Skip to main content Accessibility help
×
Home
Hostname: page-component-559fc8cf4f-6f8dk Total loading time: 0.273 Render date: 2021-03-08T07:06:25.501Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Stability of the stochastic matching model

Published online by Cambridge University Press:  09 December 2016

Jean Mairesse
Affiliation:
CNRS and UPMC
Pascal Moyal
Affiliation:
Université de Technologie de Compiègne and Northwestern University
Corresponding
E-mail address:

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.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2016 

Access options

Get access to the full version of this content by using one of the access options below.

References

[1] Adan, I. and Weiss, G. (2012).Exact FCFS matching rates for two infinite multitype sequences.Operat. Res. 60,475489.CrossRefGoogle Scholar
[2] Adan, I.,Bušić, A.,Mairesse, J. and Weiss, G. (2016).Reversibility and further properties of FCFS infinite bipartite matching.Available at http://arxiv.org/abs/1507.05939v1.Google Scholar
[3] Brémaud, P. (1999).Markov Chains: Gibbs Fields, Monte Carlo Simulation, and Queues(Texts Appl. Math. 31).Springer,New York.CrossRefGoogle Scholar
[4] Brualdi, R. A.,Harary, F. and Miller, Z. (1980).Bigraphs versus digraphs via matrices.J. Graph Theory 4,5173.CrossRefGoogle Scholar
[5] Bušić, A.,Gupta, V. and Mairesse, J. (2013).Stability of the bipartite matching model.Adv. Appl. Prob. 45,351378.CrossRefGoogle Scholar
[6] Caldentey, R.,Kaplan, E. H. and Weiss, G. (2009).FCFS infinite bipartite matching of servers and customers.Adv. Appl. Prob. 41,695730.CrossRefGoogle Scholar
[7] Fayolle, G.,Malyshev, V. A. and Menshikov, M. (1995).Topics in the Constructive Theory of Countable Markov Chains.Cambridge University Press.CrossRefGoogle Scholar
[8] Gans, N.,Koole, G. and Mandelbaum, A. (2003).Telephone call centers: tutorial, review, and research prospects.Manufacturing Serv. Operat. Manag. 5,79141.CrossRefGoogle Scholar
[9] Gurvich, I. and Ward, A. (2014).On the dynamic control of matching queues.Stoch. Systems 4,479523.CrossRefGoogle Scholar
[10] Kumar, P. R. (1993).Re-entrant lines.Queueing Systems Theory Appl. 13,87110.CrossRefGoogle Scholar
[11] McKeown, N.,Mekkittikul, A.,Anantharam, V. and Walrand, J. (1999).Achieving 100% throughput in an input-queued switch.IEEE Trans. Commun. 47,12601267.CrossRefGoogle Scholar
[12] Tassiulas, L. and Ephremides, A. (1992).Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks.IEEE Trans. Automatic Control 37,19361948.CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 84 *
View data table for this chart

* Views captured on Cambridge Core between 09th December 2016 - 8th March 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Stability of the stochastic matching model
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Stability of the stochastic matching model
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Stability of the stochastic matching model
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *