Streaming, disruptive interference and power-law behavior in the exit dynamics of confined pedestrians

We analyze the exit dynamics of pedestrians who are initially confined in a room. Pedestrians are modeled as cellular automata and compete to escape via a known exit at the soonest possible time. A pedestrian could move forward, backward, left or right within each iteration time depending on adjacent cell vacancy and in accordance with simple rules that determine the compulsion to move and physical capability relative to his neighbors. The arching signatures of jamming were observed and the pedestrians exited in bursts of various sizes. Power-law behavior is found in the burst-size frequency distribution for exit widths w greater than one cell dimension (w>1). The slope of the power-law curve varies with w from −1.3092(w=2) to −1.0720(w=20). Streaming which is a diffusive behavior, arises in large burst sizes and is more likely in a single-exit room with w=1 and leads to a counterintuitive result wherein an average exit throughput Q is obtained that is higher than with w=2,3, or 4. For a two-exit room (w=1), Q is not greater than twice the yield of a single-exit room. If the doors are not separated far enough (<4w), Q becomes even significantly less due to a collective slow-down that emerges among pedestrians crossing in each other's path (disruptive interference effect). For the same w and door number, Q is also higher with relaxed pedestrians than with anxious ones.