Decision problem for infinite duration semi-Markov process

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.