Numerical Approximation of Continuous Traffic Congestion Equilibria

Fethallah Benmansour (1) , Guillaume Carlier (1) , Gabriel Peyré (1) , Filippo Santambrogio (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Starting from a continuous congested traffic framework recently introduced by two of the authors together with C. Jimenez and generalizing Wardrop's approach on networks, 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 and numerical results are given.

Domaines: Optimisation et contrôle [math.OC]

Fethallah Benmansour, Guillaume Carlier, Gabriel Peyré, Filippo Santambrogio. Numerical Approximation of Continuous Traffic Congestion Equilibria. 2009. ⟨hal-00360970⟩