在延迟Min(N,D)-控制策略下修理设备可更换的M/G/1可修排队系统及最优控制策略

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

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~*).

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.