Asymptotic expansions for the conditional sojourn time distribution in the M/M/1-PS queue

被引：0
作者：
Qiang Zhen
Charles Knessl
机构：
[1] University of Illinois at Chicago,Department of Mathematics, Statistics, and Computer Science
来源：
Queueing Systems | 2007年 / 57卷
关键词：
Processor sharing; Asymptotics; Sojourn time; /; /1 queue; 41A60; 60K25; 90B22;
D O I：
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学科分类号：
摘要：
We consider the M/M/1 queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer’s service requirement, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less than the service rate. The asymptotic formulas relate to, and extend, some results of Morrison (SIAM J. Appl. Math. 45:152–167, [1985]) and Flatto (Ann. Appl. Probab. 7:382–409, [1997]).
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页码：157 / 168
页数：11
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