Stochastic Reservoir Calculations
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Prabhu (1958) obtained the stationary distribution of storage level Z_t in a reservoir of finite volume v, given an inflow X_t and an outflow Y_t. Time t is assumed to be discrete, X_t∼ Gamma(p,μ) are independent and p is a positive integer. The mean inflow is p/μ; the target outflow is m (constant). We attempt to clarify intricate details, often omitted in the literature, by working through several examples. Of special interest are the probabilities of depletion (Z_t=0) and spillage (Z_t=v). For prescribed v,p,μ, what value of m minimizes both of these?
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