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Networks and Heterogeneous Media

2009, Volume 4, Issue 3: 605-623. doi: 10.3934/nhm.2009.4.605
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Numerical approximation of continuous traffic congestion equilibria

  • 1.
    CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16
  • 2.
    Université Paris Dauphine, Laboratoire CEREMADE, UMR CNRS 7534, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16
  • Received: 01 March 2009 Revised: 01 June 2009

  • Primary: 49M25, 65K10, 90C25.

  • Starting from a continuous congested traffic framework recently introduced in [8], we present a consistent numerical scheme to compute equilibrium metrics. We show that equilibrium metric is the solution of a variational problem involving geodesic distances. Our discretization scheme is based on the Fast Marching Method. Convergence is proved via a Γ-convergence result and numerical results are given.

    Citation: Fethallah Benmansour, Guillaume Carlier, Gabriel Peyré, Filippo Santambrogio. Numerical approximation of continuous traffic congestion equilibria[J]. Networks and Heterogeneous Media, 2009, 4(3): 605-623. doi: 10.3934/nhm.2009.4.605

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  • Starting from a continuous congested traffic framework recently introduced in [8], we present a consistent numerical scheme to compute equilibrium metrics. We show that equilibrium metric is the solution of a variational problem involving geodesic distances. Our discretization scheme is based on the Fast Marching Method. Convergence is proved via a Γ-convergence result and numerical results are given.


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    2. Filippo Santambrogio, 2015, Chapter 6, 978-3-319-20827-5, 219, 10.1007/978-3-319-20828-2_6
    3. Filippo Santambrogio, 2015, Chapter 7, 978-3-319-20827-5, 249, 10.1007/978-3-319-20828-2_7
    4. Matthieu Bonnivard, Antoine Lemenant, Filippo Santambrogio, Approximation of Length Minimization Problems Among Compact Connected Sets, 2015, 47, 0036-1410, 1489, 10.1137/14096061X
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    7. Azam Asanjarani, A Finsler Geometrical Programming Approach to the Nonlinear Complementarity Problem of Traffic Equilibrium, 2023, 196, 0022-3239, 797, 10.1007/s10957-023-02162-y
    8. F. Benmansour, G. Carlier, G. Peyré, F. Santambrogio, Derivatives with respect to metrics and applications: subgradient marching algorithm, 2010, 116, 0029-599X, 357, 10.1007/s00211-010-0305-8
    9. L. Brasco, M. Petrache, A Continuous Model of Transportation Revisited, 2014, 196, 1072-3374, 119, 10.1007/s10958-013-1644-7
    10. Jean-David Benamou, Optimal transportation, modelling and numerical simulation, 2021, 30, 0962-4929, 249, 10.1017/S0962492921000040
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    13. G. Carlier, F. Santambrogio, A continuous theory of traffic congestion and Wardrop equilibria, 2012, 181, 1072-3374, 792, 10.1007/s10958-012-0715-5
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  • © 2009 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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