Incentives and regulations in bike-sharing systems with stations of finite capacity

As of 2011, more than 200 cities around the world have a bike sharing system. In such a system, users arrive at a station, use the bike for a while and return the bike to another station. This paper presents a model taking account of the finite number of bike locations at the stations. In case of symmetry, as the system gets large, the mean field limit provides an insight of the system behavior. Convergence of the invariant measures is proved and closed form results are obtained. The influence of the parameters and of various load balancing strategies on the performance, measured by the proportion of so called problematic stations, is discussed. Even in this symmetry case, the system exhibits a poor performance. We show that simple incentives, such as suggesting users to return to the least loaded station among two, improve dramatically the situation. An asymmetric scenario is also investigated. In that case, simple incentives are not enough and regulation mechanisms, such as redistribution of the bikes by trucks, are needed.