Semi-Markov decision processes theory delivers the methods which allow to control the operation processes of the systems. The infinite duration semi-Markov decision processes are presented in the chapter. The gain maximization problem of three tasks operation processes subject to constraint of an availability of the semi-Markov reliability model is discussed. The problem is transformed on some linear programing maximization problem.
In the paper there are presented basic concepts and some results of the theory of semi-Markov decision processes. The optimization problem for the infinite duration SM process is connsider in the paper. The Howard algoritm which enables to find the optimal stationary strategy is also discussed here. The algorithm is applied in a decision problem concerning the two components renewable series system is. It is also shown that this algorithm is equivalent to the some linear programing problem.
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