M/M/1抢占优先权排队平稳指标的尾部分析

TAIL ANALYSIS FOR STATIONARY INDICES OF M/M/1PREEMPTIVE PRIORITY QUEUE

讨论M/M/1抢占优先权排队模型,该模型可以用一个具有可数位相的拟生灭(QBD)过程来描述.对该过程,我们得到平稳状态时低优先权顾客数分布的概率母函数,结果表明它不是一个有理函数.在此基础上,进一步指出,对该过程,低优先权顾客的平稳队长和平稳逗留时间分别具有几何衰减和指数衰减的特性.

This paper considers an M/M/1 preemptive priority queue. The queue model can be described in a quasi-birth-and-death （QBD） process with infinitelymany phases. For the QBD process, we give the PGF for the stationary distribution of lower-priority customers. ~rthermore, we indicate that the tails of the stationary distributions of queue length and sojourn time for lower-priority customers have the characteristic of geometric decay and exponential decay, respectively.