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

被引：5

作者：

Zhen, Qiang ^{[1
]}

Knessl, Charles ^{[1
]}

机构：

[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

来源：

QUEUEING SYSTEMS | 2007年 / 57卷 / 04期

基金：

美国国家科学基金会;

关键词：

processor sharing; asymptotics; sojourn time; M/M/1; queue;

D O I：

10.1007/s11134-007-9054-5

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

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]).

引用

页码：157 / 168

页数：12

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