Power laws in the cluster sizes of group-crossing pedestrians: empirical evidence and modelling of causes

Abstract

.Pedestrian-vehicle mixed traffic at unsignalized crosswalks is a self-organizing system, because of the absence of external control. Consequently, pedestrian group-crossing behaviour may be expected to exhibit the power-law phenomenon, which is often an indicator of self-organized criticality. The assumption that the distribution of cluster sizes may obey power laws was theoretically supported by Xin et al. To test this claim empirically, we observed pedestrian collective motion under natural conditions, using video recordings. These real data confirmed the existence of the power-law phenomenon. A simulation study was then undertaken to uncover the mechanism that generated the observations. The observed patterns could be fully replicated if the behaviour of pedestrians and motorists were modelled, in particular the yielding behaviour of motorists, when approaching crossings and the adaptive behaviour of pedestrians as they increased in number. As well as providing empirical evidence, our findings also provide a deeper understanding of the patterns of the pedestrian collective motion. The results may have implications in the validation of mixed traffic simulation models.