SUBGEOMETRIC RATES OF CONVERGENCE OF THE GI/G/1 QUEUEING SYSTEM

doi:10.1016/S0252-9602(12)60154-4

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (5): 1983-1996.doi: 10.1016/S0252-9602(12)60154-4

SUBGEOMETRIC RATES OF CONVERGENCE OF THE GI/G/1 QUEUEING SYSTEM

李晓花¹|侯振挺²

1.School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China|2.School of Mathematics, Central South University, Changsha 410012, China

收稿日期:2010-11-26 修回日期:2011-11-01 出版日期:2012-09-20 发布日期:2012-09-20
基金资助:
This work is partially supported by the Funda-mental Research Funds for the Central Universities (BUPT2011RC0703).

SUBGEOMETRIC RATES OF CONVERGENCE OF THE GI/G/1 QUEUEING SYSTEM

LI Xiao-Hua¹, HOU Zhen-Ting²

1.School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China|2.School of Mathematics, Central South University, Changsha 410012, China

Received:2010-11-26 Revised:2011-11-01 Online:2012-09-20 Published:2012-09-20
Supported by:
This work is partially supported by the Funda-mental Research Funds for the Central Universities (BUPT2011RC0703).

摘要/Abstract

摘要：

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) = n^α, α > 0; Case 3: logarithmic rate function r(n) = log^αn, α > 0).

关键词: GI/G/1 queueing system, subgeometric rate of convergence, polynomial rate of convergence, logarithmic rate of convergence

Abstract:

Key words: GI/G/1 queueing system, subgeometric rate of convergence, polynomial rate of convergence, logarithmic rate of convergence

中图分类号:

93E15

李晓花, 侯振挺. SUBGEOMETRIC RATES OF CONVERGENCE OF THE GI/G/1 QUEUEING SYSTEM[J]. 数学物理学报(英文版), 2012, 32(5): 1983-1996.

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.

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SUBGEOMETRIC RATES OF CONVERGENCE OF THE GI/G/1 QUEUEING SYSTEM

SUBGEOMETRIC RATES OF CONVERGENCE OF THE GI/G/1 QUEUEING SYSTEM

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