A heuristic procedure for compact Markov representation of PH distributions.

The minimal Markovian representation of PH distributions is an open research problem, which was actively investigated during the last two decades. We present a numerical method for finding small Markovian representation of PH distributions and investigate the general quality of the method by comparing the size of the obtained representation with the size of the representation obtained by alternative methods. Our numerical method intends to find a small Markovian representation. We report examples when the obtained representation is larger than the minimal Markovian representation.