Calculus of Variations and Geometric Measure Theory

F. Benmansour - G. Carlier - G. Peyré - F. Santambrogio

Numerical Approximation of Continuous Traffic Congestion Equilibria

created by santambro on 09 Jan 2009
modified on 07 Jul 2009


Published Paper

Inserted: 9 jan 2009
Last Updated: 7 jul 2009

Journal: Net. Het. Media
Volume: 4
Number: 3
Pages: 577 - 604
Year: 2009


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.

Keywords: Wardrop equilibria, Fast Marching Method, subgradient descent, Eikonal equation