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.
@article{hal-01811760,
author = {Elmoussaoui, A. and Argoul, P. and El Rhabi, M. and Hakim, A.},
title = {Discrete kinetic theory for 2D modeling of a moving crowd: Application to the evacuation of a non-connected bounded domain},
journal = {HAL},
volume = {2018},
number = {0},
year = {2018},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01811760}
}
Elmoussaoui, A.; Argoul, P.; El Rhabi, M.; Hakim, A. Discrete kinetic theory for 2D modeling of a moving crowd: Application to the evacuation of a non-connected bounded domain. HAL, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/hal-01811760/