# American Institute of Mathematical Sciences

2009, 4(3): 605-623. doi: 10.3934/nhm.2009.4.605

## Numerical approximation of continuous traffic congestion equilibria

 1 CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France, France, France 2 Université Paris Dauphine, Laboratoire CEREMADE, UMR CNRS 7534, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16

Received  March 2009 Revised  June 2009 Published  July 2009

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