HAL : hal-00589710, version 1

arXiv : 1105.0203

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

Cécile Appert-Rolland 1, Pierre Degond 2, Sébastien Motsch 3

(30/04/2011)

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.

1 :	Laboratoire de Physique Théorique d'Orsay (LPT)
	CNRS : UMR8627 – Université Paris XI - Paris Sud
2 :	Institut de Mathématiques de Toulouse (IMT)
	Université Paul Sabatier [UPS] - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées (INSA) - Toulouse – CNRS : UMR5219
3 :	Department of Mathematics, University of Maryland
	University of Maryland

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Mathématiques/Physique mathématique

hal-00589710, version 1

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Contributeur : Pierre Degond <>

Soumis le : Samedi 30 Avril 2011, 18:44:01

Dernière modification le : Dimanche 1 Mai 2011, 22:40:09