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

1 March 1987

journal article
Published by Cambridge University Press (CUP) in Journal of Applied Probability

Vol. 24 (1) , 200-214
https://doi.org/10.2307/3214071

Abstract

For a sequenceξ₁,ξ₂, · ·· of i.i.d. random variables letX₀= 0 andX_{_k}= max(X_{_k}_–1+ξ_{_k}, 0) fork= 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 ofN_{_x}are derived.

Keywords

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