The gi/m/1 processor-sharing queue and its heavy traffic analysis

Abstract

In this paper, we find the Laplace-Stieltjes transform of the customer stationary distribution of time spent in the system for the GI/M/1 queue with processor-sharing discipline. This distribution is characterized in three ways. The first is a method of successive approximations, the second is an integral representation and the third is a power series representation. Finally, we find a simple form for the heavy traffic limit (as the utilization gets close to 1) for the distribution of time spent in the system, suitably scaled.