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Optimal Control of a Large Dam

Part of:Operations research and management scienceInversion theoremsSpecial processes

Published online by Cambridge University Press:  14 July 2016

Vyacheslav M. Abramov
Vyacheslav M. Abramov*
Affiliation:
Monash University
*
∗ Postal address: School of Mathematical Sciences, Monash University, Building 28M, Clayton Campus, Clayton, VIC 3800, Australia. Email address: vyacheslav.abramov@sci.monash.edu.au
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Abstract

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A large dam model is the object of study of this paper. The parameters L lower and L upper define its lower and upper levels,L = L upper - L lower is large, and if the current level of water is between these bounds, the dam is assumed to be in a normal state. Passage across one or other of the levels leads to damage. Let J 1 and J 2 denote the damage costs of crossing the lower and, respectively, the upper levels. It is assumed that the input stream of water is described by a Poisson process, while the output stream is state dependent. Let L t denote the dam level at time t, and let p 1 = limt→∞P{L t = L lower} and p 2 = limt→∞P{L t > L upper} exist. The long-run average cost,J = p 1 J 1 + p 2 J 2, is a performance measure. The aim of the paper is to choose the parameter controlling the output stream so as to minimize J.

Keywords

Damstate-dependent queueasymptotic analysiscontrol problem

MSC classification

Primary:60K30: Applications (congestion, allocation, storage, traffic, etc.)60K25: Queueing theory
Secondary:40E05: Tauberian theorems, general90B05: Inventory, storage, reservoirs

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 44 , Issue 1 , March 2007, pp. 249 - 258
Copyright
Copyright © Applied Probability Trust 2007 

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