N-Stage output procedure of a finite dam

We examine the problem of optimizing operation of a reservoir with a finite capacity, described by the following model: The input of water into the reservoir is a Wiener process with positive drift. Water may be released at one of R possible rates. At any time the output rate may be increased with cost K per unit increase or it may be decreased to zero with zero cost. There is a reward of A monetary units for each unit of output. The problem is to control the output in such a way as to maximize the long run average profit per unit time.