Asymptotic expansions for the congestion period for the M/M/∞ queue

被引：4
|
作者：
Knessl, C
Yang, YP
机构：
[1] Univ Illinois, Dept Math Stat & Comp Sci MC 249, Chicago, IL 60607 USA
[2] St Thomas Univ, Dept Math, St Paul, MN 55105 USA
来源：
QUEUEING SYSTEMS | 2001年 / 39卷 / 2-3期
基金：
美国国家科学基金会;
关键词：
M/M/infinity queue; busy period; asymptotics;
D O I：
10.1023/A:1012752719211
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/infinity queue with arrival rate lambda, service rate mu and traffic intensity rho=lambda/mu. We analyze the first passage distribution of the time the number of customers N(t) reaches the level c, starting from N(0)=m >c. If m=c+1 we refer to this time period as the congestion period above the level c. We give detailed asymptotic expansions for the distribution of this first passage time for rho --> infinity, various ranges of m and c, and several different time scales. Numerical studies back up the asymptotic results.
引用
收藏
页码：213 / 256
页数：44
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