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Numerical Approximation of Continuous Traffic Congestion Equilibria

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Date
2009
Link to item file
http://hal.archives-ouvertes.fr/hal-00360796/en/
Dewey
Probabilités et mathématiques appliquées
Sujet
Traffic congestion ; Wardrop equilibria ; Eikonal equation ; subgradient descent ; Fast Marching Method
Journal issue
Networks and Heterogeneous Media
Volume
4
Number
3
Publication date
2009
Article pages
605-623
Publisher
American institute of americal science
DOI
http://dx.doi.org/10.3934/nhm.2009.4.605
URI
https://basepub.dauphine.fr/handle/123456789/1021
Collections
  • CEREMADE : Publications
Metadata
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Author
Peyré, Gabriel
Carlier, Guillaume
Benmansour, Fethallah
Santambrogio, Filippo
Type
Article accepté pour publication ou publié
Abstract (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.

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