestion Pricing," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt80g5s1km, Institute of Transportation Studies, UC Berkeley.
    4. A. de Palma & Y. Nesterov, 1997. "Optimization formulations and static equilibrium in congested transportation networks," THEMA Working Papers 97-17, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    5. Larsson, Torbjörn & Patriksson, Michael, 1999. "Side constrained traffic equilibrium models-- analysis, computation and applications," Transportation Research Part B: Methodological, Elsevier, vol. 33(4), pages 233-264, May.
    6. Olaf Jahn & Rolf H. Möhring & Andreas S. Schulz & Nicolás E. Stier-Moses, 2005. "System-Optimal Routing of Traffic Flows with User Constraints in Networks with Congestion," Operations Research, INFORMS, vol. 53(4), pages 600-616, August.
    7. Cheng, Liang-Chieh & Wang, Heng, 2013. "Modeling User Equilibrium in Microscopic Transportation Simulation," Journal of the Transportation Research Forum, Transportation Research Forum, vol. 52(2).
    8. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2004. "Selfish Routing in Capacitated Networks," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 961-976, November.
    9. Correa, Jose R. & Schulz, Andreas S. & Stier Moses, Nicolas E., 2003. "Selfish Routing in Capacitated Networks," Working papers 4319-03, Massachusetts Institute of Technology (MIT), Sloan School of Management.
    10. Koohyun Park, 2011. "Detecting Braess Paradox Based on Stable Dynamics in General Congested Transportation Networks," Networks and Spatial Economics, Springer, vol. 11(2), pages 207-232, June.

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