Numerical approximation of continuous traffic congestion equilibria

Pages: 605 - 623, Volume 4, Issue 3, September 2009

doi:10.3934/nhm.2009.4.605       Abstract        Full Text (2614.8K)       Related Articles

Fethallah Benmansour - CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France (email)
Guillaume Carlier - CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France (email)
Gabriel Peyré - CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France (email)
Filippo Santambrogio - Université Paris Dauphine, Laboratoire CEREMADE, UMR CNRS 7534, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16, France (email)

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.

Keywords:  traffic congestion, Wardrop equilibria, eikonal equation, subgradient descent, Fast Marching Method.
Mathematics Subject Classification:  Primary: 49M25, 65K10, 90C25.

Received: March 2009;      Revised: June 2009;      Published: July 2009.