Analysis of Queues with Rational Arrival Process Components - A General Approach

Nigel Bean, Bo Friis Nielsen

    Research output: Book/ReportReportResearch

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    Abstract

    In a previous paper we demonstrated that the well known matrix-geometric solution of Quasi-Birth-and-Death processes is valid also if we introduce Rational Arrival Process (RAP) components. Here we extend those results and we offer an alternative proof by using results obtained by Tweedie. We prove the matrix-geometric form for a certain kind of operators on the stationary measure for discrete time Markov chains of GI/M/1 type. We apply this result to an embedded chain with RAP components. We then discuss the straight- forward modification of the standard algorithms for calculating the matrix R in the traditional QBD framework. Finally we present examples demonstrating great reductions in dimensionality from the traditional QBD framework to the QBD - RAP framework.
    Original languageEnglish
    Place of PublicationKgs. Lyngby
    PublisherTechnical University of Denmark
    Number of pages32
    Publication statusPublished - 2011
    SeriesIMM-Technical Report-2011
    Number05

    Keywords

    • Rational Arrival Processes
    • Quasi-Birth-and-Death Processes
    • Matrix- Analytic Methods
    • Algorithmic Probability

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