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A note on the equilibrium M/G/1 queue length
Published online by Cambridge University Press: 14 July 2016
Abstract
This note concerns the distribution of the equilibrium M/G/1 queue length. A representation for the probability generating function is given which allows for an explicit finite sum representation of the associated probabilities. The radius of convergence of the probability generating function and an asymptotic formula for the right tail of the distribution also follow from this representation, as well as infinite divisibility of the queue-length distribution when the service distribution is infinitely divisible. Extension of these results to the bulk arrival case is straightforward.
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- Copyright © Applied Probability Trust 1988
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Research supported by the Natural Sciences and Engineering Council of Canada.
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