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dc.contributor.authorAkar, N.en_US
dc.contributor.authorSohraby, K.en_US
dc.date.accessioned2016-02-08T11:46:24Z
dc.date.available2016-02-08T11:46:24Z
dc.date.issued2006en_US
dc.identifier.urihttp://hdl.handle.net/11693/27165
dc.description.abstractMarkov renewal processes with semi-Markov kernel matrices that have matrix-exponential representations form a superset of the well-known phase-type renewal process, Markovian arrival process, and the recently introduced rational arrival process. In this paper, we study the steady-state waiting time distribution in an infinite capacity single server queue with the auto-correlation in interarrival and service times modeled with this general Markov renewal process. Our method relies on the algebraic equivalence between this waiting time distribution and the output of a feedback control system certain parameters of which are to be determined through the solution of a well known numerical linear algebra problem, namely the SDC (Spectral-Divide-and- Conquer) problem. We provide an algorithmic solution to the SDC problem and in turn obtain a simple matrix exponential representation for the waiting time distribution using the ordered Schur decomposition that is known to have numerically stable and efficient implementations in various computing platforms. Copyright 2006 ACM.en_US
dc.language.isoEnglishen_US
dc.source.titleACM International Conference Proceeding Seriesen_US
dc.relation.isversionofhttp://dx.doi.org/10.1145/1190095.1190109en_US
dc.subjectLindley equationen_US
dc.subjectMarkov renewal processesen_US
dc.subjectMatrix exponential distributionen_US
dc.subjectOrdered schur decompositionen_US
dc.subjectFeedback controlen_US
dc.subjectMarkov processesen_US
dc.subjectMatrix algebraen_US
dc.subjectProblem solvingen_US
dc.subjectQuality of serviceen_US
dc.subjectServersen_US
dc.subjectLindley equationen_US
dc.subjectMarkov renewal processesen_US
dc.subjectMatrix exponential distributionen_US
dc.subjectOrdered schur decompositionen_US
dc.subjectQueueing networksen_US
dc.titleSolving the single server semi-Markov queue with matrix exponential kernel matrices for interarrivals and servicesen_US
dc.typeConference Paperen_US
dc.departmentDepartment of Electrical and Electronics Engineering
dc.citation.volumeNumber180en_US
dc.identifier.doi10.1145/1190095.1190109en_US


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