Discrete kinetic theory for 2D modelling of a moving crowd : Application to the evacuation of a non-connected bounded domain.
ELMOUSSAOUI, Abdelghani ; Argoul, Pierre ; EL RHADI, M ; HAKIM, A
HAL, hal-01684645 / Harvested from HAL
Text on HAL
This paper concerns the mathematical modelling 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 nally compared to the time obtained by a deterministic approach by means of randomly varying some of its parameters.
Publié le : 2017-01-01
Classification:  DISCRETE KINETIC THEORY,  EVACUATION,  CROWD DYNAMICS,  SPLITTING SCHEME,  SYSTEME COMPLEXE,  MOUVEMENT,  SYSTEME DISCRET,  MODELE MATHEMATIQUE,  PIETON,  FOULE,  DYNAMIQUE,  [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] 
@article{hal-01684645,
     author = {ELMOUSSAOUI, Abdelghani and Argoul, Pierre and EL RHADI, M and HAKIM, A},
     title = {Discrete kinetic theory for 2D modelling of a moving crowd : Application to the evacuation of a non-connected bounded domain.},
     journal = {HAL},
     volume = {2017},
     number = {0},
     year = {2017},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01684645}
}

ELMOUSSAOUI, Abdelghani; Argoul, Pierre; EL RHADI, M; HAKIM, A. Discrete kinetic theory for 2D modelling of a moving crowd : Application to the evacuation of a non-connected bounded domain.. HAL, Tome 2017 (2017) no. 0, . http://gdmltest.u-ga.fr/item/hal-01684645/