Mean-field type modeling of nonlocal crowd aversion in pedestrian crowd dynamics

We extend the class of pedestrian crowd models introduced by Lachapelle and Wolfram [Transp. Res. B: Methodol., 45 (2011), pp. 1572–1589] to allow for nonlocal crowd aversion and arbitrarily but finitely many interacting crowds. The new crowd aversion feature grants pedestrians a “personal space” where crowding is undesirable. We derive the model from a particle picture and treat it as a mean-field type game. Solutions to the mean-field type game are characterized via a Pontryagin-type maximum principle. The behavior of pedestrians acting under nonlocal crowd aversion is illustrated by a numerical simulation.