Numerical approximation of continuous traffic congestion equilibria

2009, Volume 4, Issue 3: 605-623. doi: 10.3934/nhm.2009.4.605

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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

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 $\Gamma$-convergence result and numerical results are given.
- traffic congestion,
- Wardrop equilibria,
- eikonal equation,
- subgradient descent,
- Fast Marching Method
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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Abstract

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 $\Gamma$-convergence result and numerical results are given.
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