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Mean field analysis of an incentive algorithm for a closed stochastic network

Abstract : The paper deals with a load-balancing algorithm for a closed stochastic network with two zones with different demands. The algorithm is motivated by an incentive algorithm for redistribution of cars in a large-scale car-sharing system. The service area is divided into two zones. When cars stay too much long in the low-demand zone, users are encouraged to pick up them and return them in the high-demand zone. The zones are divided in cells called stations. The cars are the network customers. The mean-field limit solution of an ODE gives the large scale distribution of the station state in both clusters for this incentive policy in a discrete Markovian framework. An equilibrium point of this ODE is characterized via the invariant measure of a random walk in the quarter-plane. The proportion of empty and saturated stations measures how the system is balanced. Numerical experiments illustrate the impact of the incentive policy. Our study shows that the incentive policy helps when the high-demand zone observes a lack of cars but a saturation must be prevented especially when the high-demand zone is small.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03539628
Contributor : Christine Fricker Connect in order to contact the contributor
Submitted on : Friday, January 21, 2022 - 7:07:39 PM
Last modification on : Wednesday, April 13, 2022 - 4:48:01 PM
Long-term archiving on: : Friday, April 22, 2022 - 9:07:58 PM

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  • HAL Id : hal-03539628, version 1

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Bianca Moreno, Christine Fricker, Hanene Mohamed, Amaury Philippe, Martin Trepanier. Mean field analysis of an incentive algorithm for a closed stochastic network. 2022. ⟨hal-03539628⟩

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