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.
Document type :
Journal articles
Complete list of metadatas

https://hal.inria.fr/hal-01203789
Contributor : Christine Fricker <>
Submitted on : Wednesday, September 23, 2015 - 5:52:04 PM
Last modification on : Thursday, March 21, 2019 - 2:47:30 PM

Links full text

Identifiers

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

Citation

Christine Fricker, Danielle Tibi. Equivalence of ensembles for large vehicle-sharing models. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2017, 27 (2), pp.883-916. ⟨hal-01203789⟩

Share

Metrics

Record views

230