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A thermal energy storage process with controlled input

Published online by Cambridge University Press:  01 July 2016

D. J. Daley  and
J. Haslett
D. J. Daley*
Affiliation:
The Australian National University
J. Haslett*
Affiliation:
Trinity College, Dublin
*
∗Postal address: Statistics Department (IAS), The Australian National University, P.O. Box 4, Canberra, ACT 2600, Australia.
∗∗Postal address: Statistics Department, Trinity College, Dublin, Ireland.
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Abstract

The stochastic process {Xn} satisfying Xn+1 = max{Yn+1+ αβ Xn, βXn} where {Yn} is a stationary sequence of non-negative random variables and , 0<β <1, can be regarded as a simple thermal energy storage model with controlled input. Attention is mostly confined to the study of μ = EX where the random variable X has the stationary distribution for {Xn}. Even for special cases such as i.i.d. Yn or α = 0, little explicit information appears to be available on the distribution of X or μ . Accordingly, bounding techniques that have been exploited in queueing theory are used to study μ . The various bounds are illustrated numerically in a range of special cases.

Keywords

CONTROLLED INPUT STORAGE MODELAUTOREGRESSIVE MODELQUEUEING INEQUALITIESCOMPARISON TECHNIQUES
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 2 , June 1982 , pp. 257 - 271
Copyright
Copyright © Applied Probability Trust 1982 

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Footnotes

Research carried out while this author was visiting CSIRO Division of Mathematics and Statistics, Canberra.

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