A note on the expected discounted cost of operating a finite dam

A finite dam operated under the PM[lambda],[tau] policy (Attia, 1987; Lam and Lou, 1987) is considered. The input process to the dam is either (a) the integral of an irreducible Markov chain or (b) the geometric Wiener process exp{B(t)}, where B(t) is a Wiener process with drift [mu] > 0 and variance parameter [sigma]2. The expected discounted cost of operating the dam in the two cases (a) and (b) is obtained, and the relation between this cost and the long-run average cost per unit time is established.