寿命为一般分布的M/GI/1型系统的强度保守法分析

Rate Conservation Law Analysis of an M/GI/1 Type Queue with Repairable Server of Generally Distributed Lifetime

尽管爱尔兰组合分布在所有分布函数类中的稠密性 ,以及Neuts位相型服务时间的概念为根本解决服务台寿命为一般分布的可修排队模型提供了一线光明。然而至今的研究表明 ,尚未找到寿命分布类用 pH分布唯一表达的确切形式 (事实上 ,pH分布本身就不唯一 ) 作者尝试利用以平稳点过程和Palm分布为基础的新型的强度保守法 ,来对至今尚未涉及的服务台寿命为一般分布的M /GI/1型可修排队系统进行探讨。在得到了这个模型的广义虚等待时间之后 ,求得了其首次故障前时间 ,系统可用度、平均失效概率、服务台平均失效次数和系统故障频度等可靠性指标 令人可喜的是 ,其中若干指标当寿命分布退化为负指数分布时 。

Though the density property of Erlangian distribution sets in all kinds of distribution functions and Neuts's concept about phase type service time has brought a ray of light, the research work up to now shows that the sole representation form of lifetime distribution with PH distribution has not been found. In fact, Ph distribution is not unigue itself. Using the 'Rate Conservation Law' (RCL) method, developed from the stationary point process and palm distribution theory, a study is given to a type of M/GI/1 queueing system with repairable server of generally distributed lifetimes which has not been referred to up to now. After getting the pseudo virtual waiting time expressions, we have obtained the first passage time to server failure, the probability of server availability, the average server failure probability, the mean times of server failure, and the failure rate of the system. It is interesting that some of them evidently coincide with the known results in literatures when the lifetimes of server are exponentially distributed instead of its general distributions.