The paper presents a multi-class priority queue with Bernoulli schedules which is described as follows: Let there be N classes of messages, where messages with a smaller class number have a priority (nonpreemptive) over messages with a greater class number. This schedule discipline is parameterized by a vector (p1=1,p2,...,pN), where 0•pi•1, i=1,2,...,N. For the moment, suppose that a message of class-i is served, i=1,2,...,N. At service completion of the message, if there are messages of class-i and messages of higher class-j (j<i), a class-i message will be served next with probability pi and a message of the highest class present in the system will be served with probability 1-pi. If there is no message of higher class-j (j<i), a message of the highest class present in the system will be served with probability one. It is then plausible to be defined as p1=1. The paper analyzes the two-class priority queue (M/G/1 type queue) with Bernoulli parameter (p1=1, 0•p2•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.
