Priority Queues with Random Order of Service

Calls of two priorities arrive at a single server in accordance with a Poisson process. The calls are served in order of priority and for each priority in a random manner. This paper considers cases of preemptive-resume and nonpreemptive priorities, and derives the moments of the stationary distribution of the waiting time for each priority class. The variance of the waiting time, when the order of service is random, is shown to be greater than the corresponding variance when the order of service is first-in, first-out, and smaller than the corresponding variance when the order of service is last-in, first-out.