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Discrete kinetic theory for 2D modeling of a moving crowd: Application to the evacuation of a non-connected bounded domain

Abstract : This paper concerns the mathematical modeling of the motion of a crowd in a non connected bounded domain, based on kinetic and stochastic game theories. The proposed model is a mesoscopic probabilistic approach that retains features obtained from both micro-and macro-scale representations; pedestrian interactions with various obstacles being managed from a probabilistic perspective. A proof of the existence and uniqueness of the proposed mathematical model's solution is given for large times. A numerical resolution scheme based on the splitting method is implemented and then applied to crowd evacuation in a non connected bounded domain with one rectangular obstacle. The evacuation time of the room is then calculated by our technique, according to the dimensions and position of a square-shaped obstacle, and finally compared to the time obtained by a deterministic approach by means of randomly varying some of its parameters.
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https://hal-enpc.archives-ouvertes.fr/hal-01811760
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Soumis le : lundi 11 juin 2018 - 12:11:57
Dernière modification le : mardi 13 octobre 2020 - 14:50:05
Archivage à long terme le : : jeudi 13 septembre 2018 - 00:13:41

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A. Elmoussaoui, P. Argoul, M. El Rhabi, A. Hakim. Discrete kinetic theory for 2D modeling of a moving crowd: Application to the evacuation of a non-connected bounded domain. Computers and Mathematics with Applications, Elsevier, 2018, 75 (4), pp.1159 - 1180. ⟨10.1016/j.camwa.2017.10.023⟩. ⟨hal-01811760⟩

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