Crowding and queuing at exits and bottlenecks

Michael Fischer (1) , Gaspard Jankowiak (1) , Marie-Therese Wolfram (2)

1 RICAM - Johann Radon Institute for Computational and Applied Mathematics
2 WMI - Warwick Mathematics Institute

Experiments with pedestrians revealed that the geometry of the domain, as well as the incentive of pedestrians to reach a target as fast as possible have a strong influence on the overall dynamics. In this paper we propose and validate different mathematical models on the micro-and macroscopic level to study the influence of both effects. We calibrate the models with experimental data and compare the results on the micro-as well as macroscopic level. Our numerical simulations reproduce qualitative experimental features on both levels and indicate how geometry and motivation level influence the observed pedestrian density. Furthermore, we discuss the dynamics of solutions for different modeling approaches and comment on the analysis of the respective equations.

Domaines: Equations aux dérivées partielles [math.AP]

Michael Fischer, Gaspard Jankowiak, Marie-Therese Wolfram. Crowding and queuing at exits and bottlenecks. 2019. ⟨hal-02371333v1⟩