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Transient and busy period analysis of the GIG/1 Queue as a Hilbert factorization problem
Published online by Cambridge University Press: 14 July 2016
Abstract
In this paper we find the waiting time distribution in the transient domain and the busy period distribution of the GI G/1 queue. We formulate the problem as a two-dimensional Lindley process and then transform it to a Hilbert factorization problem. We achieve the solution of the factorization problem for the GI/R/1, R/G/1 queues, where R is the class of distributions with rational Laplace transforms. We obtain simple closed-form expressions for the Laplace transforms of the waiting time distribution and the busy period distribution. Furthermore, we find closed-form formulae for the first two moments of the distributions involved.
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- Copyright © Applied Probability Trust 1991
Footnotes
The research of Dr Bertsimas was partially supported by grants from the Leaders for Manufacturing program at MIT and from Draper Laboratory.
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