A large dam model is an object of study of this paper. The parameters $L^{lower}$ and $L^{upper}$ are its lower and upper levels, $L=L^{upper}-L^{lower}$ is large, and if a current level of water is between these bounds, then the dam is assumed to be in normal state. Passage one or other bound leads to damage. It is assumed that input stream of water is described by a Poisson process, while the output stream is state-dependent (the exact formulation of the problem will be given in the report). Let $L_t$ denote the dam level at time $t$, and let $p_1=\lim_{t\to\infty}\mathbf{P}\{L_t= L^{lower}\}$, $p_2=\lim_{t\to\infty}\mathbf{P}\{L_t> L^{upper}\}$ exist. Then the expected long-run damage $J=p_1J_1+p_2J_2$ for the long time interval $T$ proportional to $L$ ($J_1$ and $J_2$ are the corresponding damage costs per time $T$ associated with passage the bounds) is a performance measure, and the aim of the paper is to choose the parameter of output stream (exactly specified in the report) minimizing $J$.
 

Convenor:Kais Hamza