UTILIZATION OF IDLE TIME IN AN M-G-1 QUEUING SYSTEM

被引：282

作者：

LEVY, Y ^{[1
]}

YECHIALI, U ^{[1
]}

机构：

[1] TEL AVIV UNIV,DEPT STATISTICS,TEL AVIV,ISRAEL

来源：

MANAGEMENT SCIENCE | 1975年 / 22卷 / 02期

关键词：

MANAGEMENT SCIENCE - MATHEMATICAL TRANSFORMATIONS - Laplace Transforms;

D O I：

10.1287/mnsc.22.2.202

中图分类号：

C93 [管理学];

学科分类号：

12 ; 1201 ; 1202 ; 120202 ;

摘要：

This paper studies an M/G/1 queue where the idle time of the server is utilized for additional work in a secondary system. As usual, the server is busy as long as there are units in the main system. However, as soon as the server becomes idle he leaves for a ″vacation.″ The duration of a vacation is a random variable with a known distribution function. Two models are considered. In the first, upon termination of a vacation the server returns to the main queue and begins to serve those units, if any, that have arrived during the vacation. If no units have arrived the server waits for the first arrival when an ordinary M/G/1 busy period is initiated. In the second model, if the server finds the system empty at the end of a vacation, he immediately takes another vacation, etc. For both models Laplace-Stieltjes transforms of the occupation period, vacation period and waiting time are derived and generating functions of the number of units in the system are calculated.

引用

页码：202 / 211

页数：10