在延迟Min (N, D)-策略M/G/1可修排队系统及最优控制策略

数学物理学报 ›› 2018, Vol. 38 ›› Issue (5): 1014-1031.

在延迟Min (N, D)-策略M/G/1可修排队系统及最优控制策略

潘取玉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:2017-04-11 出版日期:2018-10-26 发布日期:2018-11-09
通讯作者: 唐应辉 E-mail:tangyh@sicnu.edu.cn
基金资助:
国家自然科学基金(71571127);国家自然科学基金青年基金(71301111)

Analysis of M/G/1 Repairable Queueing System and Optimal Control Policy with a Replaceable Repair Facility Under Delay Min(N, D)-Policy

Quyu Pan¹,Yinghui Tang^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:2017-04-11 Online:2018-10-26 Published:2018-11-09
Contact: Yinghui Tang E-mail:tangyh@sicnu.edu.cn
Supported by:
the NSFC(71571127);the National Natural Science Foundation for Young Scholars of China(71301111)

摘要/Abstract

摘要：

该文考虑基于延迟Min（N，D）-策略M/G/1可修排队系统，其中修理设备在修理故障服务台期间可发生故障且可更换.使用全概率分解技术和拉普拉斯变换工具，分别讨论了服务台和修理设备的瞬态不可用度和稳态不可用度、（0，t]时间内的平均故障次数和稳态故障频度.最后在给定的费用结构下，用数值计算实例确定了使系统长期单位时间内期望费用最小的最优控制策略（N^*，D^*）.

关键词: Min(N, D)-策略, 修理设备, 延迟Min(N, D)-策略, 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 delay Min(N, D)-policy, in which the repair facility subject to breakdowns and then replaced during the repair facility busy period. By using the total probability decomposition technique and employing the Laplace transform tool, some reliability indices of the service station and the repair facility, such as the transient-state and steady-state unavailability, the expected failure number during (0, t] are discussed. Finally, it is determined the optimal control policy (N^*, D^*) such that the long-run expected cost rate is minimum under a given cost structure.

Key words: Repair facility, Delay Min(N, D)-policy, Queueing index, Reliability index, Optimal control policy

中图分类号:

O121

潘取玉,唐应辉. 在延迟Min (N, D)-策略M/G/1可修排队系统及最优控制策略[J]. 数学物理学报, 2018, 38(5): 1014-1031.

Quyu Pan,Yinghui Tang. Analysis of M/G/1 Repairable Queueing System and Optimal Control Policy with a Replaceable Repair Facility Under Delay Min(N, D)-Policy[J]. Acta mathematica scientia,Series A, 2018, 38(5): 1014-1031.

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