Pricing in Vehicle Sharing Systems: Optimization in queuing networks with product forms
نویسندگان
چکیده
One-way Vehicle Sharing Systems (VSS) such as Vélib’ Paris are flourishing. The usefulness of VSS for users is highly impacted by the availability of vehicles and parking spots. Most existing systems are ruled by the requests of users. We study the potential interest of influencing the users in order to improve the performance of the system. We focus on optimizing the number of trips taken in the system. We assume that each user is associated with a pair (O-D) of stations, and only interacts with the system if his O-D trip is available. We consider leverages that can influence the rate of user requests for each pair O-D. In order to provide exact formulas and analytical insights, VSS are modeled as closed queuing networks with infinite buffer capacity and Markovian demands. Transportation times are assumed to be null and the demand to be stationary over time. We propose a heuristic based on computing a Maximum Circulation together with a convex integer program solved optimally by a greedy algorithm. For M stations and N vehicles, the performance ratio of this heuristic is conjectured to be exactly N/(N +M − 1) and proved to be at least (N −M)/(N +M). The complexity of computing optimum policies remains open. Insights on this issue are provided in the appendix. The appendix also contains an example showing that VSS can have poor performances without regulation.
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