ANALYSIS OF A TWO-CLASS PRIORITY QUEUE WITH BERNOULLI SCHEDULES

Abstract

Bernoulli schedule is random service discipline for a multi-class priority queueing system which operates as follows: If queue i(1 ≤ i ≤ N) is not empty just after servicing a message in its queue, a message in queue i is served again with probability p_i, and the highest class message present in the system is served with probability 1 -p_i, where 0 ≤ p_i ≤ 1. This paper presents an analysis of a two-class priority queue (M/G/1 type queue) with Bernoulli schedules of parameter (p_1 = 1,0 ≤ p_2 ≤ 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.