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- W2085278522 abstract "The paper examines a system of two discrete stochastic reservoirs in series, and a system of two in parallel. In the ‘series’ case, the downstream reservoirs is fed not only by an inflow from its own catchment but also (after the necessary transit time lag by the controlled release plus the overflow from the upstream facility. If the inflow processes to the two reservoirs from their respective catchments are independent of one another, the pair (Zt−a, Z′t) of water levels in the two constituents form a bivariate Markov chain, the transition probabilities of which are derived. The joint equilibrium distribution of the two storage variables then requires the solution of (c + 1)(c′ + 1) simultaneous linear algebraic equations, where c, c′ are the capacities of the two reservoirs. The final yield and spillage distributions follow directly from those of the storages. If, however, the inflow processes are both Markovian, defined on the values 0, 1,…,d and 0, 1,…,d′ respectively, the number of equations to be solved increases to the impracticable level of (c + 1) (c′ + 1)(d + 1)(d′ + 1). In the ‘parallel’ case, each reservoir receives its own inflow process, and in each the release is controlled by both storage levels. The two yields are then combined. If the inflow processes are mutually independent we find that (Zt, Zt′) is bivariate Markov; if, instead, they are themselves Markovian, one has to work in terms of the quadrivariate Markov process (Zt, Zt′, Xt, Xt′), with consequences for the number of equations to be solved as in the ‘series’ system." @default.
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- W2085278522 date "1992-08-01" @default.
- W2085278522 modified "2023-10-16" @default.
- W2085278522 title "A probability treatment of storage, yield and spillage in a system of two reservoirs in series, and in two reservoirs in parallel" @default.
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- W2085278522 doi "https://doi.org/10.1016/0022-1694(92)90063-2" @default.
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