In the classical Monge-Kantorovich problem, the transportation cost only depends on the amount of mass sent from sources to destinations and not on the paths followed by each particle forming this mass. Thus, it does not allow for congestion effects, which depend instead on the proportion of mass passing through a same point or following a same path, Usually, the traveling cost (or time) of a path depends on “how crowded” this path is. Starting from a simple network model, we will define equilibria in the presence of congestion. We will then extend this theory to the continuous setting mainly following the recent papers by Brasco, Carlier, and Santambrogio and Carlier, Jimenez, and Santambrogio. After an introduction with almost no mathematical details, we will give a survey of the main features of this theory, Bibliography: 22 titles.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 390, 2011, pp. 69-91.
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Carlier, G., Santambrogio, F. A continuous theory of traffic congestion and Wardrop equilibria. J Math Sci 181, 792–804 (2012). https://doi.org/10.1007/s10958-012-0715-5
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DOI: https://doi.org/10.1007/s10958-012-0715-5