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 language | English |
|---|---|
| Pages (from-to) | 211-236 |
| Number of pages | 26 |
| Journal | Queueing Systems |
| Volume | 84 |
| Issue number | 3-4 |
| DOIs | |
| Publication status | Published - 1 Dec 2016 |
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Keywords
- Asymptotics
- Dominant pole approximation
- Heavy traffic
- Many sources
- QED regime
- Saddle point method
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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 journal › Article › Academic › peer-review
TY - JOUR
T1 - Dominant poles and tail asymptotics in the critical Gaussian many-sources regime
AU - Janssen, A.J.E.M.
AU - van Leeuwaarden, J.S.H.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - 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.
AB - 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.
KW - Asymptotics
KW - Dominant pole approximation
KW - Heavy traffic
KW - Many sources
KW - QED regime
KW - Saddle point method
UR - http://www.scopus.com/inward/record.url?scp=84988710078&partnerID=8YFLogxK
U2 - 10.1007/s11134-016-9499-5
DO - 10.1007/s11134-016-9499-5
M3 - Article
AN - SCOPUS:84988710078
VL - 84
SP - 211
EP - 236
JO - Queueing Systems: Theory and Applications
JF - Queueing Systems: Theory and Applications
SN - 0257-0130
IS - 3-4
ER -