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

Cécile Appert-Rolland, Pierre Degond, Sébastien Motsch

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)351-381
Number of pages31
JournalNetworks and Heterogeneous Media
Issue number3
StatePublished - Sep 2011
Externally publishedYes


  • Aw-Rascle model
  • Congestion constraint
  • Macroscopic model
  • Multi-lane traffic
  • Pedestrian traffic
  • Two-way trac

ASJC Scopus subject areas

  • Statistics and Probability
  • General Engineering
  • Computer Science Applications
  • Applied Mathematics


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