On the numerical solution of Kronecker-based infinite level-dependent QBD processes

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dc.citation.epage681en_US
dc.citation.issueNumber9en_US
dc.citation.spage663en_US
dc.citation.volumeNumber70en_US
dc.contributor.authorBaumann, H.en_US
dc.contributor.authorDayar, T.en_US
dc.contributor.authorOrhan, M. C.en_US
dc.contributor.authorSandmann, W.en_US
dc.date.accessioned2016-02-08T09:38:06Z
dc.date.available2016-02-08T09:38:06Z
dc.date.issued2013en_US
dc.departmentDepartment of Computer Engineeringen_US
dc.description.abstractInfinite level-dependent quasi-birth-and-death (LDQBD) processes can be used to model Markovian systems with countably infinite multidimensional state spaces. Recently it has been shown that sums of Kronecker products can be used to represent the nonzero blocks of the transition rate matrix underlying an LDQBD process for models from stochastic chemical kinetics. This paper extends the form of the transition rates used recently so that a larger class of models including those of call centers can be analyzed for their steady-state. The challenge in the matrix analytic solution then is to compute conditional expected sojourn time matrices of the LDQBD model under low memory and time requirements after truncating its countably infinite state space judiciously. Results of numerical experiments are presented using a Kronecker-based matrix-analytic solution on models with two or more countably infinite dimensions and rules of thumb regarding better implementations are derived. In doing this, a more recent approach that reduces memory requirements further by enabling the computation of steady-state expectations without having to obtain the steady-state distribution is also considered. © 2013 Elsevier B.V. All rights reserved.en_US
dc.description.provenanceMade available in DSpace on 2016-02-08T09:38:06Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2013en
dc.identifier.doi10.1016/j.peva.2013.05.001en_US
dc.identifier.issn0166-5316
dc.identifier.urihttp://hdl.handle.net/11693/20924
dc.language.isoEnglishen_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/j.peva.2013.05.001en_US
dc.source.titlePerformance Evaluationen_US
dc.subjectCall centeren_US
dc.subjectKronecker producten_US
dc.subjectLevel - dependent QBD processen_US
dc.subjectMarkov chainen_US
dc.subjectMatrix analytic methoden_US
dc.subjectSteady - state expectationen_US
dc.subjectCall centersen_US
dc.subjectKronecker producten_US
dc.subjectMatrix analytic methodsen_US
dc.subjectQBD processen_US
dc.subjectAnalytical modelsen_US
dc.subjectMarkov processesen_US
dc.subjectResponse time (computer systems)en_US
dc.subjectStochastic modelsen_US
dc.titleOn the numerical solution of Kronecker-based infinite level-dependent QBD processesen_US
dc.typeArticleen_US

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