修理设备可更换的${N}$ -策略延迟不中断单重休假 ${M/G/1}$可修排队系统分析

摘要/Abstract

摘要：

该文考虑具有$N$ -策略和延迟不中断单重休假的$M/G/1$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. 该文运用更新过程理论, 全概率分解技术和拉普拉斯变换工具, 讨论了服务台和修理设备的可靠性指标, 比如服务台和修理设备的瞬态不可用度, 稳态故障频度以及在时间$\left( 0,t \right]$ 内的平均故障次数等, 并且对服务台的稳态不可用度和稳态故障频度进行了参数敏感性分析.

关键词: $M/G/1$可修排队系统, $N$-策略, 延迟不中断休假, 可靠性指标, 参数敏感性分析

Abstract:

This paper considers an $M/G/1$ repairable queueing system with $N$-policy and delayed uninterrupted single vacation, in which the repair facility subject to breakdowns and then replaced during the repair facility busy period. By the renewal process theory, the total probability decomposition technique and the Laplace transform tool, some reliability indices of the service station and the repair facility are discussed, such as the transient-state and steady-state unavailability, and the expected failure number during $(0,t]$, etc., and the parameter sensitivity analysis is carried out on the steady-state unavailability and the steady-state failure frequency.

Key words: $M/G/1$ repairable queueing system, $N$-policy, Delayed uninterrupted vacation, Reliability index, Parameter sensitivity analysis

中图分类号:

O213.2

何亚兴, 唐应辉, 刘琼琳. 修理设备可更换的${N}$ -策略延迟不中断单重休假 ${M/G/1}$可修排队系统分析[J]. 数学物理学报, 2023, 43(2): 625-645.

He Yaxing, Tang Yinghui, Liu Qionglin. Analysis of ${M/G/1}$ Repairable Queueing System with a Replaceable Repair Facility, ${N}$-policy and Delayed Uninterrupted Single Vacation[J]. Acta mathematica scientia,Series A, 2023, 43(2): 625-645.

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