Micro- and macroscopic modeling of crowding and pushing in corridors

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 at the micro- and macroscopic levels to study the influence of both effects. We calibrate the models with experimental data and compare the results at themicro- as well as macroscopic levels. 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.

Mots clés: microscopic and macroscopic pedestrian models; Fokker-Planck equation; parameter estimation; scalar conservation laws; eikonal equation

Domaines: Equations aux dérivées partielles [math.AP]

Michael Fischer, Gaspard Jankowiak, Marie-Therese Wolfram. Micro- and macroscopic modeling of crowding and pushing in corridors. Networks and Heterogeneous Media, 2020, 15 (3), pp.405-426. ⟨10.3934/nhm.2020025⟩. ⟨hal-02371333v2⟩