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Optimal Control of a Large Dam

Part of: Inversion theorems Operations research and management science Special 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: [email protected]
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Abstract

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A large dam model is the object of study of this paper. The parameters Llower and Lupper define its lower and upper levels, L = Lupper - Llower 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 J1 and J2 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 Lt denote the dam level at time t, and let p1 = limt→∞P{Lt = Llower} and p2 = limt→∞P{Lt > Lupper} exist. The long-run average cost, J = p1J1 + p2J2, 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, general 90B05: Inventory, storage, reservoirs
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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