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An Incentive Algorithm for a Closed Stochastic Network: Data and Mean-Field Analysis

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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 long in the low-demand zone, users are encouraged to pick them up 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 ordinary differential equation (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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Acknowledgements

The authors would like to thank Communauto for providing data, funding, and allowing to do this study. They also thank the Natural Science and Engineering Research Council of Canada (NSERC) for funding.

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Author notes

  1. Bianca Marin Moreno, Christine Fricker, Hanene Mohamed, Amaury Philippe and Martin Trépanier contributed equally to this work.

Authors and Affiliations

  1. INRIA de Paris, DI-ENS, PSL Research University, Paris, France

    Bianca Marin Moreno & Christine Fricker

  2. MODAL’X, UMR CNRS 9023, UPL, Université Paris Nanterre, Paris, France

    Hanene Mohamed

  3. Mathematical and Industrial Engineering, Polytechnique Montreal, Montreal, H3T 1J4, Canada

    Amaury Philippe & Martin Trépanier

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  1. Bianca Marin Moreno
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  2. Christine Fricker
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  3. Hanene Mohamed
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  5. Martin Trépanier
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Correspondence to Hanene Mohamed.

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Marin Moreno, B., Fricker, C., Mohamed, H. et al. An Incentive Algorithm for a Closed Stochastic Network: Data and Mean-Field Analysis. La Matematica (2024). https://doi.org/10.1007/s44007-024-00098-x

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