A Note on the Solution of Dam Equations

Abstract

The object of this paper is to provide an algorithm for solving the equations giving the equilibrium distribution of reservoir levels, both for Moran's formulation in terms of independent inflows and for Lloyd's formulation involving Markovian inflows. In the case of independent inflows, the equilibrium distribution may be expressed linearly in terms of powers of the roots of a certain polynomial. When the inputs form a Markov chain, the solution may be similarly expressed in terms of the latent roots of a certain matrix, or (more conveniently for computation) directly in terms of powers of that matrix. The method is illustrated by simple examples.