Numerical Approximation of Continuous Traffic Congestion Equilibria
Abstract
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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