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 -