Optimal control of a finite dam with diffusion input and state dependent release rates

In this paper, we consider the optimal control of a finite dam using Pλ,τM policies; assuming that the dam has capacity v, the water input is a diffusion process reflected at 0, v. The release rates depend on the water content in the dam. There is a certain cost of maintaining the dam as well as a reward received. We obtain an explicit formulas for the total discounted cost over the infinite horizon as well as the long-run average cost per a unit of time.