Modelling crowd movements in domains with boundaries

This paper contributes to the macroscopic modeling of crowd movements. The presented model is non local, i.e., it takes into account interactions among pedestrians at different distances. Particular care is given to how non local interactions are influenced by walls, obstacles and exits. The resulting dynamics captures various well known patterns of crowd movements, such as the clogging of exits and the spontaneous formation of queues. The careful choice of obstacles near an exit is shown to be able to reduce evacuation times. An ad hoc numerical algorithm is detailed, some of its properties discussed and the convergence of the corresponding approximate solutions is investigated.