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Section: New Results

Stochastic networks: vehicle rental networks

Participant : Christine Fricker.

This is a collaboration with Frédéric Meunier (LVMT, ENPC). A vehicle rental network where it is always possible to park the vehicle after using it has been modeled in the literature as a closed network where the vehicles represent the customers. We revisit the existing results, especially asymptotics when the fleet size gets large, with a fixed number of stations. The results prove that the capacities of some stations are crucial. To introduce them in the model, we study a a mean field limit for the symmetrical case of the most natural policy: A user, who finds no idle place to put his vehicle when he arrives to a station, tries to park it at another station at random. Using standard arguments, it is proved that the empirical measure of the model converges to a dynamical system as the system gets large. The queueing interpretation of the equilibrium point, which exists, gives the proof of its uniqueness. A different model where the user always returns the vehicle in a non-saturated station should be compared to the previous one. The aim is to examine the impact of the parking policy. A framework with different clusters is under investigation.


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