A new stochastic model for carsharing suited to free-floating

In car-sharing, free-floating is becoming increasingly popular. It means that the shared cars are parked in the public space without dedicated parking spaces. For the operator, this solves the problem of parking space requirements. But the acute imbalance problem shows the need of stochastic modelling and analysis. In this paper, a new stochastic model adapted to free-floating is proposed, taking into account the sharing of public space between private and free-floating cars. As is generally the case, the model consists of dividing the service area into small zones, with free-foating car dynamics adapted to usage, meaning car reservation, one-way trip and no parking space reservation. The originality of our model is that, due to the presence of private cars, the capacity of a zone seen by free-floating cars is random. We show that, unlike in station-based car-sharing systems, it is not limited. In addition, a stochastic averaging principle governs the behavior of free-floating cars. We exhibit a phase transition between a non-saturated regime where free-floating cars can always be parked and a saturated regime where free-floating cars cannot find an available parking space with positive probability. This probability is entirely determined by the environment - parameters of private cars and public space- which means that the operator cannot act on the proportion of zones without available parking spaces. The solution of the dimensioning problem -finding the optimal feet size to minimize the number of zones without available free-floating cars or parking spaces- is completely different from that of station-based car-sharing which is a trade-of. It consists in claiming that the more free-floating cars there are in the system, the more satisfied users are, assuming always that private cars are much more numerous that free-floating cars.

Mots clés

• free-floating car-sharing
• stochastic model
• mean-field approach
• averaging principle
• dimensioning problem