On the use of exact lumpability in partially symmetrical well-formed nets

Well-formed nets (WNs) have proved an efficient model for building quotient reachability graphs that can be used either for qualitative or performance analysis. However, local asymmetries often break any possibility of grouping states into classes, thus drastically reducing the interest of the approach. An efficient solution has been proposed for qualitative analysis, which relies on a separate representation of the asymmetries in a so called control automaton. The quotient graph is then obtained by synchronizing the transitions of the WN model with the transitions of the control automaton. In this paper, we improve this approach to quantitative analysis. We show that it can be used to build an aggregated graph that is isomorphic to a Markov chain which verifies exact lumpability. Theoretical considerations and practical experiments show that our method outperforms previous approaches.