A retrial BMAP/PH/N system
Identifieur interne : 001D27 ( Main/Exploration ); précédent : 001D26; suivant : 001D28A retrial BMAP/PH/N system
Auteurs : Lothar Breuer [Allemagne] ; Alexander Dudin [Biélorussie] ; Valentina Klimenok [Biélorussie]Source :
- Queueing systems [ 0257-0130 ] ; 2002.
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- Pascal (Inist)
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Abstract
A multi-server retrial queueing model with Batch Markovian Arrival Process and phase-type service time distribution is analyzed. The continuous-time multi-dimensional Markov chain describing the behavior of the system is investigated by means of reducing it to the corresponding discrete-time multi-dimensional Markov chain. The latter belongs to the class of multi-dimensional quasi-Toeplitz Markov chains in the case of a constant retrial rate and to the class of multi-dimensional asymptotically quasi-Toeplitz Markov chains in the case of an infinitely increasing retrial rate. It allows to obtain the existence conditions for the stationary distribution and to elaborate the algorithms for calculating the stationary state probabilities.
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Computer Science</s1><s2>54286 Trier</s2><s3>DEU</s3><sZ>1 aut.</sZ></inist:fA14><country>Allemagne</country><wicri:noRegion>54286 Trier</wicri:noRegion><wicri:noRegion>Department IV - Computer Science</wicri:noRegion><wicri:noRegion>54286 Trier</wicri:noRegion><orgName type="university">Université de Trèves</orgName><placeName><settlement type="city">Trèves (Allemagne)</settlement><region type="land" nuts="1">Rhénanie-Palatinat</region></placeName></affiliation></author><author><name sortKey="Dudin, Alexander" sort="Dudin, Alexander" uniqKey="Dudin A" first="Alexander" last="Dudin">Alexander Dudin</name><affiliation wicri:level="1"><inist:fA14 i1="02"><s1>Department of Applied Mathematics and Computer Science, Belarus State University, 4 F Skorina Ave</s1><s2>220050, Minsk</s2><s3>BLR</s3><sZ>2 aut.</sZ><sZ>3 aut.</sZ></inist:fA14><country>Biélorussie</country><wicri:noRegion>220050, Minsk</wicri:noRegion></affiliation></author><author><name sortKey="Klimenok, Valentina" sort="Klimenok, Valentina" uniqKey="Klimenok V" first="Valentina" last="Klimenok">Valentina Klimenok</name><affiliation wicri:level="1"><inist:fA14 i1="02"><s1>Department of Applied Mathematics and Computer Science, Belarus State University, 4 F Skorina Ave</s1><s2>220050, Minsk</s2><s3>BLR</s3><sZ>2 aut.</sZ><sZ>3 aut.</sZ></inist:fA14><country>Biélorussie</country><wicri:noRegion>220050, Minsk</wicri:noRegion></affiliation></author></analytic><series><title level="j" type="main">Queueing systems</title><title level="j" type="abbreviated">Queueing syst.</title><idno type="ISSN">0257-0130</idno><imprint><date when="2002">2002</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Queueing systems</title><title level="j" type="abbreviated">Queueing syst.</title><idno type="ISSN">0257-0130</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Arrival process</term><term>Asymptotic approximation</term><term>Conditional distribution</term><term>Continuous time</term><term>Discrete time</term><term>Markov chain</term><term>Markov process</term><term>Service time</term><term>Time distribution</term><term>Toeplitz matrix</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Loi conditionnelle</term><term>Approximation asymptotique</term><term>Matrice Toeplitz</term><term>Temps discret</term><term>Chaîne Markov</term><term>Temps continu</term><term>Distribution temporelle</term><term>Temps service</term><term>Processus arrivée</term><term>Processus Markov</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">A multi-server retrial queueing model with Batch Markovian Arrival Process and phase-type service time distribution is analyzed. The continuous-time multi-dimensional Markov chain describing the behavior of the system is investigated by means of reducing it to the corresponding discrete-time multi-dimensional Markov chain. The latter belongs to the class of multi-dimensional quasi-Toeplitz Markov chains in the case of a constant retrial rate and to the class of multi-dimensional asymptotically quasi-Toeplitz Markov chains in the case of an infinitely increasing retrial rate. It allows to obtain the existence conditions for the stationary distribution and to elaborate the algorithms for calculating the stationary state probabilities.</div></front></TEI><affiliations><list><country><li>Allemagne</li><li>Biélorussie</li></country><region><li>Rhénanie-Palatinat</li></region><settlement><li>Trèves (Allemagne)</li></settlement><orgName><li>Université de Trèves</li></orgName></list><tree><country name="Allemagne"><region name="Rhénanie-Palatinat"><name sortKey="Breuer, Lothar" sort="Breuer, Lothar" uniqKey="Breuer L" first="Lothar" last="Breuer">Lothar Breuer</name></region></country><country name="Biélorussie"><noRegion><name sortKey="Dudin, Alexander" sort="Dudin, Alexander" uniqKey="Dudin A" first="Alexander" last="Dudin">Alexander Dudin</name></noRegion><name sortKey="Klimenok, Valentina" sort="Klimenok, Valentina" uniqKey="Klimenok V" first="Valentina" last="Klimenok">Valentina Klimenok</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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