Numerical approximation of continuous traffic congestion equilibria
Fethallah Benmansour Guillaume Carlier Gabriel Peyré Filippo Santambrogio
Networks & Heterogeneous Media 2009, 4(3): 605-623 doi: 10.3934/nhm.2009.4.605
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: Fast Marching Method. traffic congestion eikonal equation subgradient descent Wardrop equilibria

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