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The dominant pole approximation (DPA) is a classical analytic method toobtain from a generating function asymptotic estimates for its underlyingcoefficients. We apply DPA to a discrete queue in a critical many-sourcesregime, in order to obtain tail asymptotics for the stationary queue length. Asit turns out, this regime leads to a clustering of the poles of the generatingfunction, which renders the classical DPA useless, since the dominant pole isnot sufficiently dominant. To resolve this, we design a new DPA method, whichmight also find application in other areas of mathematics, like combinatorics,particularly when Gaussian scalings related to the central limit theorem areinvolved.

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