A hierarchy of heuristic-based models of crowd dynamics

Abstract

We derive a hierarchy of kinetic and macroscopic models from a noisy variant of the heuristic behavioral Individual-Based Model of Moussaid et al, PNAS 2011, where the pedestrians are supposed to have constant speeds. This IBM supposes that the 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 the pedestrians. Then, we derive fluid models and propose three different closure relations. The first two closures assume that the velocity distribution functions are 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 equilibia in a game theoretic framework. In each case, we discuss the features of the models and their suitability for practical use.

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• The effect of environment knowledge in evacuation scenarios involving fire and smoke - a multiscale modelling and simulation approach
• Pedestrian Models based on Rational Behaviour
• A kinetic description for the herding behavior in financial market
• A kinetic equation for economic value estimation with irrationality and herding
• Time-delayed Follow-the-Leader model for pedestrians walking in line
• Pedestrian models with congestion effects
• Density-induced Consensus Protocol
• From individual behaviour to an evaluation of the collective evolution of crowds along footbridges
• Mean Field Limit and Propagation of Chaos for a Pedestrian Flow Model
• A dynamic state-based model of crowds
• On a three dimensional vision based collision avoidance model
• Uncovering migration systems through spatio-temporal tensor co-clustering
• Comparing first order microscopic and macroscopic crowd models for an increasing number of massive agents
• Modeling of pedestrians