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Asymptotic behaviour of a stopping time related to cumulative sum procedures and single-server queues

Published online by Cambridge University Press:  14 July 2016

Wolfgang Stadje
Wolfgang Stadje*
Affiliation:
Universität Osnabrück
*
∗Postal address: Universität Osnabrück, Fachbereich Mathematik/Informatik, 45 Osnabrück, Postfach 4469, W. Germany.
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Abstract

For a sequence ξ1, ξ2, · ·· of i.i.d. random variables let X0 = 0 and Xk = max(Xk–1 + ξ k, 0) for k = 1, 2, ···. Let . These stopping times are used in Page's (1954) one-sided cusum procedures and are also important in queueing theory. Various asymptotic properties of Nx are derived.

Keywords

CUSUM PROCEDURESQUEUE LENGTH PROCESSGI/M/1: ASYMPTOTIC BEHAVIOUR
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987 , pp. 200 - 214
Copyright
Copyright © Applied Probability Trust 1987 

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