Optimal Density in a Queue with Starting-Wave

The propagation speed of people’s reaction in a relaxation process of a queue, so-called starting-wave, has an essential role for pedestrians and vehicles to achieve smooth movement. For example, a queue of vehicles with appropriate headway (density) alleviates the traffic jams, since the delay of reaction to start is minimized. In the previous study (Tomoeda et al., Fifth international conference on pedestrian and evacuation dynamics. Springer), it was found that the fundamental relation between the propagation speed of starting-wave and density is well approximated by the power law function. We have revealed the existence of optimal density, where the travel time of last pedestrian in a queue with the starting-wave to pass the head position of the initial queue is minimized. This optimal density inevitably plays a significant role to achieve smooth movement of crowds.