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GI/G/1 processor sharing queue in heavy traffic

Part of: Special processes Markov processes

Published online by Cambridge University Press:  01 July 2016

Sergei Grishechkin
Sergei Grishechkin*
Affiliation:
Moscow State University
*
* Postal address: Warshavskoje shosse, d.88 kv. 43, Moscow 113556, Russia.
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Abstract

Consider GI/G/1 processor sharing queues with traffic intensity tending to 1. Using the theory of random measures and the theory of branching processes we investigate the limiting behaviour of the queue length, sojourn time and random measures describing attained and residual processing times of customers present.

Keywords

RANDOM MEASURESBRANCHING PROCESSES

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 26 , Issue 2 , June 1994 , pp. 539 - 555
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

Research supported by ISF.

References

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