Section: New Results

Stochastic networks: large bike sharing systems

Participants : Christine Fricker, Hanène Mohamed, Cédric Bourdais, Yousra Chabchoub.

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 a hot topic in Operation Research and now the impact of stochasticity on the 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 stochastic model is the first studying the impact of the finite number of spots at the stations on the system behavior.

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

Second we investigate the impact of finite capacity of stations and reservation in car-sharing systems. The large-scale asymptotic joint stationary distribution of the numbers of vehicles and reserved parking places is given as the joint distribution in a tandem of queues with a constrained total capacity where rates are solutions of a system of two fixed point equations. Analytical expressions are given for performance in light and heavy traffic cases. As expected, reservation impact drastically increases with traffic. Even if the equilibrium is identified and analyzed, the question of convergence is still open.

JC Decaux provides us data describing Velib' user trips. These data are useful to measure the system behavior. With Yousra Chabchoub, we test clustering to obtain a typology of the stations. Then we focus on the resources availability (free docks and available bikes) and separate the Velib’ stations into three clusters (balanced, overloaded and underloaded stations), using Kmeans clustering algorithm, along with the Dynamic Time Wraping (DTW) metric. We choose to update the centers of the clusters using the efficient Dtw Barycenter Averaging (DBA) method.