带关闭期的随机N-策略的M/G/1排队系统

The M/G/1 Queue under Vacation Policies with Closedown Time and the Random N-policy

本文通过向量Markov过程方法研究了带关闭期的随机N-策略M/G/1系统的排队指标。证得了系统达到稳态平衡的充要条件。并且在系统达到平衡时,讨论了稳态队长、等待时间、休假期、闲期,以及一个顾客被服务完之后系统中留下的队长和刚进入系统的顾客看到系统中的队长。

This paper studies the characteristics of an M/G/1 queueing system with closedown time, the random N-policy and vacation policies, by the vector Markov process method. We derive the necessary and sufficient condition for the system being steady state. The system is analyzed in steady state by deriving expressions for the Laplace-Stieltjes transformations of the system characteristics, including the steady state queue length, the distributions of waiting time, vacation, idle period and two special queue length, i.e., the queue length after a served customer leaves and the one that the customer who just arrives the system.