Journal of Applied Probability

Stability of the stochastic matching model

Jean Mairesse and Pascal Moyal

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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.

Article information

J. Appl. Probab., Volume 53, Number 4 (2016), 1064-1077.

First available in Project Euclid: 7 December 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx] 05C75: Structural characterization of families of graphs

Markovian queueing theory stability matching graph


Mairesse, Jean; Moyal, Pascal. Stability of the stochastic matching model. J. Appl. Probab. 53 (2016), no. 4, 1064--1077.

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