Some results for dams with Markovian inputs

The paper considers the dam problem with Markovian inputs, with special reference to the serial correlation coefficient of the input process. An input model is proposed which by giving particular values to the parameters makes the stationary distribution of the inputs one of the standard discrete distributions. The probabilities of first emptiness before overflow are first obtained by using the Markovian analogue of Wald's Identity. From these, the stationary distributions of the dam content are obtained by a duality argument. Both, finite and infinite dams are considered. MARKOVIAN INPUT OF LINEAR REGRESSIVE KIND; MARKOVIAN ANALOGUE OF WALD'S IDENTITY; PROBABILITIES OF EMPTINESS; STATIONARY DISTRIBUTIONS OF DAM CONTENT; DEPENDENCE ON SERIAL CORRELATION COEFFICIENT