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.Download publication