Stochastic bounds for the single-server queue

Julian Kollerstrom

17 citations0/0 files storedMathematical Proceedings of the Cambridge Philosophical Society

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

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).

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References

1952The theory of queues with a single server 1983The Single Server Queue.1970Inequalities in the Theory of Queues 1962Some Inequalities for the Queue GI/G/1 1953On the distribution of queueing times 1964A martingale inequality in the theory of queues 1966On the algebra of queues 1974Bounds on the delay distribution inGI/G/1 queues

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