Section: New Results

Ressource allocation in vehicle sharing systems

Participants : Christine Fricker, Hanene Mohamed, Thanh-Huy Nguyen.

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 availability of the resources: vehicles or free slots to return them. These systems became an important 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.

Equivalence of ensembles We used 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 the asymptotic independence property for node states. This widely extends the existing results on heterogeneous bike-sharing systems.

Load balancing policies. Recently we investigated some load balancing algorithms for stochastic networks to improve the bike sharing system behavior. We focus on the choice of the least loaded station among two to return the bike. In real systems, this choice is local. Thus the main challenge is to deal with the choice between two neighboring stations.

For that, a set of $N$ queues, with a local choice policy, is studied. When a customer arrives at queue $i$, he joins the least loaded queue between queues $i$ and $i+1$. When the load tends to zero, we obtain an asymptotic for the stationary distribution of the number of customers at a queue. It allows to compare local choice, no choice and choice between two chosen at random.

For a bike-sharing homogeneous model, we study a deterministic cooperation between the stations, two by two. Analytic results are achieved in an homogeneous bike-sharing model. They concern the limit as the system is large, the so-called mean-field limit, and its equilibrium point. Results on performance mainly involve an original closed form expression of the stationary blocking probability in the classical join-the-shortest-queue model. These results are compared by simulations with the policy where the users choose the least loaded station between two stations to return close to their destination. It turns out that, because of randomness, the choice between two neighbours gives better performance than grouping stations two by two.

Bike-sharing model with waiting In real systems, if the customer does not find the resource (a bike or an place to return), he can either leave, or search in a neighbouring station, or wait. We extend a basic model to take into account waiting.