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On a mean field game approach modeling congestion and aversion in pedestrian crowds

A. Lachapelle, M.-T. Wolfram in Transportation Research Part B, Volume 15, Issue 10, 2011

In this paper we present a new class of pedestrian crowd models based on the mean field games theory introduced by Lasry and Lions in 2006. This macroscopic approach is based on a micro- scopic model, that considers smart pedestrians who rationally interact and anticipate the future.

This leads to a forward-backward structure in time. We focus on two-population interactions and validate the modeling with simple examples such as self-organization behavior as for in- stance lane formation. Two complementary classes of problems are addressed, namely the case of crowd aversion and the one of congestion.

In both cases we describe the model, build a nu- merical solver (respectively based on optimization formulation and partial differential equations), and finally provide some numerical tests involving complex group behaviors such as symmetry breaking and lane formation.

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