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The M/G/1 processor sharing queue as the almost sure limit of feedback queues

Published online by Cambridge University Press:  14 July 2016

J. A. C. Resing ,
G. Hooghiemstra  and
M. S. Keane
J. A. C. Resing*
Affiliation:
Delft University of Technology
G. Hooghiemstra*
Affiliation:
Delft University of Technology
M. S. Keane*
Affiliation:
Delft University of Technology
*
∗ Postal address for all authors: Faculty of Technical Mathematics and Informatics, Delft University of Technology, P.O. Box 356, 2600 AJ Delft, The Netherlands.
∗ Postal address for all authors: Faculty of Technical Mathematics and Informatics, Delft University of Technology, P.O. Box 356, 2600 AJ Delft, The Netherlands.
∗ Postal address for all authors: Faculty of Technical Mathematics and Informatics, Delft University of Technology, P.O. Box 356, 2600 AJ Delft, The Netherlands.
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Abstract

In the paper a probabilistic coupling between the M/G/1 processor sharing queue and the M/M/1 feedback queue, with general feedback probabilities, is established. This coupling is then used to prove the almost sure convergence of sojourn times in the feedback model to sojourn times in the M/G/1 processor sharing queue. Using the theory of regenerative processes it follows that for stable queues the stationary distribution of the sojourn time in the feedback model converges in law to the corresponding distribution in the processor sharing model. The results do not depend on Poisson arrival times, but are also valid for general arrival processes.

Keywords

SOJOURN TIMESCOUPLING METHODS
Type
Short Communication
Information
Journal of Applied Probability , Volume 27 , Issue 4 , December 1990 , pp. 913 - 918
Copyright
Copyright © Applied Probability Trust 1990 

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References

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