Section: New Results

Stochastic networks: large bike sharing systems

Participants : Christine Fricker, Hanène Mohamed, Nicolas Servel.

This is a collaboration with Nicolas Gast (EPFL). Bike sharing systems were launched by numerous cities to be a urban mode of transportation, for example Velib in Paris. One of the major issues is the availability of the resources: bikes or free slots to return the bikes. These systems became a hot topic in Operation Research and now the importance of stochasticity of such system behavior is commonly admitted. The problem is to understand their behavior and how to manage them in order to provide both resources to users.

Our model is the first one taking into account the finite number of spots at the stations. In a homogeneous model, mean field limit theorems give the dynamic of a large system. Analytical results are obtained and convergence proved in a 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. We investigate also redistribution of bikes by trucks. Further results deal with heterogeneous system. By mean field techniques, analytical results were recently obtained on systems consisting in several clusters. In a work with Nicolas Servel, we discuss the improvement of choosing between two stations in the same cluster. Our goal is to propose, via a theoretical study and tests, simple algorithms to improve the system behavior.

With Hanene Mohamed, we study the problem of impact of geometry on incentive mechanisms. Our first model under investigation is very close from the Gates-Westcott crystal growth model with its underlying random deposition process.