Solving the ME/ME/1 queue with state–space methods and the matrix sign function

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dc.citation.epage145en_US
dc.citation.issueNumber2en_US
dc.citation.spage131en_US
dc.citation.volumeNumber63en_US
dc.contributor.authorAkar, N.en_US
dc.date.accessioned2016-02-08T10:20:18Z
dc.date.available2016-02-08T10:20:18Z
dc.date.issued2006en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractMatrix exponential (ME) distributions not only include the well-known class of phase-type distributions but also can be used to approximate more general distributions (e.g., deterministic, heavy-tailed, etc.). In this paper, a novel mathematical framework and a numerical algorithm are proposed to calculate the matrix exponential representation for the steady-state waiting time in an ME/ME/1 queue. Using state-space algebra, the waiting time calculation problem is shown to reduce to finding the solution of an ordinary differential equation in state-space form with order being the sum of the dimensionalities of the inter-arrival and service time distribution representations. A numerically efficient algorithm with quadratic convergence rates based on the matrix sign function iterations is proposed to find the boundary conditions of the differential equation. The overall algorithm does not involve any transform domain calculations such as root finding or polynomial factorization, which are known to have potential numerical stability problems. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.en_US
dc.description.provenanceMade available in DSpace on 2016-02-08T10:20:18Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 70227 bytes, checksum: 26e812c6f5156f83f0e77b261a471b5a (MD5) Previous issue date: 2006en
dc.identifier.doi10.1016/j.peva.2004.12.002en_US
dc.identifier.issn
dc.identifier.issn0166-5316
dc.identifier.urihttp://hdl.handle.net/11693/23856
dc.language.isoEnglishen_US
dc.publisherElsevier BV * North-Hollanden_US
dc.relation.isversionofhttps://doi.org/10.1016/j.peva.2004.12.002en_US
dc.source.titlePerformance Evaluationen_US
dc.subjectGI/GI/1 queueen_US
dc.subjectLindley's equationen_US
dc.subjectMatrix exponential distributionen_US
dc.subjectRealization theoryen_US
dc.subjectMatrix sign functionen_US
dc.titleSolving the ME/ME/1 queue with state–space methods and the matrix sign functionen_US
dc.typeArticleen_US

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