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

A. J. E. M. Janssen () and J. S. H. van Leeuwaarden ()
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A. J. E. M. Janssen: Eindhoven University of Technology
J. S. H. van Leeuwaarden: Eindhoven University of Technology

Queueing Systems: Theory and Applications, 2016, vol. 84, issue 3, No 1, 236 pages

Abstract: 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.

Keywords: Heavy traffic; Many sources; Asymptotics; Dominant pole approximation; Saddle point method; QED regime; 60K25; 80M35 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11134-016-9499-5

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