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

The article deals with the waiting time process of the GI/G/1 queueing system.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...

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Bibliographic Details
Published in:Acta mathematica scientia 2012-09, Vol.32 (5), p.1983-1996
Main Authors: Xiaohua, Li, Zhenting, Hou
Format: Article
Language:English
Subjects:
1排队系统
60J27
60K25
93E15
Alpha decay
Convergence
Criteria
Decay rate
GI/G/1 queueing system
logarithmic rate of convergence
Mathematical analysis
polynomial rate of convergence
Queues
subgeometric rate of convergence
价格
对数函数
平稳分布
收敛速度
时间过程
案例
速率函数
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Summary:The article deals with the waiting time process of the GI/G/1 queueing system.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 convergence and decay of stationary tail for three specific types of subgeometric cases（Case 1：the rate function r（n）=exp（sn1/1＋α）,α〉0,s〉0;Case 2：polynomial rate function r（n）=nα,α〉0;Case 3：logarithmic rate function r（n）=logαn,α〉0）.
ISSN:0252-9602
1572-9087
DOI:10.1016/S0252-9602(12)60154-4