A Single-Server Priority Queuing System with General Holding Times, Poisson Input, and Reverse-Order-of-Arrival Queuing Discipline

This paper gives an explicit formula for the waiting-time distribution in a single-server system with general holding times subject to a Poisson input from any number of priority classes. In the general case, where the holding-time distributions of the demands in each priority case are different, the Laplace-Stieltjes transform and the moments of the distribution are found. The queue discipline is last-come first-served in each priority class. The cases of preemptive resume and nonpreemptive priorities are considered. It is shown that the variance of the waiting-time distribution (whatever the holding-time distribution) is greater than the corresponding variance when the queue discipline is first-come first-served.