Stochastic bounds for the single-server queue
- 1 September 1976
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 80 (3) , 521-525
- https://doi.org/10.1017/s0305004100053135
Abstract
Various elegant properties have been found for the waiting time distributionGfor 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 forGwhich augment the bounds obtained by Kingman (5), (6), (8) and by Ross (10).Keywords
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