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From discrete to continuous Wardrop equilibria

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  • The notion of Wardrop equilibrium in congested networks has been very popular in congested traffic modelling since its introduction in the early 50's, it is also well-known that Wardrop equilibria may be obtained by some convex minimization problem. In this paper, in the framework of $\Gamma$-convergence theory, we analyze what happens when a cartesian network becomes very dense. The continuous model we obtain this way is very similar to the continuous model of optimal transport with congestion of Carlier, Jimenez and Santambrogio [6] except that it keeps track of the anisotropy of the network.
    Mathematics Subject Classification: Primary: 90C46, 90C35; Secondary: 49N15.

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    G. Carlier, C. Jimenez and F. Santambrogio, Optimal transportation with traffic congestion and Wardrop equilibria, SIAM J. Control Optim., 47 (2008), 1330-1350.doi: 10.1137/060672832.

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    C. Villani, "Topics in Optimal Transportation," Graduate Studies in Mathematics, 58, American Mathematical Society, Providence, RI, 2003.

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    J. G. Wardrop, Some theoretical aspects of road traffic research, Proc. Inst. Civ. Eng., 2 (1952), 325-378.

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