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Journal of Statistical Physics

, Volume 152, Issue 6, pp 1033–1068 | Cite as

A Hierarchy of Heuristic-Based Models of Crowd Dynamics

  • P. Degond
  • C. Appert-Rolland
  • M. Moussaïd
  • J. Pettré
  • G. Theraulaz
Article

Abstract

We derive a hierarchy of kinetic and macroscopic models from a noisy variant of the heuristic behavioral Individual-Based Model of Ngai et al. (Disaster Med. Public Health Prep. 3:191–195, 2009) where pedestrians are supposed to have constant speeds. This IBM supposes that pedestrians seek the best compromise between navigation towards their target and collisions avoidance. We first propose a kinetic model for the probability distribution function of pedestrians. Then, we derive fluid models and propose three different closure relations. The first two closures assume that the velocity distribution function is either a Dirac delta or a von Mises-Fisher distribution respectively. The third closure results from a hydrodynamic limit associated to a Local Thermodynamical Equilibrium. We develop an analogy between this equilibrium and Nash equilibria in a game theoretic framework. In each case, we discuss the features of the models and their suitability for practical use.

Keywords

Pedestrian dynamics Behavioral heuristics Rational agents Individual-based models Kinetic model Fluid model Game theory Closure relation Monokinetic von Mises-Fisher distribution Nash equilibrium 

Notes

Acknowledgements

This work has been supported by the French ‘Agence Nationale pour la Recherche (ANR)’ in the frame of the contracts ‘Pedigree’ (ANR-08-SYSC-015-01) and ‘CBDif-Fr’ (ANR-08-BLAN-0333-01).

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • P. Degond
    • 1
    • 2
  • C. Appert-Rolland
    • 3
    • 4
  • M. Moussaïd
    • 5
  • J. Pettré
    • 6
  • G. Theraulaz
    • 7
    • 8
  1. 1.UPS, INSA, UT1, UTM, Institut de Mathématiques de ToulouseUniversité de ToulouseToulouseFrance
  2. 2.CNRSInstitut de Mathématiques de Toulouse UMR 5219ToulouseFrance
  3. 3.Laboratoire de Physique ThéoriqueUniversité Paris SudOrsay cedexFrance
  4. 4.CNRS, UMR 8627Laboratoire de Physique ThéoriqueOrsayFrance
  5. 5.Center for Adaptive Behavior and CognitionMax Planck Institute for Human DevelopmentBerlinGermany
  6. 6.INRIA Rennes – Bretagne AtlantiqueRennesFrance
  7. 7.Centre de Recherches sur la Cognition Animale, UMR-CNRS 5169Université Paul SabatierToulouse cedex 9France
  8. 8.CNRSCentre de Recherches sur la Cognition AnimaleToulouseFrance

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