Hostname: page-component-586b7cd67f-vdxz6 Total loading time: 0 Render date: 2024-11-23T00:52:30.006Z Has data issue: false hasContentIssue false

An explicit upper bound for the mean busy period in a GI/G/1 queue

Published online by Cambridge University Press:  14 July 2016

Richard Loulou*
Affiliation:
McGill University, Montreal

Abstract

In this paper, an upper bound is derived for the mean busy cycle duration in GI/G/1 queues. The bound is of the form A/(1 – ρ), where ρ is the traffic intensity and A involves three moments of the basic random variables of the queue. The proof uses a well-known result of random walk theory.

Type
Short Communications
Copyright
Copyright © Applied Probability Trust 1978 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Berry, A. C. (1941) The accuracy of the Gaussian approximation to the sum of independent variates. Trans. Amer. Math. Soc. 49, 121137.CrossRefGoogle Scholar
Dwight, H. B. (1958) Mathematical Tables of Elementary and Some Higher Mathematical Functions. Dover, New York.Google Scholar
Dwight, H. B. (1961) Tables of Integrals and Other Mathematical Data. MacMillan, New York.Google Scholar
Esséen, G. (1944) Fourier analysis of distribution functions: a study of the Laplace-Gaussian Law. Acta Math. 7, 209225.Google Scholar
Feller, W. (1966) An Introduction to Probability Theory and its Applications, Vol. II. Wiley, New York.Google Scholar
Sparre-Andersen, E. (1953), (1954) On the fluctuations of sums of random variables. Math. Scand. 1, 263285 and 2, 195–223.Google Scholar
Whitt, W. (1972) Embedded renewal processes in the GI/G/s queue. J. Appl. Prob. 9, 650658.Google Scholar