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

A. Elmoussaoui (1) , P. Argoul (2) , M. El Rhabi (3) , A. Hakim (1)

1 UCA - Université Cadi Ayyad [Marrakech]
2 IFSTTAR/MAST/SDOA - Sécurité et Durabilité des Ouvrages d'Art
3 IMI - Département Ingénierie Mathématique et Informatique, École des Ponts ParisTech

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.

Mots clés: Evacuation; Complex system; Discrete kinetic theory; Splitting scheme; Crowd dynamics

Domaines: Mathématiques [math]; Mathématiques [math]; Analyse numérique [math.NA]; Informatique [cs]; Informatique [cs]; Modélisation et simulation

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 & Mathematics with Applications, 2018, 75 (4), pp.1159 - 1180. ⟨10.1016/j.camwa.2017.10.023⟩. ⟨hal-01811760⟩