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A note on the number of busy servers in a GI/G/s queue in light traffic

Published online by Cambridge University Press:  14 July 2016

Douglas P. Kennedy
Douglas P. Kennedy*
Affiliation:
University of Sheffield
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Abstract

It is proved that in a GI/G/s queue with the traffic intensity ρ < (S – m + l)/S, m ≧ 1, at least m servers are simultaneously idle infinitely often with probability one.

Keywords

QUEUESERVICE SYSTEMCONGESTION THEORYGI/G/S QUEUEMULTI-SERVER QUEUEBUSY SERVERS
Type
Short Communications
Information
Journal of Applied Probability , Volume 9 , Issue 4 , December 1972 , pp. 868 - 869
Copyright
Copyright © Applied Probability Trust 1972 

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References

[1] Iglehart, D. L. (1971) Functional limit theorems for the GI/G/1 queue in light traffic. Adv. Appl. Prob. 3, 269–281.CrossRefGoogle Scholar
[2] Kiefer, J. and Wolfowitz, J. (1955) On the theory of queues with many servers. Trans. Amer. Math. Soc. 78, 1–18.CrossRefGoogle Scholar
[3] Whitt, W. (1971) Embedded renewal processes in the GI/G/s queue. Technical Report, Dept. of Administrative Sciences, Yale University.Google Scholar