分析M/M/1多重工作休假排队的一种新方法

A new approach for analyzing the M/M/1 queue with multiple working vacations

用一种新方法对经典的M/M/1工作休假排队系统建立模型.对该模型,用无限位相GI/M/1型Markov过程和矩阵解析方法进行分析,不但得到了所讨论排队模型平稳队长分布的具体结果,还给出了平稳状态时服务台具体位于第几次工作休假的概率.这些关于服务台状态更为精确的描述是该排队系统的新结果.

A new approach to model the M/M/1 queue with multiple working vacations is provided. By the GI/M/1 type Markov process and matrix analytic method, the explicit expression for the stationary queue length distribution is given firstly. Furthermore, the probability of the exact number of vacations that the sever has taken is also obtained. The more accurate descriptions for the status of the server are new results for the queue model.