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

Fingerprint

Tail Asymptotics
Pole
Poles
Generating Function
Approximation
Asymptotic Estimates
Queue Length
Combinatorics
Approximation Methods
Central limit theorem
Queue
Resolve
Clustering
Scaling
Coefficient
Generating function

Keywords

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

Cite this

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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.",
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Dominant poles and tail asymptotics in the critical Gaussian many-sources regime. / Janssen, A.J.E.M.; van Leeuwaarden, J.S.H.

In: Queueing Systems, Vol. 84, No. 3-4, 01.12.2016, p. 211-236.

Research output: Contribution to journalArticleAcademicpeer-review

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