Height map-based social force model for stairway evacuation

The stairway is ubiquitous in public places like shopping mall, theater and stadium. Due to the unevenness of the ground, the staircase often brings about undesirable effects in emergency evacuation, such as stumble, trampling and falling. Therefore, it is necessary to study the evacuation dynamics of pedestrians on the stairway in-depth. However, the widely studies social force model fails to take into account the effect of ground topography on stair movement. In this paper, an extended social force model based on height map is proposed. This kind of model can accurately reproduce the temporal-spatial pedestrian dynamics on the stairway. Simulations indicate that the pedestrian flow on the stairway is not only constrained by geometric narrowing, but also restricted by the ground topography. Most of all, the discontinuous feature of height variance led to the fluctuation of velocity and further constrain the traffic capacity of stairs. Higher aspiration levels result in speed variance during emergency evacuation, and further induce congestion near the transitions between horizontal way and the stairs. The danger of clogging induced by transitions can be minimized by replacing staircases with ramps.