Networks and Heterogeneous Media (NHM)

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

Pages: 351 - 381, Volume 6, Issue 3, September 2011      doi:10.3934/nhm.2011.6.351

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Cécile Appert-Rolland - 1-University Paris-Sud, Laboratory of Theoretical Physics, Batiment 210, F-91405 ORSAY Cedex, France (email)
Pierre Degond - 1-Université de Toulouse; UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, F-31062 Toulouse, France (email)
Sébastien Motsch - 5-Department of Mathematics, University of Maryland, College Park, MD 20742-4015, United States (email)

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.

Keywords:  Pedestrian traffic, two-way traffic, multi-lane traffic, macroscopic model, Aw-Rascle model, Congestion constraint.
Mathematics Subject Classification:  90B20, 35L60, 35L65, 35L67, 35R99, 76L05.

Received: December 2010;      Revised: April 2011;      Available Online: August 2011.