A kinetic modeling of crowd evacuation with several groups in complex venues

Abstract

The evacuation of human crowds consisting of several groups in complex venues is studied, in this paper, by the kinetic theory of active particles. We consider a complex venue that consists of several chambers which are separated by interior walls and doors, for which the geometrical effects may come from the walls both on the boundary and inside the domain, the exits, and the doors connecting the chambers. The geometrical properties are incorporated in the geometrical preferred direction, which is specified such that an individual can avoid the wall and approach the exit through the evacuation vector. The notion of group is corresponding to the concept of functional subsystem in the mathematical theory of active particles. In the present framework of several groups, the rules of interactions can be specified for both the interactions among the same group and the interactions between different groups. Furthermore, the motility is assigned for each group, which serves as the average activity of a group. Some interesting features and phenomena are shown in the numerical tests of the evacuation of a crowd with one, two or three groups.