Kinetic model for bidirectional pedestrian flow in an evacuation scenario

In this paper, a kinetic model for bidirectional pedestrian flow is proposed and inspired in a one-dimensional evacuation scenario. Walkers exiting the building are assumed mostly passive while the ones moving in the wrong direction are considered aggressive. A two-Boltzmann-moment approach is considered, where densities and mean velocities of each species are the state variables. The corresponding system of transport equations is studied in a linear approximation in two cases: first considering the exiting crowd as being completely passive (intended to simulate a drill) and second, allowing for a disparate aggressiveness in both species (proposed as a real evacuation situation). Stability is found in the first case whereas the second scenario is always unstable. The characteristic time for the onset of instabilities in the second case is established which could be interpreted as the time-frame in which complete evacuation needs to be achieved in order to avoid a congestion in the context of this particular model.