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Article: Iterative methods for queuing systems with batch arrivals and negative customers

TitleIterative methods for queuing systems with batch arrivals and negative customers
Authors
Ching, WK
KeywordsCirculant matrix
Negative customers
Preconditioning
Queuing systems
Toeplitz matrix
Issue Date2003
PublisherSpringer Verlag Dordrecht. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0006-3835
Citation
Bit Numerical Mathematics, 2003, v. 43 n. 2, p. 285-296 How to Cite?
DOI: http://dx.doi.org/10.1023/A:1026031011953
AbstractIn this paper, we are interested in solving the stationary probability distributions of Markovian queuing systems having batch arrivals and negative customers by using the Preconditioned Conjugate Gradient Squared (PCGS) method. The preconditioner is constructed by exploiting the near-Toeplitz structure of the generator matrix of the system. We proved that under some mild conditions the preconditioned linear systems have singular values clustered around one when the size of the queue tends to infinity. Numerical results indicated that the convergence rate of the proposed method is very fast.
Persistent Identifierhttp://hdl.handle.net/10722/75130
ISSN
0006-3835
2021 Impact Factor: 1.856
2020 SCImago Journal Rankings: 0.904
ISI Accession Number ID
WOS:000187391100004
References
References in Scopus

 

DC FieldValueLanguage
dc.contributor.authorChing, WKen_HK
dc.date.accessioned2010-09-06T07:08:12Z-
dc.date.available2010-09-06T07:08:12Z-
dc.date.issued2003en_HK
dc.identifier.citationBit Numerical Mathematics, 2003, v. 43 n. 2, p. 285-296en_HK
dc.identifier.issn0006-3835en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75130-
dc.description.abstractIn this paper, we are interested in solving the stationary probability distributions of Markovian queuing systems having batch arrivals and negative customers by using the Preconditioned Conjugate Gradient Squared (PCGS) method. The preconditioner is constructed by exploiting the near-Toeplitz structure of the generator matrix of the system. We proved that under some mild conditions the preconditioned linear systems have singular values clustered around one when the size of the queue tends to infinity. Numerical results indicated that the convergence rate of the proposed method is very fast.en_HK
dc.languageengen_HK
dc.publisherSpringer Verlag Dordrecht. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0006-3835en_HK
dc.relation.ispartofBIT Numerical Mathematicsen_HK
dc.subjectCirculant matrixen_HK
dc.subjectNegative customersen_HK
dc.subjectPreconditioningen_HK
dc.subjectQueuing systemsen_HK
dc.subjectToeplitz matrixen_HK
dc.titleIterative methods for queuing systems with batch arrivals and negative customersen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0006-3835&volume=43&spage=285&epage=296&date=2003&atitle=Iterative+Methods+for+Queuing+Systems+with+Batch+Arrivals+and+Negative+Customersen_HK
dc.identifier.emailChing, WK:wching@hku.hken_HK
dc.identifier.authorityChing, WK=rp00679en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1023/A:1026031011953en_HK
dc.identifier.scopuseid_2-s2.0-4043071990en_HK
dc.identifier.hkuros88728en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-4043071990&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume43en_HK
dc.identifier.issue2en_HK
dc.identifier.spage285en_HK
dc.identifier.epage296en_HK
dc.identifier.isiWOS:000187391100004-
dc.publisher.placeNetherlandsen_HK
dc.identifier.scopusauthoridChing, WK=13310265500en_HK
dc.identifier.issnl0006-3835-

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