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

We extend the Aw-Rascle macroscopic model of car trac into a two-way multi-lane model of pedestrian trac. 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 rst step, we propose a singularly perturbed pres-sure 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 com-pressible 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 dif-fusive correction of these models and discuss the characteristic time and length scales of the instability.