第二类故障期间以概率p进入的M/G/1可修排队

M/G/1 repairable queue with p-entering discipline during second type failure times

假设服务台在忙期和闲期内都可能发生故障,且具有不同的故障率,并且在闲期的故障状态期间到达顾客以概率p进入系统.使用全概率分解技术和利用拉普拉斯变换工具,研究了服务台的瞬态不可用度、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,获得服务台一些重要的可靠性结果,并且分别讨论了当p取值为0和取值为1时的特殊情况.

This paper considers the M/G/1 repairable queueing system in which the service station may fail and have different failure rates during its busy and idle periods. While the customers who arrive during second type failure times enter the system with probability p. By using the total probability decomposition and Laplace transform, some reliability indices of the service station, such as the transient-state and steady-state unavailabil- ity, the expected failure number during （0, t] and the steady-state failure frequency are studied. Some important reliability results of the service station are obtained. At last, the special case, such as the probability p is equal to 0 or 1, is also discussed.