The stationary waiting time process in single-server priority queues with general low priority arrival process

Abstract

For the stationary virtual waiting time process (w(^k)(t)) of customers of fixed priority k (k=1,2,…,N) in single-server queues with the preemptive-resume discipline and with the head-of-the-line discipline, respectively, a relationship is derived between the time-stationary virtual waiting time distribution and the customer-weighted actual waiting time distribution w _k(x) of customers of priority k, where it is assumed that only the arrival epochs of the customers of priority higher than A; must- form a Poisson process. If, additionally, the arrival epochs of the customers of priority h form a renewal process, this relationship can be used to obtain bounds in terms of the well-known formulas for the priority queue.