Macroscopic Models for Pedestrian Flows

Abstract : In this paper we present macroscopic models for pedestrian flows that recently appeared in the literature. The first one was proposed by Colombo, Rosini, 2005. In a 1D setting, this model properly describes the movements of pedestrians, the onset of panic and the dynamics of a panicking crowd. Furthermore, its assumptions were experimentally confirmed by an empirical study of a crowd crush, see Helbing, Johansson, Al-Abideen, 2007. Then, we consider a 2D model that aims at describing similar phenomena while taking care of more complex geometries. Numerical integrations show that some realistic features are captured