A note on the expected discounted cost of operating a finite dam (Q1118260)

A finite dam operated under the \(P^ M_{\lambda,\tau}\) policy [see the author, Resolvent operators of Markov processes and their applications in the control of a finite dam. J. Appl. Probab. (to appear); and \textit{Lam Yeh} and \textit{Lou Jiann Hua}, ibid. 24, 186-189 (1987; Zbl 0617.93078)] 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.