Effects of an Obstacle Position for Pedestrian Evacuation: SF Model Approach

In order to study pedestrian dynamics, mathematical models play an important role. It is well-known that a social force model exhibits clogging or what is called the “faster-is-slower effect” (Helbing et al., Nature 407:487–490, 2000). Also, the authors in Frank and Dorso (Phys A 390:2135–2145, 2011) and Kirchner et al. (Phys Rev E 67:056122, 2003) reported that an obstacle facilitates and obstructs evacuation of pedestrians trying to get out of a room with an exit, dependently on its position, size, and shape. In particular, as stated in Frank and Dorso (Phys A 390:2135–2145, 2011), an obstacle has a strong influence on pedestrians if it is put in a site shifted a little from the front of the exit. However, it has not been shown where and how it is the most efficiency to set up an obstacle. Thus we investigate the dynamics of pedestrians and clarify the effect of a disk-shaped obstacle with various sizes placed in several positions via numerical simulations for a social force model. Finally, we calculate a leaving time of pedestrians for each size and position of an obstacle, and determine an “optimal size” of an obstacle in the case that it is set up in a site shifted from the front of the exit.