A Point Processes approach to bicycle sharing systems’ design and management

Public bicycle systems have attracted a great deal of attention in recent years. The success of this service heavily depends on the topology of the city and on the locations of bike stations in relation to potential demand. In fact, it is primarily important that users find bike stations in convenient locations, sufficiently close both to the origins of their trips and to their destinations, and that each rental station guarantees the availability both of enough bicycles and of enough empty docking slots.This paper proposes a point processes approach to the study of bike-sharing systems, allowing us to quantify and control parameters having a key role in decisions both of strategic and operational type. Differently from previous studies, the point processes approach catches both the interdependence among the stations and the links between spatial and time aspects of the problem.The application of point processes, in particular spatial mixed Poisson processes, to this field requires the statement and proof of an invariance property of such processes under stochastic dependent transformations, that may be of interest also from a theoretical point of view.