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.
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