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Structured Markov Chains Arising from Finite-Source Retrial Queues with Orital Search

Authors: Patrick Wüchner, János Sztrik, and Hermann de Meer

Published in: Dagstuhl Seminar Proceedings, Volume 7461, Numerical Methods for Structured Markov Chains (2008)

Abstract

We consider retrial queueing systems with a finite number of homogeneous sources of calls, a single reliable server, and the search for orbiting customers by the server after job completion. During this investigation, the infinitesimal generator of the underlying (finite) continuous-time Markov chain takes a (level-dependent) QBD-like form. After solving for the steady state probabilities using the MOSEL-2 tool, the results show a surprising maximum of the mean response time. This maximum was already discovered by other researchers dealing with finite-source retrial queues. However, to our best knowledge, no thorough investigation was done yet why this maximum exists and in which way it depends on the system parameters. In the talk, after introducing the backgrounds of finite-source retrial queues with orbital search, a generalized stochastic Petri net is used to derive the underlying continuous-time Markov chain and its generator. Finally, using the seminar, we can hopefully bring forward discussions how to make more general statements on the parameter-dependent behavior of the response time’s maximum.

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Patrick Wüchner, János Sztrik, and Hermann de Meer. Structured Markov Chains Arising from Finite-Source Retrial Queues with Orital Search. In Numerical Methods for Structured Markov Chains. Dagstuhl Seminar Proceedings, Volume 7461, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{wuchner_et_al:DagSemProc.07461.15,
  author =	{W\"{u}chner, Patrick and Sztrik, J\'{a}nos and de Meer, Hermann},
  title =	{{Structured Markov Chains Arising from Finite-Source Retrial Queues with Orital Search}},
  booktitle =	{Numerical Methods for Structured Markov Chains},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7461},
  editor =	{Dario Bini and Beatrice Meini and Vaidyanathan Ramaswami and Marie-Ange Remiche and Peter Taylor},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07461.15},
  URN =		{urn:nbn:de:0030-drops-13895},
  doi =		{10.4230/DagSemProc.07461.15},
  annote =	{Keywords: Structured Markov chain, finite source, retrial queues, orbital search, performance measures, performance tool}
}

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Structured Markov Chains Arising from Finite-Source Retrial Queues with Orital Search

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