Equivalence of ensembles for large vehicle-sharing models

Abstract : For a class of large closed Jackson networks submitted to capacity constraints, asymptotic independence of the nodes in normal traffic phase is proved at stationarity under mild assumptions, using a Local Limit Theorem. The limiting distributions of the queues are explicit. In the Statistical Mechanics terminology, the equivalence of ensembles - canonical and grand canonical - is proved for specific marginals. The framework includes the case of networks with two types of nodes: single server/finite capacity nodes and infinite servers/infinite capacity nodes, that can be taken as basic models for bike-sharing systems. The effect of local saturation is modeled by generalized blocking and rerouting procedures, under which the stationary state is proved to have product-form. The grand canonical approximation can then be used for adjusting the total number of bikes and the capacities of the stations to the expected demand.
Type de document :
Pré-publication, Document de travail
2015
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https://hal.inria.fr/hal-01203789
Contributeur : Christine Fricker <>
Soumis le : mercredi 23 septembre 2015 - 17:52:04
Dernière modification le : lundi 29 mai 2017 - 14:23:17

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  • HAL Id : hal-01203789, version 1
  • ARXIV : 1507.07792

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INRIA | INSMI | UPMC | USPC | PMA

Citation

Christine Fricker, Danielle Tibi. Equivalence of ensembles for large vehicle-sharing models. 2015. <hal-01203789>

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