具有Min(N,D)-策略控制的M/G/1可修排队系统及最优控制策略

数学物理学报 ›› 2017, Vol. 37 ›› Issue (2): 352-365.

具有Min(N,D)-策略控制的M/G/1可修排队系统及最优控制策略

高丽君¹, 唐应辉^1,2

1 四川师范大学数学与软件科学学院成都 610068;
2 四川师范大学基础教学学院成都 610068

收稿日期:2016-06-16 修回日期:2016-12-19 出版日期:2017-04-26 发布日期:2017-04-26
通讯作者: 唐应辉 E-mail:tangyh@uestc.edu.cn
基金资助:
国家自然科学基金（71571127）和国家自然科学基金青年基金（71301111）

M/G/1 Repairable Queueing System and Optimal Control Policy with Min(N,D)-Policy

Gao Lijun¹, Tang Yinghui^1,2

1 School of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068;
2 School of Fundamental Education, Sichuan Normal University, Chengdu 610068

Received:2016-06-16 Revised:2016-12-19 Online:2017-04-26 Published:2017-04-26
Supported by:
Supported by the NSFC (71571127) and the National Natural Science Foundation for Young Scholars (71301111)

摘要/Abstract

摘要： 考虑基于Min（N，D）-策略控制的M/G/1可修排队系统，其中服务台在服务员忙期中可能发生故障.使用全概率分解技术和拉普拉斯变换工具，讨论了系统的排队指标，同时重点讨论了服务台的一些可靠性指标，即服务台首次失效前的寿命分布、不可用度和（0，t]时间内的平均失效次数.最后，通过建立系统的费用模型，用数值计算实例讨论了最优控制策略（N^*，D^*）.

关键词: Min(N, D)-策略, 可修排队系统, 排队指标, 可靠性指标, 最优控制策略

Abstract: This paper considers the M/G/1 repairable queueing system with Min(N,D)-policy, in which the service station may fail during the server busy period. By using the total probability decomposition technique and employing the Laplace transform tool, the queueing indices of the system are discussed. Meanwhile, the emphasis is upon obtained some reliability indices of the service station, such as the probability distribution of the first failure time, the unavailability and the expected failure number during a given time interval (0,t]. Finally, we numerically determined the optimal control policy (N^*，D^*) under a constructed cost model.

Key words: Min(N,D)-policy, Repairable queueing system, Queueing indices, Reliability indices, Optimal control policy

中图分类号:

O121

高丽君, 唐应辉. 具有Min(N,D)-策略控制的M/G/1可修排队系统及最优控制策略[J]. 数学物理学报, 2017, 37(2): 352-365.

Gao Lijun, Tang Yinghui. M/G/1 Repairable Queueing System and Optimal Control Policy with Min(N,D)-Policy[J]. Acta mathematica scientia,Series A, 2017, 37(2): 352-365.

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