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A stochastic matching model on hypergraphs

Part of: Markov processes Computer system organization Graph theory

Published online by Cambridge University Press:  22 November 2021

Youssef Rahme  and
Pascal Moyal Open the ORCID record for Pascal Moyal [Opens in a new window]
Youssef Rahme*
Affiliation:
Université de Technologie de Compiègne
Pascal Moyal*
Affiliation:
Université de Lorraine
*
*Postal address: LMAC, Université de Technologie de Compiègne, 60203 Compiègne Cedex, France. Email: youssef.rahme@utc.fr
**Postal address: Institut Elie Cartan, Université de Lorraine, F-54506 Nancy Cedex, France. Email: pascal.moyal@univ-lorraine.fr
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Abstract

Motivated by applications to a wide range of areas, including assemble-to-order systems, operations scheduling, healthcare systems, and the collaborative economy, we study a stochastic matching model on hypergraphs, extending the model of Mairesse and Moyal (J. Appl. Prob.53, 2016) to the case of hypergraphical (rather than graphical) matching structures. We address a discrete-event system under a random input of single items, simply using the system as an interface to be matched in groups of two or more. We primarily study the stability of this model, for various hypergraph geometries.

Keywords

Markovian queueing theorystabilitymatchinghypergraph

MSC classification

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 68M20: Performance evaluation; queueing; scheduling 05C65: Hypergraphs
Type
Original Article
Information
Advances in Applied Probability , Volume 53 , Issue 4 , December 2021 , pp. 951 - 980
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Copyright
© The Author(s) 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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