On the relations between Lumpability and Reversibility

In the literature devoted to the efficient solution of Continuous Time Markov Chains (CTMCs) the notions of lump ability and reversibility have a central role. In the context of lump able Markov chains several definitions have been introduced: strong, exact and strict, just to mention a few of them. On the side of the analysis of reversible CTMCs the research community has shown great interest in the application of this notion with the aim of efficiently computing the stationary distribution of large models (e.g., obtained by composition of several processes). In this paper we show for the first time the relations between the above mentioned notions of lump ability and the concept of reversibility. The major outcome of our research is proving a strong connection between the notion of strict lump ability and that of reversibility.