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dc.contributor.authorAkar, Nailen_US
dc.contributor.authorSohraby, K.en_US
dc.coverage.spatialPisa, Italyen_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.descriptionDate of Conference: 11-13 October 2006en_US
dc.descriptionConference Name: 1st International Conference on Performance Evaluation Methodolgies and Tools, VALUETOOLS 2006en_US
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.en_US
dc.language.isoEnglishen_US
dc.source.titleProceedings of the 1st International Conference on Performance Evaluation Methodolgies and Tools, VALUETOOLS 2006en_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.subjectMarkov processesen_US
dc.subjectMatrix algebraen_US
dc.subjectQuality of serviceen_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 Engineeringen_US
dc.identifier.doi10.1145/1190095.1190109en_US
dc.publisherACMen_US


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