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This paper studies a discrete model of a large dam where the differencebetween lower and upper levels, $L$, is assumed to be large. Passage across thelevels leads to damage, and the damage costs of crossing the lower or upperlevel are proportional to the large parameter $L$. Input stream of water isdescribed by compound Poisson process, and the water cost depends upon currentlevel of water in the dam. The aim of the paper is to choose the parameters ofoutput stream (specifically defined in the paper) minimizing the long-runexpenses that include the damage costs and water costs. The present paperaddresses the important question \emph{How does the structure of water costsaffect the optimal solution?} We prove the existence and uniqueness of asolution. A special attention is attracted to the case of linear structure ofthe costs.  As well, the paper contributes to the theory of state-dependent queueingsystems. The inter-relations between important characteristics of astate-dependent queueing system are established, and their asymptotic analysisthat involves analytic techniques of Tauberian theory and heavy trafficapproximations is provided.

Optimal control of a large dam with compound Poisson input and costs depending on water levels