Optimal Control of an M/G/1 Priority Queue Via N-Control

Abstract

In this paper we consider an M/G/1 queue with non-preemptive priority service discipline and N-control policy (of Heyman, Yadin and Naor). The Laplace-Stieltjes transforms of the waiting times are derived using properties of level crossings of regenerative processes and delayed busy cycles. The mean waiting times, the mean cost rate, and the optimal policy are also derived. Use of these results is illustrated through two numerical examples.