We consider the classical M/G/l queue with two priority classes and the nonpre-emptive and preemptive-resume disciplines. We show that the low-priority steady-state waiting-time can be expressed as a geometric random sum of i.i.d. random variables, just like the M/G/l FIFO waiting-time distribution. We exploit this structures to determine the asymptotic behavior of the tail probabilities. Unlike the FIFO case, there is routinely a region of the parameters such that the tail probabilities have non-exponential asymptotics. When non-exponential asymptotics holds, the asymptotic form tends to be determined by the asymptotics for the high-priority busy-period distribution.
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机译：我们考虑经典的M / G / l队列，它具有两个优先级类别以及非抢占式和抢占式恢复规则。我们表明，低优先级的稳态等待时间可以表示为i.i.d的几何随机和。随机变量，就像M / G / l FIFO等待时间分布一样。我们利用这种结构来确定尾部概率的渐近行为。与FIFO情况不同，通常存在一个参数区域，使得尾部概率具有非指数渐近性。当非指数渐近性成立时，渐近形式往往由渐近性决定，对于高优先级的忙时分布。
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