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A note on stochastic bounds for queueing networks

Published online by Cambridge University Press:  01 July 2016

Pantelis Tsoucas  and
Jean Walrand
Pantelis Tsoucas*
Affiliation:
University of California, Berkeley
Jean Walrand*
Affiliation:
University of California, Berkeley
*
∗Postal address: Department of Electrical Engineering and Computer Sciences and Electronics Research Laboratory, University of California, Berkeley, CA 94720, USA.
∗Postal address: Department of Electrical Engineering and Computer Sciences and Electronics Research Laboratory, University of California, Berkeley, CA 94720, USA.
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Abstract

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Recently, Massey [1] proved that the vector of queue lengths of some queueing networks is stochastically dominated at any given time by that of a corresponding system of parallel M/M/l queues. This result is interesting, even though the bounds are generally quite conservative, in that the transient behavior of independent parallel M/M/l queues is considerably easier to analyze than that of a network.

This note provides an alternative proof of a generalized form of that result.

Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 16 , Issue 4 , December 1984 , pp. 926 - 928
Copyright
Copyright © Applied Probability Trust 1984 

Footnotes

Research supported in part by NSF Grant No. ECS-8205428.

References

[1] Massey, W. (1984) Open networks of queues: their algebraic structure and estimating their transient behavior. Adv. Appl. Prob. 16, 176–201.CrossRefGoogle Scholar
[2] Massey, W. (1984) An operator-analytic approach to the Jackson network. J. Appl. Prob. 21, 379–393.Google Scholar