Quasi-Birth-and-Death Processes with Rational Arrival Process Components

Nigel G. Bean, Bo Friis Nielsen

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    Abstract

    In this paper we introduce the concept of a Quasi-Birth-and-Death process (QBD) with Rational Arrival Process components. We use the physical interpretation of a Rational Arrival Process (RAP), developed by Asmussen and Bladt, to consider such a Markov process. We exploit this interpretation to develop an analytic method for such a process, that parallels the analysis of a traditional QBD. We demonstrate the analysis by considering a queue where the arrival process and the sequence of service times are derived from two different RAPs that are not just Markovian Arrival processes. We also introduce an element of correlation between the arrival process and the sequence of service times.
    Original languageEnglish
    Place of PublicationLyngby
    PublisherInformatics and Mathematical Modelling, Technical University of Denmark, DTU
    Publication statusPublished - 2007
    SeriesD T U Compute. Technical Report
    Number20
    ISSN1601-2321

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