Control of dams using \(P^M_{\lambda,\tau}\) policies when the input process is a nonnegative Lévy process (Q655232)

Summary: We consider \(P^M_{\lambda,\tau}\) policy of a dam in which the water input is an increasing Lévy process. The release rate of the water is changed from 0 to \(M\) and from \(M\) to 0 \((M > 0)\) at the moments when the water level upcrosses level \(\lambda\) and downcrosses level \(\tau (\tau < \lambda)\), respectively. We determine the potential of the dam content and compute the total discounted as well as the long-run average cost. We also find the stationary distribution of the dam content. Our results extend the results in the literature when the water input is assumed to be a Poisson process.