Mean-field type modeling of nonlocal crowd aversion in pedestrian crowd dynamics

Alexander Aurell, Boualem Djehiche

Research output: Contribution to journalArticlepeer-review


We extend the class of pedestrian crowd models introduced by Lachapelle and Wolfram [Transp. Res. B: Methodol., 45 (2011), pp. 1572–1589] to allow for nonlocal crowd aversion and arbitrarily but finitely many interacting crowds. The new crowd aversion feature grants pedestrians a “personal space” where crowding is undesirable. We derive the model from a particle picture and treat it as a mean-field type game. Solutions to the mean-field type game are characterized via a Pontryagin-type maximum principle. The behavior of pedestrians acting under nonlocal crowd aversion is illustrated by a numerical simulation.

Original languageEnglish (US)
Pages (from-to)434-455
Number of pages22
JournalSIAM Journal on Control and Optimization
Issue number1
StatePublished - 2018


  • Crowd aversion
  • Crowd dynamics
  • Interacting populations
  • Mean-field approximation
  • Mean-field type game
  • Optimal control

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics


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