N-控制策略且温储备失效M/G/1可修排队的可靠性指标

Reliability Indices of M/G/1 Repairable Queue with N-Control Policy and Warm Standby Failure

本文研究N-门限值进入控制策略且温储备失效M/G/1可修排队系统,其中系统在处于温储备失效的状态下最多容许N(1)个顾客进入系统。运用全概率分解技术和拉普拉斯变换工具,对服务台第一次失效前的寿命概率分布、不可用度、(0,t]时间内的平均失效次数以及处于温储备失效而等待修理的概率等可靠性指标进行了讨论,并给出了其稳态结果表达式。最后,通过数值实例分析了服务台因温储备故障的稳态不可用度和稳态故障频度随一些参数的变化情况。

The M/G/1 repairable queueing system with N-threshold entering-control policy and warm standby failure is studied in this paper. Under such a policy, at most N（≥1 ）customers are allowed to enter into the system during warm standby failure times. We use the probability decomposition method and the tool of the Laplace transform, the probability distribution of the first failure time,the unavailability,the expected failure number during a given time interval （0, t ] and the probability that the service station is waiting for repairing in the warm standby failure are discussed. Furthermore, we obtain the expressions of these reliability indices under the steady state. Finally, several numerical examples are presented to analyze the sensitivity of the steady-state unavailability and the failure frequency in the second tvoe failure of the service station.