Managing river flow in arid regions with matrix analytic methods

Matrix analytic methods (MAM) support non-geometric transitions between sets of states, termed levels, by introducing states, known as phases, within levels. The phases can correspond to an observed variable or they can be hidden. MAM models have been extensively used in telecommunications, and efficient algorithms for evaluation of performance continue to be developed. Following a review of MAM in discrete time, the daily flows of the ephemeral Cooper Creek, in South Australia, are modelled. Hidden phases are used in the distribution of the duration of the dry spells, whereas observed phases, are used within non-zero flow levels. Seasonal and non-seasonal models are compared. A second application is managing the level of a reservoir in Queensland, using MAM within stochastic dynamic programming. Inflows to the reservoir are seasonal and influenced by the value of the Southern Oscillation Index (SOI), which is used to define phases. The benefit of including SOI in the decision process is shown.