Compositionality for Markov reward chains with fast and silent transitions
Performance Evaluation
Compositionality for Markov reward chains with fast transitions
EPEW'07 Proceedings of the 4th European performance engineering conference on Formal methods and stochastic models for performance evaluation
Weak markovian bisimulation congruences and exact CTMC-Level aggregations for sequential processes
TGC'11 Proceedings of the 6th international conference on Trustworthy Global Computing
Hi-index | 0.00 |
A silent step in a dynamic system is a step that is considered unobservable and that can be eliminated. We define a Markov chain with silent steps as a class of Markov chains parameterized with a special real number ô. When ô goes to infinity silent steps become immediate, i.e. timeless, and therefore unobservable. To facilitate the elimination of these steps while preserving performance measures, we introduce a notion of lumping for the new setting. To justify the lumping we first extend the standard notion of ordinary lumping to the setting of discontinuous Markov chains, processes that can do infinitely many transitions in finite time. Then, we give a direct connection between the two lumpings for the case when ô is infinite. The results of this paper can serve as a correctness criterion and a method for the elimination of silent (ô ) steps in Markovian process algebras.