Escape Velocity of the Leader in a Queue of Pedestrians

Abstract

The relaxation process in a queue is very important for the smooth movement of pedestrians. As previously reported, the propagation speed of a starting wave, that is, a wave of people’s successive reactions in the relaxation process of a queue, and the initial density of a queue are fundamentally related by a power law. In addition, when the walking velocity of the leader of a queue, called “escape velocity”, is optimal, the flow of the queue is maximized and the queue is not separated. In order to investigate how the behaviour of the followers in a queue changes with the leader’s velocity, we performed experimental measurements on real pedestrians. In our experiment, we set the walking velocity of the leader of a queue using three metronome tempos (fast, normal, and slow) transmitted through earphones. The experimental results show that the escape velocities corresponding to the fast and slow tempos cause empty spaces in a queue and limit the walking velocities of the queue members, respectively.