Abstract
This article analyzes discrete Markov processes that arise in some general control problems of a storage (or a dam) with an infinite capacity. Employing a special “step-wise” structure of the transition matrices of these processes, the author obtains conditions for their ergodicity and develops an implementable algorithm for finding the generating function of the corresponding distributions. This algorithm is applied to a dam with a multilevel state-dependent control strategy, according to which parameters of the input and output processes may depend on the amount of the water in the dam. The method is illustrated with a case of a single-level control strategy where explicit results are obtained.