Statistical characteristics of evacuation without visibility in random walk model

The evacuation process from a dark room with an exit is investigated by the use of the biased random walk model. We clarify the statistical properties of the walker escaping from the room through the exit. The evacuation from the room without visibility consists of two processes: (1) the biased random walk from an initial position to the wall and (2) the second walk following the wall. The following statistical quantities are derived by using a lot of simulating trajectories: the probability density distributions of (1) the number of steps of the biased random walk to the wall, (2) the first contact point on the wall, and (3) the number of steps of the second walk on the wall. The third statistical distribution is connected closely with the first and second distributions. Their distributions depend highly on the scenarios of the walker. We show the effects of the initial position, drift, and scenario on the mean escape time.