An efficient computation algorithm for a multiserver feedback retrial queue with a large queueing capacity
Kumar et al. consider the M/M/c/N+c feedback queue with constant retrial rate [1]. They provide a solution for the steady state probabilities based on the matrix-geometric method. We show that there exists a more efficient computation method to calculate the steady state probabilities when N + c is...
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| Veröffentlicht in: | Applied mathematical modelling 2010-08, Vol.34 (8), p.2272-2278 |
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| creator | Do, Tien Van |
| description | Kumar et al. consider the M/M/c/N+c feedback queue with constant retrial rate
[1]. They provide a solution for the steady state probabilities based on the matrix-geometric method. We show that there exists a more efficient computation method to calculate the steady state probabilities when
N
+
c
is large. We prove that the number of zero-eigenvalues of the characteristic matrix polynomial associated with the balance equation is
⌊
(
N
+
c
+
2
)
/
2
⌋
. As consequence, the remaining eigenvalues inside the unit circle can be computed in a quick manner based on the Sturm sequences. Therefore, the steady state probabilities can be determined in an efficient way. |
| doi_str_mv | 10.1016/j.apm.2009.10.025 |
| format | Article |
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[1]. They provide a solution for the steady state probabilities based on the matrix-geometric method. We show that there exists a more efficient computation method to calculate the steady state probabilities when
N
+
c
is large. We prove that the number of zero-eigenvalues of the characteristic matrix polynomial associated with the balance equation is
⌊
(
N
+
c
+
2
)
/
2
⌋
. As consequence, the remaining eigenvalues inside the unit circle can be computed in a quick manner based on the Sturm sequences. Therefore, the steady state probabilities can be determined in an efficient way.</description><identifier>ISSN: 0307-904X</identifier><identifier>DOI: 10.1016/j.apm.2009.10.025</identifier><identifier>CODEN: AMMODL</identifier><language>eng</language><publisher>Kidlington: Elsevier Inc</publisher><subject>Applied sciences ; Computational efficiency ; Efficient Algorithm ; Eigenvalues ; Exact sciences and technology ; Feedback ; Feedback queue ; Mathematical analysis ; Mathematical models ; Operational research and scientific management ; Operational research. Management science ; Queues ; Queuing theory. Traffic theory ; Steady state</subject><ispartof>Applied mathematical modelling, 2010-08, Vol.34 (8), p.2272-2278</ispartof><rights>2009 Elsevier Inc.</rights><rights>2015 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c403t-9ba585b1349ed36096c5c0642ccb87de7f6ac36c9862f382e3777cc35cde343a3</citedby><cites>FETCH-LOGICAL-c403t-9ba585b1349ed36096c5c0642ccb87de7f6ac36c9862f382e3777cc35cde343a3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0307904X09003576$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,3537,27901,27902,65534</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=22591379$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Do, Tien Van</creatorcontrib><title>An efficient computation algorithm for a multiserver feedback retrial queue with a large queueing capacity</title><title>Applied mathematical modelling</title><description>Kumar et al. consider the M/M/c/N+c feedback queue with constant retrial rate
[1]. They provide a solution for the steady state probabilities based on the matrix-geometric method. We show that there exists a more efficient computation method to calculate the steady state probabilities when
N
+
c
is large. We prove that the number of zero-eigenvalues of the characteristic matrix polynomial associated with the balance equation is
⌊
(
N
+
c
+
2
)
/
2
⌋
