The numerical solution of stochastic automata networks

Article Abstract:

The numerical difficulties of solving stochastic automata network (SAN) models of parallel and complex systems are considered. Specifically, it is shown that SAN works best when there are few synchronizing events and 'the functional transitions are such that a small set of automata' greatly impacts the network. The derivation of a product from a vector and a SAN descriptor is also discussed along with a comparison between the power method, the method of W.E. Arnoldi and the generalized minimal residual technique.

Probabilistic automata

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Lower bounding aggregation and direct computation for an infinite horizon one-reservoir model

Article Abstract:

A policy iteration procedure for deriving optimal and sub-optimal policies for a discrete-time, stationary Markov decision model of a reservoir hydroelectric system is introduced. The procedure, which is based on piecewise affine approximations of optimal return functions, reduces to a finite method for obtaining an optimal policy in O(n3) time and another finite method for directly computing the lower bound on the optimal value function in O(m2n) time.

Operations research, Management science, Case studies

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A reservoir hydroelectric system: exactly and approximately optimal policies

Article Abstract:

Traditional multireservoir river basin models carry dimensionality problems in stochastic optimization. These problems are addressed in the analysis of a discrete-time model of a reservoir hydroelectric system. A structure defining optimal policy for the model is used to evaluate a Markov decision process function. The value function illustrates the applicability of piecewise linear approximation because sample errors were less than 1%.

Mathematical optimization, Optimization theory, Discrete-time systems, Discrete time systems

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