A numerically efficient method for the MAP/D/1/K queue via rational approximations

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dc.citation.epage120en_US
dc.citation.issueNumber1-2en_US
dc.citation.spage97en_US
dc.citation.volumeNumber22en_US
dc.contributor.authorAkar, N.en_US
dc.contributor.authorArıkan, E.en_US
dc.date.accessioned2016-02-08T10:50:43Z
dc.date.available2016-02-08T10:50:43Z
dc.date.issued1996-03en_US
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractThe Markovian Arrival Process (MAP), which contains the Markov Modulated Poisson Process (MMPP) and the Phase-Type (PH) renewal processes as special cases, is a convenient traffic model for use in the performance analysis of Asynchronous Transfer Mode (ATM) networks. In ATM networks, packets are of fixed length and the buffering memory in switching nodes is limited to a finite numberK of cells. These motivate us to study the MAP/D/1/K queue. We present an algorithm to compute the stationary virtual waiting time distribution for the MAP/D/1/K queue via rational approximations for the deterministic service time distribution in transform domain. These approximations include the well-known Erlang distributions and the Padé approximations that we propose. Using these approximations, the solution for the queueing system is shown to reduce to the solution of a linear differential equation with suitable boundary conditions. The proposed algorithm has a computational complexity independent of the queue storage capacityK. We show through numerical examples that, the idea of using Padé approximations for the MAP/D/1/K queue can yield very high accuracy with tractable computational load even in the case of large queue capacities.en_US
dc.identifier.eissn1572-9443
dc.identifier.issn0257-0130
dc.identifier.urihttp://hdl.handle.net/11693/25812
dc.language.isoEnglishen_US
dc.publisherSpringer New York LLCen_US
dc.source.titleQueueing Systems : Theory and Applicationsen_US
dc.subjectPerformance analysis of ATM networksen_US
dc.subjectMarkovian arrival processen_US
dc.subjectFinite buffer queuesen_US
dc.subjectLoss probabilityen_US
dc.subjectState-space representationsen_US
dc.subjectPadé approximationsen_US
dc.titleA numerically efficient method for the MAP/D/1/K queue via rational approximationsen_US
dc.typeArticleen_US

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