First-passage time criteria for the operation of reservoirs

Abstract

Summary A multi-objective optimisation for reservoir operation based on expected monetary value and expected first passage-time criterion is proposed. The computations are facilitated by the algorithms of matrix analytic methods. The formal structure, classifying states as levels and phases within levels, and associated algorithms of matrix analytic methods are introduced in the context of multi-reservoir systems. The algorithms underpin the feasibility of the computations for large systems and enable the calculation of the full distribution of first passage time. A new algorithm for computing results for a seasonal model, which reduces computing time by an order of magnitude for monthly time steps is presented. The methods are illustrated for a two reservoir system, with an option of pumping additional water from a transfer scheme, in the East of England. The Pareto front of Pareto optimal policies is shown.