Two-way multi-lane traffic model for pedestrians in corridors

Abstract

We extend the Aw-Rascle macroscopic model of car traffic into a two-way multi-lane model of pedestrian traffic. Within this model, we propose a technique for the handling of the congestion constraint, i.e. the fact that the pedestrian density cannot exceed a maximal density corresponding to contact between pedestrians. In a first step, we propose a singularly perturbed pressure relation which models the fact that the pedestrian velocity is considerably reduced, if not blocked, at congestion. In a second step, we carry over the singular limit into the model and show that abrupt transitions between compressible flow (in the uncongested regions) to incompressible flow (in congested regions) occur. We also investigate the hyperbolicity of the two-way models and show that they can lose their hyperbolicity in some cases. We study a diffusive correction of these models and discuss the characteristic time and length scales of the instability.

References in corpus (2)

• All speed scheme for the low mach number limit of the Isentropic Euler equation
• Pedestrian flows in bounded domains with obstacles

Cited by in corpus (6)

• A hierarchy of heuristic-based models of crowd dynamics
• Vision-based macroscopic pedestrian models
• Self-Organized Hydrodynamics with congestion and path formation in crowds
• Time-delayed Follow-the-Leader model for pedestrians walking in line
• Stochastic and Coarse-Grained Two-Dimensional Modeling of Directional Particle Movement
• Modeling of pedestrians