带有阈值和优先权的三队列轮询排队系统

Three-queue priority polling system with a threshold service policy

本文研究了一个带有阈值的优先权轮询排队系统,其中队列1有最高优先权,队列2次之,队列3最低。排队系统由3个M/M/1队列和一个服务台组成,采用阈值服务策略,队列1和队列2的阈值分别为1和N,队列3无阈值。在忽略转换时间和抢占情形下,利用分析的方法,给出了3个队长的稳态联合概率分布的母函数。借助母函数,得到了平均队长和平均等待时间。

A priority polling system consisting of three M/M/1 queues and served by a single server is investigated.Queue 1 has the highest priority and Queue 2 follows.Threshold service policy is implemented,in which 1 and N are the corresponding thresholds of Queue 1 and Queue 2.Queue 3 has no threshold.All the switches are instantaneous and preempting.We derive the generating functions of the stationary joint queue length using analytic techniques.These generating functions yield exact expres-sions for the mean queue lengths and mean waiting time.