Large-scale analysis of load-balancing policies for free-floating car-sharing models

In free-floating (FF) car-sharing systems, FF cars share parking spaces in public space with much more numerous private cars. The system is modelled as a closed queuing network with two classes of customers, FF and private cars, with different orders of magnitude. They move between N nodes, each with a large capacity CN, C > 0. Mean-field techniques are adapted to the presence of private cars, which act as a fast-varying random environment. This allows us to study the impact of load-balancing policies on the distribution of the number of FF cars per zone when the system gets large. For two load-balancing policies, respectively modifying the routing probabilities and the pick-up rates, we obtain an explicit distribution, a binomial negative distribution driven by a fixed point equation. The influence of parameters on performance is derived.