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This paper studies large dam models where the difference between lower andupper levels, $L$, is assumed to be large. Passage across the levels leads todamage, and the damage costs of crossing the lower or upper level areproportional to the large parameter $L$. Input stream of water is described bycompound Poisson process, and the water cost depends upon current level ofwater in the dam. The aim of the paper is to choose the parameters of outputstream (specifically defined in the paper) minimizing the long-run expenses.The particular problem, where input stream is ordinary Poisson and water costsare not taken into account, has been studied in [Abramov, \emph{J. Appl.Prob.}, 44 (2007), 249-258]. The present paper addresses the question\textit{How does the structure of water costs affect the optimal solution?}Under natural assumptions we prove an existence and uniqueness of a solutionand study the case of linear structure of the costs.

Optimal control of a large dam, taking into account the water costs [New Edition]