Waiting Time Distributions for Processor-Sharing Systems

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Abstract
A basic probability model that has arisen in the study of time-shared or multi- programmed systems is the so-called processor-sharing model. Ill this model it is assumed that the processor is shared simultaneously by each unit in the system (e.g. job or program in com- put er systems, or message in communication systems). In particular, if there are n units in the system, then any given unit is being processed at a rate which is (1/n)-th the rate at which it would be processed if it had the system to itself. We make the assumptions of a Poisson arrival process and exponential service times and then derive an expression for the Laplace transform of the waiting time distribution of an arriving unit conditioned on the service it requires and the number it finds in the system oil arrival. From this result we obtain the first two moments of the waiting times, the Laplace transform of the equilibrium waiting time distribution, and the first two moments of this latter distribution. The paper concludes with a discussion of the results, especially as they compare with similar results for the first-come-first-served discipline.

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