Acta mathematica scientia, Series B >
SUBGEOMETRIC RATES OF CONVERGENCE OF THE GI/G/1 QUEUEING SYSTEM
Received date: 2010-11-26
Revised date: 2011-11-01
Online published: 2012-09-20
Supported by
This work is partially supported by the Funda-mental Research Funds for the Central Universities (BUPT2011RC0703).
The article deals with the waiting time process of the GI/G/1 queueing sys-tem. We shall give that the rate of convergence to the stationary distribution and the decay of the stationary tail only depend on the tail of the service distribution, but not on the interarrival distribution. We shall also give explicit criteria for the rate of con-vergence and decay of stationary tail for three specific types of subgeometric cases (Case
1: the rate function r(n) = exp(sn 1/1+α ), α > 0, s > 0; Case 2: polynomial rate function r(n) = nα, α > 0; Case 3: logarithmic rate function r(n) = logα n, α > 0).
LI Xiao-Hua , HOU Zhen-Ting . SUBGEOMETRIC RATES OF CONVERGENCE OF THE GI/G/1 QUEUEING SYSTEM[J]. Acta mathematica scientia, Series B, 2012 , 32(5) : 1983 -1996 . DOI: 10.1016/S0252-9602(12)60154-4
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