Dominant poles and tail asymptotics in the critical Gaussian many-sources regime

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    Abstract

    The dominant pole approximation (DPA) is a classical analytic method to obtain from a generating function asymptotic estimates for its underlying coefficients. We apply DPA to a discrete queue in a critical many-sources regime, in order to obtain tail asymptotics for the stationary queue length. As it turns out, this regime leads to a clustering of the poles of the generating function, which renders the classical DPA useless, since the dominant pole is not sufficiently dominant. To resolve this, we design a new DPA method, which might also find application in other areas of mathematics, like combinatorics, particularly when Gaussian scalings related to the central limit theorem are involved.

    Original languageEnglish
    Pages (from-to)211-236
    Number of pages26
    JournalQueueing Systems
    Volume84
    Issue number3-4
    DOIs
    Publication statusPublished - 1 Dec 2016

    Keywords

    • Asymptotics
    • Dominant pole approximation
    • Heavy traffic
    • Many sources
    • QED regime
    • Saddle point method

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