Markov Decision Petri Net and Markov Decision Well-Formed Net Formalisms

Abstract

In this work, we propose two high-level formalisms, Markov Decision Petri Nets (MDPNs) and Markov Decision Well-formed Nets (MDWNs), useful for the modeling and analysis of distributed systems with probabilistic and non deterministic features: these formalisms allow a high level representation of Markov Decision Processes. The main advantages of both formalisms are: a macroscopic point of view of the alternation between the probabilistic and the non deterministic behaviour of the system and a syntactical way to define the switch between the two behaviours. Furthermore, MDWNs enable the modeller to specify in a concise way similar components. We have also adapted the technique of the symbolic reachability graph, originally designed for Well-formed Nets, producing a reduced Markov decision process w.r.t. the original one, on which the analysis may be performed more efficiently. Our new formalisms and analysis methods are already implemented and partially integrated in the GreatSPN tool, so we also describe some experimental results.