An M/G/1 queue with second optional service

被引：90

作者：

Madan, KC ^{[1
]}

机构：

[1] Yarmouk Univ, Fac Sci, Dept Stat, Irbid, Jordan

来源：

QUEUEING SYSTEMS | 2000年 / 34卷 / 1-4期

关键词：

first essential service; second optional service; supplementary variable technique;

D O I：

10.1023/A:1019144716929

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We study an M/G/1 queue with second optional service. Poisson arrivals with mean arrival rate lambda (>0) all demand the first 'essential' service, whereas only some of them demand the second 'optional' service. The service times of the first essential service are assumed to follow a general (arbitrary) distribution with distribution function B(v) and that of the second optional service are exponential with mean service time 1/mu(2) (mu(2)>0). The time-dependent probability generating functions have been obtained in terms of their Laplace transforms and the corresponding steady state results have been derived explicitly. Also the mean queue length and the mean waiting time have been found explicitly. The well-known Pollaczec-Khinchine formula and some other known results including M/D/1, M/E-k/1 and M/M/1 have been derived as particular cases.

引用

页码：37 / 46

页数：10

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