Steady-state indices of M/G/1 queueing system based on the Max(N,D)-policy

被引：0
|
作者：
Liu R. [1 ]
Tang Y. [2 ]
Yu M. [3 ]
机构：
[1] School of Science, Chongqing University of Technology, Chongqing
[2] School of Mathematics & Software Science, Sichuan Normal University, Chengdu
[3] School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong
来源：
Xitong Gongcheng Lilun yu Shijian/System Engineering Theory and Practice | 2020年 / 40卷 / 04期
基金：
中国国家自然科学基金;
关键词：
Cost; Max(N; D); policy; Queue length; Service time backlog; Sojourn time;
D O I：
10.12011/1000-6788-2018-2474-14
中图分类号：
学科分类号：
摘要：
This paper considers an M/G/1 queueing system controlled by the N and D policies. When the number of arriving customers is larger or equal to N, and the sum of service times of waiting customers exceeds a predetermined non-negative real number D, the idle server resumes its service (this service start policy is called the Max(N,D) policy). Under this policy, since the service times of customers arriving during the idle period are conditionally dependent, the stochastic decomposition of queue length does not hold. By two classifications of customers, Laplace transform and probabilistic analysis, the steady-state distributions of queue length, idle and busy periods, service time backlog, and sojourn time, are studied. The effect of N, D and Max(N,D) policies on mean steady-state queue length is numerically analyzed. Numerically, the optimal threshold policies minimizing the steady-state cost are obtained, and the superiority of N, D, Max(N,D) and Min(N,D) policies is compared. © 2020, Editorial Board of Journal of Systems Engineering Society of China. All right reserved.
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页码：1031 / 1044
页数：13
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