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Runs of a discrete time regenerative phenomenon

Published online by Cambridge University Press:  14 July 2016

J. P. Imhof
J. P. Imhof*
Affiliation:
University of Geneva
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Abstract

The limiting behavior of the number of runs up to time n of a regenerative phenomenon on the positive integers is related to the one of the number of regenerations. Applications are considered in fluctuation theory, and for the GI/G/1 queue.

Keywords

REGENERATIVE PHENOMENARUNSSTABLE LAWSFLUCTUATIONS OF SUMSARC SINE LAWGI/G/1 QUEUE
Type
Short Communications
Information
Journal of Applied Probability , Volume 11 , Issue 3 , September 1974 , pp. 588 - 593
Copyright
Copyright © Applied Probability Trust 1974 

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References

[1] Feller, W. (1966) An Introduction to Probability Theory and its Applications. Vol. II. John Wiley, New York.Google Scholar
[2] Heyde, C. C. (1967) Some local limit results in fluctuation theory. J. Austral. Math. Soc. 7, 455–464.CrossRefGoogle Scholar
[3] Prabhu, N. U. (1970) Limit theorems for the single server queue with traffic intensity one. J. Appl. Prob. 7, 227–233.CrossRefGoogle Scholar