License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.07461.15
URN: urn:nbn:de:0030-drops-13895
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2008/1389/
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Wüchner, Patrick ; Sztrik, János ; de Meer, Hermann

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

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07461.WuechnerPatrick.Paper.1389.pdf (0.2 MB)

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.

BibTeX - Entry

@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/opus/volltexte/2008/1389},
  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}
}

Keywords: Structured Markov chain, finite source, retrial queues, orbital search, performance measures, performance tool
Collection: 07461 - Numerical Methods for Structured Markov Chains
Issue Date: 2008
Date of publication: 07.04.2008

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