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Stochastic bounds for the single-server queue

Published online by Cambridge University Press:  24 October 2008

J. Köllerström
J. Köllerström
Affiliation:
University of Kent, Canterbury
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Extract

Various elegant properties have been found for the waiting time distribution G for the queue GI/G/1 in statistical equilibrium, such as infinite divisibility ((1), p. 282) and that of having an exponential tail ((11), (2), p. 411, (1), p. 324). Here we derive another property which holds quite generally, provided the traffic intensity ρ < 1, and which is extremely simple, fitting in with the above results as well as yielding some useful properties in the form of upper and lower stochastic bounds for G which augment the bounds obtained by Kingman (5), (6), (8) and by Ross (10).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 80 , Issue 3 , November 1976 , pp. 521 - 525
Copyright
Copyright © Cambridge Philosophical Society 1976

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References

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