On the convergence to stationarity of birth-death processes

P. Coolen-Schrijner, Erik A. van Doorn

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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.