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On the Existence of Equilibria in Asymmetrical Multiclass-User Transportation Networks

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  • D. Braess

    (Ruhr Universität Bochum, Bochum, West Germany)

  • G. Koch

    (Ruhr Universität Bochum, Bochum, West Germany)

Abstract

When studying multiclass-user transportation networks Dafermos made a strong assumption on symmetry in order to prove existence of a user-optimizing flow pattern. In this paper existence is proved without the symmetry-hypothesis and it is shown that the methods of convex programming are not applicable.

Suggested Citation

  • D. Braess & G. Koch, 1979. "On the Existence of Equilibria in Asymmetrical Multiclass-User Transportation Networks," Transportation Science, INFORMS, vol. 13(1), pages 56-63, February.
    • Handle: RePEc:inm:ortrsc:v:13:y:1979:i:1:p:56-63
    DOI: 10.1287/trsc.13.1.56
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    Cited by:

    1. Anna Nagurney & David Boyce, 2005. "Preface to “On a Paradox of Traffic Planning”," Transportation Science, INFORMS, vol. 39(4), pages 443-445, November.
    2. Watling, David, 1996. "Asymmetric problems and stochastic process models of traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 30(5), pages 339-357, October.
    3. A. Wang & I. Ziedins, 2018. "Probabilistic selfish routing in parallel batch and single-server queues," Queueing Systems: Theory and Applications, Springer, vol. 88(3), pages 389-407, April.
    4. Farokhi, Farhad & Johansson, Karl H., 2015. "A piecewise-constant congestion taxing policy for repeated routing games," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 123-143.
    5. Meneguzzer, Claudio, 1995. "An equilibrium route choice model with explicit treatment of the effect of intersections," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 329-356, October.
    6. Mehr, Negar & Li, Ruolin & Horowitz, Roberto, 2021. "A game theoretic macroscopic model of lane choices at traffic diverges with applications to mixed–autonomy networks," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 45-59.
    7. Watling, David, 1998. "Perturbation stability of the asymmetric stochastic equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 32(3), pages 155-171, April.

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