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Numerical Approximation of Continuous Traffic Congestion Equilibria

Peyré, Gabriel; Carlier, Guillaume; Benmansour, Fethallah; Santambrogio, Filippo (2009), Numerical Approximation of Continuous Traffic Congestion Equilibria, Networks and Heterogeneous Media, 4, 3, p. 605-623. http://dx.doi.org/10.3934/nhm.2009.4.605

Type
Article accepté pour publication ou publié
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http://hal.archives-ouvertes.fr/hal-00360796/en/
Date
2009
Nom de la revue
Networks and Heterogeneous Media
Volume
4
Numéro
3
Éditeur
American institute of americal science
Pages
605-623
Identifiant publication
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Auteur(s)
Peyré, Gabriel
Carlier, Guillaume
Benmansour, Fethallah
Santambrogio, Filippo
Résumé (EN)
Starting from a continuous congested traffic framework recently introduced in [Carlier, Jimenez, Santambrogio, 2008], 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.
Mots-clés
Traffic congestion ; Wardrop equilibria ; Eikonal equation ; subgradient descent ; Fast Marching Method