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

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    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.

    Originele taal-2Engels
    Pagina's (van-tot)211-236
    Aantal pagina's26
    TijdschriftQueueing Systems
    Volume84
    Nummer van het tijdschrift3-4
    DOI's
    StatusGepubliceerd - 1 dec 2016

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