A matrix analytical method for the discrete time Lindley equation using the generalized Schur decomposition

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dc.contributor.authorAkar, Nailen_US
dc.coverage.spatialPisa, Italyen_US
dc.date.accessioned2016-02-08T11:46:26Z
dc.date.available2016-02-08T11:46:26Z
dc.date.issued2006en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.descriptionDate of Conference: 10 October 2006en_US
dc.descriptionConference Name: 1st International ICST Workshop on Tools for solving Structured Markov Chains, SMCTools 2006en_US
dc.description.abstractIn this paper, we study the discrete time Lindley equation governing an infinite size GI/GI/1 queue. In this queuing system, the arrivals and services are independent and identically distributed but they obey a discrete time matrix geometric distribution not necessarily with finite support. Our GI/GI/1 model allows geometric batch arrivals and also treats late, early, and hybrid arrival models in a unified manner. We reduce the problem of finding the steady state probabilities for the Lindley equation to finding the generalized ordered Schur form of a matrix pair (E, A) where the size of these matrices are the sum, not the product, of the orders of individual arrival and service distributions. The approach taken in this paper is purely matrix analytical and we obtain a matrix geometric representation for the related quantities (queue lengths or waiting times) for the discrete time GI/GI/1 queue using this approach.en_US
dc.identifier.doi10.1145/1190366.1190377en_US
dc.identifier.urihttp://hdl.handle.net/11693/27167
dc.language.isoEnglishen_US
dc.publisherACMen_US
dc.relation.isversionofhttp://dx.doi.org/10.1145/1190366.1190377en_US
dc.source.titleSMCTools'06: Proceeding from the 2006 Workshop on Tools for Solving Structured Markov Chainsen_US
dc.subjectDiscrete-time queuesen_US
dc.subjectGeneralized ordered Schur decompositionen_US
dc.subjectLindley equationen_US
dc.subjectMatrix geometric distributionen_US
dc.subjectMatrix analytical methodsen_US
dc.subjectProbability distributionsen_US
dc.subjectQueueing networksen_US
dc.titleA matrix analytical method for the discrete time Lindley equation using the generalized Schur decompositionen_US
dc.typeConference Paperen_US

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