Analysis of a Two-class Priority Queue with Bernoulli Schedules

A Bernoulli schedule is random service discipline for a multi-class priority queueing system which operates as follows: If queue i(l :s i :s N) is not empty just after servicing a message in its queue, a message in queue i is served again with probability Pi, and the highest class message present in the system is served with probability 1-Pi, where 0 :s Pi :s 1. This paper presents an analysis of a two-class priority queue (M/C/1 type queue) with Bernoulli schedules of parameter (Pi = 1,0:S P2 :s 1) and class-dependent set-up times. The generating functions of joint queue-length distributions and the Laplace-Stieltjes transforms of waiting time distributions are determined. A closed-form expression with infinite summations is obtained for the mean waiting times.