. As consequence, the remaining eigenvalues inside the unit circle can be computed in a quick manner based on the Sturm sequences. Therefore, the steady state probabilities can be determined in an efficient way.</description><subject>Applied sciences</subject><subject>Computational efficiency</subject><subject>Efficient Algorithm</subject><subject>Eigenvalues</subject><subject>Exact sciences and technology</subject><subject>Feedback</subject><subject>Feedback queue</subject><subject>Mathematical analysis</subject><subject>Mathematical models</subject><subject>Operational research and scientific management</subject><subject>Operational research. Management science</subject><subject>Queues</subject><subject>Queuing theory. Traffic theory</subject><subject>Steady state</subject><issn>0307-904X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kElLQzEQgN9Bwbr8AG-5CF5as7wteBJxA8GLgrcwnTepqW8zyVP6701p8ehpmOGb7cuyc8EXgovyar2AsVtIznXKF1wWB9mMK17NNc_fj7LjENac8yJls2x90zOy1qGjPjIcunGKEN3QM2hXg3fxo2N28AxYN7XRBfLf5JklapaAn8xT9A5a9jXRROwn4Ylswa9oV3L9iiGMgC5uTrNDC22gs308yd7u715vH-fPLw9PtzfPc8y5inO9hKIulkLlmhpVcl1igbzMJeKyrhqqbAmoStR1Ka2qJamqqhBVgQ2pXIE6yS53c0c_pCNCNJ0LSG0LPQ1TMKKshFR1rmVCxQ5FP4TgyZrRuw78xghuti7N2iSXZutyW0ouU8_FfjwEhNZ66NGFv0YpCy1UpRN3veMo_frtyJuwlYzUOE8YTTO4f7b8AjHKjSo</recordid><startdate>20100801</startdate><enddate>20100801</enddate><creator>Do, Tien Van</creator><general>Elsevier Inc</general><general>Elsevier</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>20100801</creationdate><title>An efficient computation algorithm for a multiserver feedback retrial queue with a large queueing capacity</title><author>Do, Tien Van</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c403t-9ba585b1349ed36096c5c0642ccb87de7f6ac36c9862f382e3777cc35cde343a3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Applied sciences</topic><topic>Computational efficiency</topic><topic>Efficient Algorithm</topic><topic>Eigenvalues</topic><topic>Exact sciences and technology</topic><topic>Feedback</topic><topic>Feedback queue</topic><topic>Mathematical analysis</topic><topic>Mathematical models</topic><topic>Operational research and scientific management</topic><topic>Operational research. Management science</topic><topic>Queues</topic><topic>Queuing theory. Traffic theory</topic><topic>Steady state</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Do, Tien Van</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>Technology Research Database</collection><collection>ProQuest Computer Science Collection</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 mathematical modelling</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Do, Tien Van</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An efficient computation algorithm for a multiserver feedback retrial queue with a large queueing capacity</atitle><jtitle>Applied mathematical modelling</jtitle><date>2010-08-01</date><risdate>2010</risdate><volume>34</volume><issue>8</issue><spage>2272</spage><epage>2278</epage><pages>2272-2278</pages><issn>0307-904X</issn><coden>AMMODL</coden><abstract>Kumar et al. consider the M/M/c/N+c feedback queue with constant retrial rate
[1]. They provide a solution for the steady state probabilities based on the matrix-geometric method. We show that there exists a more efficient computation method to calculate the steady state probabilities when
N
+
c
is large. We prove that the number of zero-eigenvalues of the characteristic matrix polynomial associated with the balance equation is
⌊
(
N
+
c
+
2
)
/
2
⌋
. As consequence, the remaining eigenvalues inside the unit circle can be computed in a quick manner based on the Sturm sequences. Therefore, the steady state probabilities can be determined in an efficient way.</abstract><cop>Kidlington</cop><pub>Elsevier Inc</pub><doi>10.1016/j.apm.2009.10.025</doi><tpages>7</tpages><oa>free_for_read</oa></addata></record> |
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| source | Elsevier ScienceDirect Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals |
| subjects | Applied sciences Computational efficiency Efficient Algorithm Eigenvalues Exact sciences and technology Feedback Feedback queue Mathematical analysis Mathematical models Operational research and scientific management Operational research. Management science Queues Queuing theory. Traffic theory Steady state |
| title | An efficient computation algorithm for a multiserver feedback retrial queue with a large queueing capacity |
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