A general stochastic matching model on multigraphs

AbstractWe 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.

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Approximating the First-Come, First-Served Stochastic Matching Model with Ohm’s Law

Operations Research ◽

10.1287/opre.2018.1737 ◽

2018 ◽

Vol 66 (5) ◽

pp. 1423-1432 ◽

Cited By ~ 2

Author(s):

Mohammad M. Fazel-Zarandi ◽

Edward H. Kaplan

Keyword(s):

Matching Model ◽

Ohm’S Law ◽

Ohm's Law ◽

Stochastic Matching

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A stochastic matching model on hypergraphs

Advances in Applied Probability ◽

10.1017/apr.2021.8 ◽

2021 ◽

Vol 53 (4) ◽

pp. 951-980

Author(s):

Youssef Rahme ◽

Pascal Moyal

Keyword(s):

Discrete Event ◽

Healthcare Systems ◽

Discrete Event System ◽

Random Input ◽

Matching Model ◽

Operations Scheduling ◽

Event System ◽

Wide Range ◽

The Stability ◽

Stochastic Matching

AbstractMotivated 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.

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Stability of the stochastic matching model

Journal of Applied Probability ◽

10.1017/jpr.2016.65 ◽

2016 ◽

Vol 53 (4) ◽

pp. 1064-1077 ◽

Cited By ~ 8

Author(s):

Jean Mairesse ◽

Pascal Moyal

Keyword(s):

Markov Chain ◽

Matching Model ◽

New Model ◽

Buffer Content ◽

Finite Set ◽

Matching Graph ◽

Stochastic Matching ◽

Independent And Identically Distributed

Abstract We introduce and study a new model that we call the matching model. Items arrive one by one in a buffer and depart from it as soon as possible but by pairs. The items of a departing pair are said to be matched. There is a finite set of classes 𝒱 for the items, and the allowed matchings depend on the classes, according to a matching graph on 𝒱. Upon arrival, an item may find several possible matches in the buffer. This indeterminacy is resolved by a matching policy. When the sequence of classes of the arriving items is independent and identically distributed, the sequence of buffer-content is a Markov chain, whose stability is investigated. In particular, we prove that the model may be stable if and only if the matching graph is nonbipartite.

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