The Properties of Recurrent-Event Processes

Publisher Website
Google Scholar
Abstract
The theory of recurrent events is often used in operational models to describe the stochastic repetition of a certain event—for instance, customers arriving at a queue. This paper explores in some detail the relation between the distributions of (1) the spacings between the events, and (2) the cumulative number of events that occur in a given time interval. It is shown that different results are obtained for the second class of distributions (called the state probabilities) and their averages, depending upon the location of the origin of the measurement interval relative to the process. Two situations of interest—starting after an event has occurred, and starting “at random”—are explored, and various asymptotic results are obtained. Special results for the Poisson, Erlang, and Stuttering-Poisson processes are presented. A condition for the asymptotic normality of the state probabilities is also found.

This publication has 0 references indexed in Scilit: