The evolution of a clogging sidewalk caused by a dockless bicycle-sharing system: A stochastic particles model

Abstract The operation of a dockless bicycle-sharing system is modeled by a stochastic system characterized by two kinds of interacting components, the distribution of bicycles on a sidewalk and behaviors of riders, whose simple and basic actions lead to complex results. From the model, the collective behavior emerging in the bicycle-sharing system is described by a nonlinear evolutionary equation for the density of bicycles on the sidewalk, which has a non-trivial lump solution. The solution describes a heap of bicycles at somewhere on the sidewalk, and the width and the movement of the heap is determined by the mean behaviors of riders. Such a lump solution implies that the phenomenon of clogging sidewalks may be an endogenous processes within some dockless bicycle-sharing system.