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Optimal Control of a Model for a System Subject to Continuous Wear

Published online by Cambridge University Press:  27 July 2009

Laurence A. Baxter  and
Eui Yong Lee
Laurence A. Baxter
Affiliation:
Department of Applied Mathematics andStatistics State University of New York at Stony Brook Stony Brook, New York 11794
Eui Yong Lee
Affiliation:
Department of Applied Mathematics andStatistics State University of New York at Stony Brook Stony Brook, New York 11794
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Abstract

The state of a system is modelled by Brownian motion with negative drift and an absorbing barrier at the origin. A repairman arrives according to a Poisson process of rate λ. If the state of the system at arrival of the repairman does not exceed a certain threshold, he/she increases it by a random amount, otherwise no action is taken. Costs are assigned to each visit of the repairman, to each repair, and to the system being in state 0. It is shown that there exists a unique arrival rate λ which minimizes the average cost per unit time over an infinite horizon.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 2 , Issue 3 , July 1988 , pp. 321 - 328
Copyright
Copyright © Cambridge University Press 1988

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References

Baxter, L.A. & Lee, E.Y. (1987). A diffusion model for a system subject to continuous wear. Probability in the Engineering and Informational Sciences 1: 405–416.CrossRefGoogle Scholar