Numerical approximation of continuous traffic congestion equilibria
Fethallah Benmansour - CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, France (email)
Abstract: Starting from a continuous congested traffic framework recently introduced in , 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.
congestion, Wardrop equilibria, eikonal equation, subgradient
descent, Fast Marching Method.
Received: March 2009; Revised: June 2009; Published: July 2009.
2010 Impact Factor.909