An exact solution for an M(t)/M(t)/1 queue with time-dependent arrivals and service

被引：16

作者：

Knessl, C

Yang, YZP

机构：

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

[2] Univ St Thomas, Dept Math, St Paul, MN 55105 USA

来源：

QUEUEING SYSTEMS | 2002年 / 40卷 / 03期

基金：

美国国家科学基金会;

关键词：

time-dependent queues; integral representations;

D O I：

10.1023/A:1014786928831

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We consider an M/M/1 queue with a time dependent arrival rate lambda(t) and service rate mu(t). For a special form of the traffic intensity, we obtain an exact, explicit expression for the probability p(n)(t) that there are n customers at time t. If the service rate is constant (= mu), this corresponds to rho(t) = lambda(t)/mu = (b - amut)(-2). We also discuss the heavy traffic diffusion approximation to this model. We evaluate our results numerically.

引用

页码：233 / 245

页数：13

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