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

Numerical approximation of continuous traffic congestion equilibria

Fethallah Benmansour 1, , Guillaume Carlier 1, , Gabriel Peyré 1, and  Filippo Santambrogio 2,

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.
Keywords: Fast Marching Method., traffic congestion, eikonal equation, subgradient descent, Wardrop equilibria.
Mathematics Subject Classification: Primary: 49M25, 65K10, 90C2.
Citation: Fethallah Benmansour, Guillaume Carlier, Gabriel Peyré, Filippo Santambrogio. Numerical approximation of continuous traffic congestion equilibria. Networks and Heterogeneous Media, 2009, 4 (3) : 605-623. doi: 10.3934/nhm.2009.4.605
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