Optimal control of Markov regenerative processes

In this paper the integration of available results on semi-Markov decision processes and on Markov regenerative processes is attempted, in order to define the mathematical framework for solving decision problems where the underlying structure state process is a Markov regenerative process, referred to a Markov regenerative decision process. The essential question investigated here is which description of Markov regenerative processes is needed to analyze the investigation decision model.