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

Cécile Appert-Rolland; Pierre Degond; Sébastien Motsch

doi:10.3934/nhm.2011.6.351

Article Contents

2011, Volume 6, Issue 3: 351-381. Doi: 10.3934/nhm.2011.6.351

This issue Previous Article Preface Next Article On the modeling of crowd dynamics: Looking at the beautiful shapes of swarms

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

1.
1-University Paris-Sud, Laboratory of Theoretical Physics, Batiment 210, F-91405 ORSAY Cedex
2.
1-Université de Toulouse; UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, F-31062 Toulouse
3.
5-Department of Mathematics, University of Maryland, College Park, MD 20742-4015

Received: November 30, 2010

Revised: March 31, 2011

Published: August 2011

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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:

Mathematics Subject Classification: 90B20, 35L60, 35L65, 35L67, 35R99, 76L05.

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