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

Queueing Systems, Sep 2016

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.

This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2Fs11134-016-9499-5.pdf

A. J. E. M. Janssen, J. S. H. van Leeuwaarden. Dominant poles and tail asymptotics in the critical Gaussian many-sources regime, Queueing Systems, 2016, 211-236, DOI: 10.1007/s11134-016-9499-5