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Clustering of events in a stochastic process

Published online by Cambridge University Press:  14 July 2016

Joseph Glaz
Joseph Glaz*
Affiliation:
The University of Connecticut
*
∗Postal address: Department of Statistics, The University of Connecticut, Storrs, CT06268, U.S.A.
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Abstract

In this paper we derive bounds for the expected waiting time of clustering of at least n events of a stochastic process within a fixed interval of length p. Using this approach of clustering, we derive bounds for the expected duration of the period of time that at least n servers are busy in an ∞-server queue with constant service time. For the case of Poisson arrivals we derive the exact distribution of the duration of that period.

Keywords

CLUSTERINGSTOCHASTIC PROCESSLOSS SYSTEMGI/D/n/n QUEUEBUSY PERIODGI/D/∞ QUEUE
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 1 , March 1981 , pp. 268 - 275
Copyright
Copyright © Applied Probability Trust 

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