The power-series algorithm. A numerical approach to Markov processes

W.B. van den Hout

    Research output: ThesisDoctoral ThesisScientific

    424 Downloads (Pure)

    Abstract

    The development of computer and communication networks and flexible manufacturing systems has led to new and interesting multidimensional queueing models. The Power-Series Algorithm is a numerical method to analyze and optimize the performance of such models. In this thesis, the applicability of the algorithm is extended. This is illustrated by introducing and analyzing a wide class of queueing networks with very general dependencies between the different queues. The theoretical basis of the algorithm is strengthened by proving analyticity of the steady-state distribution in light traffic and finding remedies for previous imperfections of the method. Applying similar ideas to the transient distribution renders new analyticity results. Various aspects of Markov processes, analytic functions and extrapolation methods are reviewed, necessary for a thorough understanding and efficient implementation of the Power-Series Algorithm.
    Original languageEnglish
    QualificationDoctor of Philosophy
    Awarding Institution
    • Tilburg University
    Supervisors/Advisors
    • Boxma, O.J., Promotor, External person
    • Blanc, Hans, Promotor
    Award date27 Mar 1996
    Place of PublicationTilburg
    Publisher
    Publication statusPublished - 1996

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    communication network
    numerical method
    manufacturing
    distribution
    method
    thesis
    traffic

    Cite this

    van den Hout, W. B. (1996). The power-series algorithm. A numerical approach to Markov processes. Tilburg: CentER, Center for Economic Research.
    van den Hout, W.B.. / The power-series algorithm. A numerical approach to Markov processes. Tilburg : CentER, Center for Economic Research, 1996. 143 p.
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    title = "The power-series algorithm. A numerical approach to Markov processes",
    abstract = "The development of computer and communication networks and flexible manufacturing systems has led to new and interesting multidimensional queueing models. The Power-Series Algorithm is a numerical method to analyze and optimize the performance of such models. In this thesis, the applicability of the algorithm is extended. This is illustrated by introducing and analyzing a wide class of queueing networks with very general dependencies between the different queues. The theoretical basis of the algorithm is strengthened by proving analyticity of the steady-state distribution in light traffic and finding remedies for previous imperfections of the method. Applying similar ideas to the transient distribution renders new analyticity results. Various aspects of Markov processes, analytic functions and extrapolation methods are reviewed, necessary for a thorough understanding and efficient implementation of the Power-Series Algorithm.",
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    year = "1996",
    language = "English",
    series = "CentER Dissertation Series",
    publisher = "CentER, Center for Economic Research",
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    van den Hout, WB 1996, 'The power-series algorithm. A numerical approach to Markov processes', Doctor of Philosophy, Tilburg University, Tilburg.

    The power-series algorithm. A numerical approach to Markov processes. / van den Hout, W.B.

    Tilburg : CentER, Center for Economic Research, 1996. 143 p.

    Research output: ThesisDoctoral ThesisScientific

    TY - THES

    T1 - The power-series algorithm. A numerical approach to Markov processes

    AU - van den Hout, W.B.

    PY - 1996

    Y1 - 1996

    N2 - The development of computer and communication networks and flexible manufacturing systems has led to new and interesting multidimensional queueing models. The Power-Series Algorithm is a numerical method to analyze and optimize the performance of such models. In this thesis, the applicability of the algorithm is extended. This is illustrated by introducing and analyzing a wide class of queueing networks with very general dependencies between the different queues. The theoretical basis of the algorithm is strengthened by proving analyticity of the steady-state distribution in light traffic and finding remedies for previous imperfections of the method. Applying similar ideas to the transient distribution renders new analyticity results. Various aspects of Markov processes, analytic functions and extrapolation methods are reviewed, necessary for a thorough understanding and efficient implementation of the Power-Series Algorithm.

    AB - The development of computer and communication networks and flexible manufacturing systems has led to new and interesting multidimensional queueing models. The Power-Series Algorithm is a numerical method to analyze and optimize the performance of such models. In this thesis, the applicability of the algorithm is extended. This is illustrated by introducing and analyzing a wide class of queueing networks with very general dependencies between the different queues. The theoretical basis of the algorithm is strengthened by proving analyticity of the steady-state distribution in light traffic and finding remedies for previous imperfections of the method. Applying similar ideas to the transient distribution renders new analyticity results. Various aspects of Markov processes, analytic functions and extrapolation methods are reviewed, necessary for a thorough understanding and efficient implementation of the Power-Series Algorithm.

    M3 - Doctoral Thesis

    T3 - CentER Dissertation Series

    PB - CentER, Center for Economic Research

    CY - Tilburg

    ER -

    van den Hout WB. The power-series algorithm. A numerical approach to Markov processes. Tilburg: CentER, Center for Economic Research, 1996. 143 p. (CentER Dissertation Series).