Journal of Applied Probability

Stability of the stochastic matching model

Jean Mairesse and Pascal Moyal

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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.

Article information

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

Dates
First available in Project Euclid: 7 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.jap/1481132837

Mathematical Reviews number (MathSciNet)
MR3581242

Zentralblatt MATH identifier
1356.60147

Subjects
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

Keywords
Markovian queueing theory stability matching graph

Citation

Mairesse, Jean; Moyal, Pascal. Stability of the stochastic matching model. J. Appl. Probab. 53 (2016), no. 4, 1064--1077. https://projecteuclid.org/euclid.jap/1481132837


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