First-passage time criteria for the operation of reservoirs

•We consider a new criterion for the operation of reservoirs based on expected first-passage time.•The first-passage time criterion is contrasted with maximal expected monetary value by comparing how policies perform using both measures.•Alternative policies are found using an algorithm based on the Metropolis-Hastings algorithm.•A Pareto front is found using the policies that are Pareto optimal for the two criteria.

SummaryA 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.