Section: New Results

Resource allocation in vehicle sharing systems

Participants : Christine Fricker, Plinio Santini Dester, Hanene Mohamed, Yousra Chabchoub.

This is a collaboration with Danielle Tibi, Université Denis Diderot.

Vehicle sharing systems are becoming an urban mode of transportation, and launched in many cities, as Velib' and Autolib' in Paris. One of the major issues is the avail ability of the resources: vehicles or free slots to return them. These systems became a hot topic in Operation Research and now the importance of stochasticity on the system behavior is commonly admitted. The problem is to understand the system behavior and how to manage these systems in order to provide both resources to users. Our stochastic model is the first one taking into account the finite number of spots at the stations.

With Danielle Tibi, we use limit local theorems to obtain the asymptotic stationary joint distributions of several station states when the system is large (both numbers of stations and bikes), in the case of finite capacities of the stations. This gives an asymptotic independence property for node states. This widely extends the existing results on heterogeneous bike-sharing systems.

Recently we investigate some network load balancing algorithms to improve the bike sharing system behavior. We focus on the choice of the least loaded station among two t o return the bike. A problem is the influence of the delay between the choice time (the beginning of the trip) and the time the station is joined (the end of the trip). However the main challenge is to deal with the choice between two neighboring stations. For that, a system of infinite queues is studied in light traffic. For a bike-shar ing homogeneous model, we restrict our study to a deterministic cooperation of two by two stations. It relies on new results for the classical system of two queues under the join-the-shortest-queue policy.

JC Decaux provides us data describing Velib' user trips. These data are useful to measure the system parameters, validate our models and test our algorithms. Indeed, we use these data to investigate load balancing algorithms such as two-choice policies.