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dc.contributor.authorAkar, N.en_US
dc.contributor.authorSohraby, K.en_US
dc.date.accessioned2016-02-08T10:01:55Z
dc.date.available2016-02-08T10:01:55Z
dc.date.issued2009-05-07en_US
dc.identifier.issn0166-5316
dc.identifier.urihttp://hdl.handle.net/11693/22577
dc.description.abstractMarkov renewal processes with matrix-exponential semi-Markov kernels provide a generic tool for modeling auto-correlated interarrival and service times in queueing systems. In this paper, we study the steady-state actual waiting time distribution in an infinite capacity single-server semi-Markov queue with the auto-correlation in interarrival and service times modeled by Markov renewal processes with matrix-exponential kernels. Our approach is based on the equivalence between the waiting time distribution of this semi-Markov queue and the output of a linear feedback interconnection system. The unknown parameters of the latter system need to be determined through the solution of a SDC (Spectral-Divide-and-Conquer) problem for which we propose to use the ordered Schur decomposition. This approach leads us to a completely matrix-analytical algorithm to calculate the steady-state waiting time which has a matrix-exponential distribution. Besides its unifying structure, the proposed algorithm is easy to implement and is computationally efficient and stable. We validate the effectiveness and the generality of the proposed approach through numerical examples.en_US
dc.language.isoEnglishen_US
dc.source.titlePerformance Evaluationen_US
dc.relation.isversionofhttp://dx.doi.org/10.1016/j.peva.2009.05.001en_US
dc.subjectCorrelated arrivals and servicesen_US
dc.subjectLindley equationen_US
dc.subjectMatrix-analytical approachen_US
dc.subjectSchur decompositionen_US
dc.subjectSemi-Markov queuesen_US
dc.titleSystem-theoretical algorithmic solution to waiting times in semi-Markov queuesen_US
dc.typeArticleen_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.citation.spage587en_US
dc.citation.epage606en_US
dc.citation.volumeNumber66en_US
dc.citation.issueNumber11en_US
dc.identifier.doi10.1016/j.peva.2009.05.001en_US
dc.publisherELSEVIERen_US


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