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

David L. Jagerman · Bhaskar Sengupta

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

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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References

1970Waiting Time Distributions for Processor-Sharing Systems 1987Processor-sharing queues: Some progress in analysis 1984The sojourn-time distribution in the M/G/1 queue by processor sharing 1984A new approach to the M / G /1 processor-sharing queue 1985Response-Time Distribution for a Processor-Sharing System 1992An approximation for the sojourn-time distribution for the gi/g/1 processor-sharing queue 1984On processor sharing and random service

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