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The Prevalence of Paradoxes in Transportation Equilibrium Problems

Author

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  • Richard Steinberg

    (AT&T Bell Laboratories, Holmdel, New Jersey 07733)

  • Richard E. Stone

    (AT&T Bell Laboratories, Holmdel, New Jersey 07733)

Abstract

Consider a congested transportation network, where the cost along each arc is affine, i.e., consists of a fixed cost plus a variable cost proportional to the flow. We present a new paradox demonstrating that, in a congested transportation network, a sufficiently high increase in the congestion effect along a route can result in the abandonment of a different route having the same origin and destination while the original route continues to be used. We also present a method for testing whether or not the paradox will occur in an arbitrary transportation network by viewing the question as a parametric linear complementarity problem. The new paradox is contrasted with Braess' paradox, and intuition is developed to explain the prevalence of such paradoxes in transportation equilibrium problems.

Suggested Citation

  • Richard Steinberg & Richard E. Stone, 1988. "The Prevalence of Paradoxes in Transportation Equilibrium Problems," Transportation Science, INFORMS, vol. 22(4), pages 231-241, November.
    • Handle: RePEc:inm:ortrsc:v:22:y:1988:i:4:p:231-241
    DOI: 10.1287/trsc.22.4.231
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    Citations

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    Cited by:

    1. Di, Xuan & He, Xiaozheng & Guo, Xiaolei & Liu, Henry X., 2014. "Braess paradox under the boundedly rational user equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 67(C), pages 86-108.
    2. Eyran Gisches & Amnon Rapoport, 2012. "Degrading network capacity may improve performance: private versus public monitoring in the Braess Paradox," Theory and Decision, Springer, vol. 73(2), pages 267-293, August.
    3. Penchina, Claude M., 1997. "Braess paradox: Maximum penalty in a minimal critical network," Transportation Research Part A: Policy and Practice, Elsevier, vol. 31(5), pages 379-388, September.
    4. Yang, Chao & Chen, Anthony, 2009. "Sensitivity analysis of the combined travel demand model with applications," European Journal of Operational Research, Elsevier, vol. 198(3), pages 909-921, November.
    5. Daniel Q. Naiman & Richard E. Stone, 1998. "A Homological Characterization of Q -Matrices," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 463-478, May.
    6. Rapoport, Amnon & Kugler, Tamar & Dugar, Subhasish & Gisches, Eyran J., 2009. "Choice of routes in congested traffic networks: Experimental tests of the Braess Paradox," Games and Economic Behavior, Elsevier, vol. 65(2), pages 538-571, March.
    7. Wei-Hua Lin & Hong K. Lo, 2009. "Investigating Braess' Paradox with Time-Dependent Queues," Transportation Science, INFORMS, vol. 43(1), pages 117-126, February.
    8. Rapoport, Amnon & Mak, Vincent & Zwick, Rami, 2006. "Navigating congested networks with variable demand: Experimental evidence," Journal of Economic Psychology, Elsevier, vol. 27(5), pages 648-666, October.
    9. Yang, Hai, 1997. "Sensitivity analysis for the elastic-demand network equilibrium problem with applications," Transportation Research Part B: Methodological, Elsevier, vol. 31(1), pages 55-70, February.

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