有单移除策略的M/G/1重试可修排队系统

An M/G/1 Retrial Queue with Individual Removal and Repair

采取补充变量和母函数方法研究了有负顾客的M/G/1重试可修排队系统,其中负顾客的机制是带走正在接受服务的正顾客和使得服务器处于修理状态。文中给出了系统存在稳态的充分必要条件,系统状态和orbit(重试组)队长的联合分布的母函数,服务器处于空闲、工作和修理状态的概率,orbit的平均人数L,系统的平均人数K和系统可靠度的Laplace变换。

This paper studies an M/G/1 retrial queuing system with negative customers and repair in which the mechanism of negative customers is not only to take the positive customers being served away, but also to make the server under repair. Applying the supplementary variable and generating function approach , we derive some important indexes such as the necessary and sufficient condition for the system to be stable, the combined generating function of system status and orbit length, the probability of system is busy, idle or under repair. In the last part of the paper, the Laplace transformation of the reliability function is presented.