Asymptotic regimes and approximations for discriminatory processor sharing

Gijs van Kessel · R. Núñez Queija · Sem C. Borst

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Advanced Queuing Theory Analysis Network Traffic and Congestion Control Age of Information Optimization

Abstract

We study the joint queue length distribution of the Discriminatory Processor Sharing model, assuming all classes have phase-type service requirement distributions. We show that the moments of the joint queue length distribution can be obtained by solving linear equations. We use this to study the system in two asymptotic regimes. In the first regime, the different user classes operate on strictly separated time scales. Then we study the system in heavy traffic.

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References

1967Time-shared Systems 1979The multiple phase service network with generalized processor sharing 1980Sharing a Processor Among Many Job Classes 1971An Analysis of the M/G/1 Queue Under Round-Robin Scheduling 1991TheM/G/1 queue with processor sharing and its relation to a feedback queue 1996Queue-Length Distribution for the Discriminatory Processor-Sharing Queue

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