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A product form for the general stochastic matching model

Part of: Graph theory Special processes Markov processes

Published online by Cambridge University Press:  23 June 2021

Pascal Moyal Open the ORCID record for Pascal Moyal [Opens in a new window] ,
Ana Bušić  and
Jean Mairesse
Pascal Moyal*
Affiliation:
UTC/Université de Lorraine
Ana Bušić*
Affiliation:
Inria and DI ENS, PSL Research University
Jean Mairesse*
Affiliation:
CNRS, Sorbonne Université
*
*Postal address: LMAC, Université de Technologie de Compiègne, 60203 Compiègne Cedex, France and Institut Elie Cartan, Université de Lorraine, F-54506 Nancy Cedex, France. Email address: pascal.moyal@univ-lorraine.fr
**Postal address: INRIA/Département d’Informatique (ENS), Université PSL, 2 rue Simone Iff, 75012 Paris, France. Email address: ana.busic@inria.fr
***Postal address: Sorbonne Université, CNRS, LIP6, F-75005, Paris, France. Email address: jean.mairesse@lip6.fr
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Abstract

We consider a stochastic matching model with a general compatibility graph, as introduced by Mairesse and Moyal (2016). We show that the natural necessary condition of stability of the system is also sufficient for the natural ‘first-come, first-matched’ matching policy. To do so, we derive the stationary distribution under a remarkable product form, by using an original dynamic reversibility property related to that of Adan, Bušić, Mairesse, and Weiss (2018) for the bipartite matching model.

Keywords

Markov chainsreversibilitygraphs

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60K25: Queueing theory
Secondary: 05C70: Factorization, matching, partitioning, covering and packing 05C63: Infinite graphs 05C80: Random graphs
Type
Original Article
Information
Journal of Applied Probability , Volume 58 , Issue 2 , June 2021 , pp. 449 - 468
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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References

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