Section: New Results

Stochastic networks: large bike sharing systems

Participant : Christine Fricker.

This is a collaboration with Nicolas Gast (EPFL) started in December 2010. Bike sharing systems were launched by numerous cities as a serious alternative in urban transportation, for example Velib (20 000 bikes, 1 500 stations). One of the major issues is the availability of the resources: bikes or free slots to return the bikes. These systems have become a hot topic in Operation Research but there are few studies on these stochastic networks. To our knowledge, no theoretical study of such bike sharing systems exists taking into account the limited capacity of the stations.

We modeled this system in a symmetrical case. Mean field limit theorems give the dynamic of a large system and the stationary behavior of a single station. Analytical results are obtained and convergence proved in the standard model via Lyapunov functions. It allows to find the best ratio of bikes per station and to measure the improvement of incentive mechanisms, as choosing among two stations for example, or redistribution of bikes by trucks. It is under investigation. Further results deal with heterogeneous systems. Our goal is to propose via a theoretical study and tests simple algorithms to improve the system behavior.