On the convergence to stationarity of birth-death processes

P. Coolen-Schrijner, Erik A. van Doorn

    Research output: Book/ReportReportOther research output

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    Abstract

    Taking up a recent proposal by Stadje and Parthasarathy in the \linebreak[4] setting of the many-server Poisson queue, we consider the integral \linebreak[4] $\int_0^{\infty}[\lim_{u\to\infty} E(X(u))-E(X(t))]dt$ as a measure of the speed of convergence towards stationarity of the process $\{X(t), t \geq 0\}$, and evaluate the integral explicitly in terms of the parameters of the process in the case that $\{X(t), t \geq 0\}$ is an ergodic birth-death process on $\{0,1,\ldots\}$ starting in 0. We also discuss the discrete-time counterpart of this result, and examine some specific examples.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Publication statusPublished - 2000

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1554
    ISSN (Print)0169-2690

    Keywords

    • MSC-60J80
    • IR-65741
    • EWI-3374

    Cite this

    Coolen-Schrijner, P., & van Doorn, E. A. (2000). On the convergence to stationarity of birth-death processes. (Memorandum / Department of Applied Mathematics; No. 1554). Enschede: University of Twente, Department of Applied Mathematics.
    Coolen-Schrijner, P. ; van Doorn, Erik A. / On the convergence to stationarity of birth-death processes. Enschede : University of Twente, Department of Applied Mathematics, 2000. (Memorandum / Department of Applied Mathematics; 1554).
    @book{aa4b824bbcb74b6c8a2a02ebc3d62e22,
    title = "On the convergence to stationarity of birth-death processes",
    abstract = "Taking up a recent proposal by Stadje and Parthasarathy in the \linebreak[4] setting of the many-server Poisson queue, we consider the integral \linebreak[4] $\int_0^{\infty}[\lim_{u\to\infty} E(X(u))-E(X(t))]dt$ as a measure of the speed of convergence towards stationarity of the process $\{X(t), t \geq 0\}$, and evaluate the integral explicitly in terms of the parameters of the process in the case that $\{X(t), t \geq 0\}$ is an ergodic birth-death process on $\{0,1,\ldots\}$ starting in 0. We also discuss the discrete-time counterpart of this result, and examine some specific examples.",
    keywords = "MSC-60J80, IR-65741, EWI-3374",
    author = "P. Coolen-Schrijner and {van Doorn}, {Erik A.}",
    note = "Imported from MEMORANDA",
    year = "2000",
    language = "Undefined",
    series = "Memorandum / Department of Applied Mathematics",
    publisher = "University of Twente, Department of Applied Mathematics",
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    }

    Coolen-Schrijner, P & van Doorn, EA 2000, On the convergence to stationarity of birth-death processes. Memorandum / Department of Applied Mathematics, no. 1554, University of Twente, Department of Applied Mathematics, Enschede.

    On the convergence to stationarity of birth-death processes. / Coolen-Schrijner, P.; van Doorn, Erik A.

    Enschede : University of Twente, Department of Applied Mathematics, 2000. (Memorandum / Department of Applied Mathematics; No. 1554).

    Research output: Book/ReportReportOther research output

    TY - BOOK

    T1 - On the convergence to stationarity of birth-death processes

    AU - Coolen-Schrijner, P.

    AU - van Doorn, Erik A.

    N1 - Imported from MEMORANDA

    PY - 2000

    Y1 - 2000

    N2 - Taking up a recent proposal by Stadje and Parthasarathy in the \linebreak[4] setting of the many-server Poisson queue, we consider the integral \linebreak[4] $\int_0^{\infty}[\lim_{u\to\infty} E(X(u))-E(X(t))]dt$ as a measure of the speed of convergence towards stationarity of the process $\{X(t), t \geq 0\}$, and evaluate the integral explicitly in terms of the parameters of the process in the case that $\{X(t), t \geq 0\}$ is an ergodic birth-death process on $\{0,1,\ldots\}$ starting in 0. We also discuss the discrete-time counterpart of this result, and examine some specific examples.

    AB - Taking up a recent proposal by Stadje and Parthasarathy in the \linebreak[4] setting of the many-server Poisson queue, we consider the integral \linebreak[4] $\int_0^{\infty}[\lim_{u\to\infty} E(X(u))-E(X(t))]dt$ as a measure of the speed of convergence towards stationarity of the process $\{X(t), t \geq 0\}$, and evaluate the integral explicitly in terms of the parameters of the process in the case that $\{X(t), t \geq 0\}$ is an ergodic birth-death process on $\{0,1,\ldots\}$ starting in 0. We also discuss the discrete-time counterpart of this result, and examine some specific examples.

    KW - MSC-60J80

    KW - IR-65741

    KW - EWI-3374

    M3 - Report

    T3 - Memorandum / Department of Applied Mathematics

    BT - On the convergence to stationarity of birth-death processes

    PB - University of Twente, Department of Applied Mathematics

    CY - Enschede

    ER -

    Coolen-Schrijner P, van Doorn EA. On the convergence to stationarity of birth-death processes. Enschede: University of Twente, Department of Applied Mathematics, 2000. (Memorandum / Department of Applied Mathematics; 1554).