A hierarchy of heuristic-based models of crowd dynamics (2013)
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.
Bibliographic entry
Degond, P., Appert-Rolland, C., Moussaïd, M., Pettré, J., & Theraulaz, G. (2013). A hierarchy of heuristic-based models of crowd dynamics. Journal of Statistical Physics, 152, 1033-1068. doi:10.1007/s10955-013-0805-x (Full text)
Miscellaneous
| Publication year | 2013 | |
|---|---|---|
| Document type: | Article | |
| Publication status: | Published | |
| External URL: | http://dx.doi.org/10.1007/s10955-013-0805-x View | |
| Categories: | EmotionExperimental GamesHealthEconomic BehaviorProbability | |
| Keywords: | behavioral heuristicsclosure relationfluid modelgame theoryindividual-based modelskinetic modelmonokineticnash equilibriumpedestrian dynamicsrational agentsvon mises-fisher distribution |