An efficient method to compute the rate matrix for retrial queues with large number of servers
The approximate solution technique for the main M / M / c retrial queue based on the homogenization of the model employs a quasi-birth–death (QBD) process in which the maximum retrial rate is restricted above a certain level. This approximated continuous-time Markov chain (CTMC) can be solved by the...
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| Veröffentlicht in: | Applied mathematics letters 2010-05, Vol.23 (5), p.638-643 |
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| creator | Do, Tien Van Chakka, Ram |
| description | The approximate solution technique for the main
M
/
M
/
c
retrial queue based on the homogenization of the model employs a quasi-birth–death (QBD) process in which the maximum retrial rate is restricted above a certain level. This approximated continuous-time Markov chain (CTMC) can be solved by the matrix-geometric method, which involves the computation of the rate matrix
R
. This paper is motivated by two observations. Firstly, retrial queues for the performability analysis of telecommunication systems often involve the number of servers in the order of several hundreds of thousands. Secondly, there are no workable solutions till now for systems with such large number of servers, due to ill-conditioning or prohibitively large computation times. Our paper is the first to tackle the problem of large number of servers, very efficiently, in the homogenized
M
/
M
/
c
retrial queue which has paramount applications in networks. We present an efficient algorithm with the time complexity of only
O
(
c
)
to compute the rate matrix
R
. |
| doi_str_mv | 10.1016/j.aml.2010.02.003 |
| format | Article |
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M
/
M
/
c
retrial queue based on the homogenization of the model employs a quasi-birth–death (QBD) process in which the maximum retrial rate is restricted above a certain level. This approximated continuous-time Markov chain (CTMC) can be solved by the matrix-geometric method, which involves the computation of the rate matrix
R
. This paper is motivated by two observations. Firstly, retrial queues for the performability analysis of telecommunication systems often involve the number of servers in the order of several hundreds of thousands. Secondly, there are no workable solutions till now for systems with such large number of servers, due to ill-conditioning or prohibitively large computation times. Our paper is the first to tackle the problem of large number of servers, very efficiently, in the homogenized
M
/
M
/
c
retrial queue which has paramount applications in networks. We present an efficient algorithm with the time complexity of only
O
(
c
)
to compute the rate matrix
R
.</description><identifier>ISSN: 0893-9659</identifier><identifier>EISSN: 1873-5452</identifier><identifier>DOI: 10.1016/j.aml.2010.02.003</identifier><language>eng</language><publisher>Kidlington: Elsevier Ltd</publisher><subject>Algebra ; Algorithms ; Approximation ; Computation ; Exact sciences and technology ; Homogenization ; Homogenizing ; Linear and multilinear algebra, matrix theory ; Mathematical analysis ; Mathematical models ; Mathematics ; Matrix-geometric method ; Networks ; Numerical analysis ; Numerical analysis. Scientific computation ; Numerical methods in probability and statistics ; Partial differential equations ; Queues ; Retrial queues ; Sciences and techniques of general use ; Sequences, series, summability ; Servers ; Spectral expansion ; Stochastic models ; Telecommunications</subject><ispartof>Applied mathematics letters, 2010-05, Vol.23 (5), p.638-643</ispartof><rights>2010 Elsevier Ltd</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-a8adc677112bd82fdb6b40fd94daa33903a7c0d11b6961dc29a853a47dbd82113</citedby><cites>FETCH-LOGICAL-c359t-a8adc677112bd82fdb6b40fd94daa33903a7c0d11b6961dc29a853a47dbd82113</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S089396591000042X$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65306</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22580177$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Do, Tien Van</creatorcontrib><creatorcontrib>Chakka, Ram</creatorcontrib><title>An efficient method to compute the rate matrix for retrial queues with large number of servers</title><title>Applied mathematics letters</title><description>The approximate solution technique for the main
M
/
M
/
c
retrial queue based on the homogenization of the model employs a quasi-birth–death (QBD) process in which the maximum retrial rate is restricted above a certain level. This approximated continuous-time Markov chain (CTMC) can be solved by the matrix-geometric method, which involves the computation of the rate matrix
R
. This paper is motivated by two observations. Firstly, retrial queues for the performability analysis of telecommunication systems often involve the number of servers in the order of several hundreds of thousands. Secondly, there are no workable solutions till now for systems with such large number of servers, due to ill-conditioning or prohibitively large computation times. Our paper is the first to tackle the problem of large number of servers, very efficiently, in the homogenized
M
/
M
/
c
retrial queue which has paramount applications in networks. We present an efficient algorithm with the time complexity of only
O
(
c
)
to compute the rate matrix
R
.</description><subject>Algebra</subject><subject>Algorithms</subject><subject>Approximation</subject><subject>Computation</subject><subject>Exact sciences and technology</subject><subject>Homogenization</subject><subject>Homogenizing</subject><subject>Linear and multilinear algebra, matrix theory</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Matrix-geometric method</subject><subject>Networks</subject><subject>Numerical analysis</subject><subject>Numerical analysis. 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Scientific computation</topic><topic>Numerical methods in probability and statistics</topic><topic>Partial differential equations</topic><topic>Queues</topic><topic>Retrial queues</topic><topic>Sciences and techniques of general use</topic><topic>Sequences, series, summability</topic><topic>Servers</topic><topic>Spectral expansion</topic><topic>Stochastic models</topic><topic>Telecommunications</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Do, Tien Van</creatorcontrib><creatorcontrib>Chakka, Ram</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Applied mathematics letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Do, Tien Van</au><au>Chakka, Ram</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An efficient method to compute the rate matrix for retrial queues with large number of servers</atitle><jtitle>Applied mathematics letters</jtitle><date>2010-05-01</date><risdate>2010</risdate><volume>23</volume><issue>5</issue><spage>638</spage><epage>643</epage><pages>638-643</pages><issn>0893-9659</issn><eissn>1873-5452</eissn><abstract>The approximate solution technique for the main
M
/
M
/
c
retrial queue based on the homogenization of the model employs a quasi-birth–death (QBD) process in which the maximum retrial rate is restricted above a certain level. This approximated continuous-time Markov chain (CTMC) can be solved by the matrix-geometric method, which involves the computation of the rate matrix
R
. This paper is motivated by two observations. Firstly, retrial queues for the performability analysis of telecommunication systems often involve the number of servers in the order of several hundreds of thousands. Secondly, there are no workable solutions till now for systems with such large number of servers, due to ill-conditioning or prohibitively large computation times. Our paper is the first to tackle the problem of large number of servers, very efficiently, in the homogenized
M
/
M
/
c
retrial queue which has paramount applications in networks. We present an efficient algorithm with the time complexity of only
O
(
c
)
to compute the rate matrix
R
.</abstract><cop>Kidlington</cop><pub>Elsevier Ltd</pub><doi>10.1016/j.aml.2010.02.003</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Applied mathematics letters, 2010-05, Vol.23 (5), p.638-643 |
| issn | 0893-9659 1873-5452 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_753740210 |
| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Algebra Algorithms Approximation Computation Exact sciences and technology Homogenization Homogenizing Linear and multilinear algebra, matrix theory Mathematical analysis Mathematical models Mathematics Matrix-geometric method Networks Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Partial differential equations Queues Retrial queues Sciences and techniques of general use Sequences, series, summability Servers Spectral expansion Stochastic models Telecommunications |
| title | An efficient method to compute the rate matrix for retrial queues with large number of servers |
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