Author:
Baxter Laurence A.,Lee Eui Yong
Abstract
A model for a system whose state changes continuously with time is introduced. It is assumed that the system is modeled by Brownian motion with negative drift and an absorbing barrier at the origin. A repairman arrives according to a Poisson process and increases the state of the system by a random amount if the state is below a threshold α. Explicit expressions are deduced for the distribution function of X(t), the state of the system at time 1, if X(t) ≤ α and for the Laplace transform of the density of X( t). The stationary case is examined in detail.
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability
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