Three partition refinement algorithms
SIAM Journal on Computing
A compositional approach to performance modelling
A compositional approach to performance modelling
Optimal state-space lumping in Markov chains
Information Processing Letters
Trace Machines for Observing Continuous-Time Markov Chains
Electronic Notes in Theoretical Computer Science (ENTCS)
A survey of Markovian behavioral equivalences
SFM'07 Proceedings of the 7th international conference on Formal methods for performance evaluation
Weighted lumpability on markov chains
PSI'11 Proceedings of the 8th international conference on Perspectives of System Informatics
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Markovian behavioral equivalences can be exploited for state space reduction before performance evaluation takes place. It is known that Markovian bisimilarity corresponds to ordinary lumpability and that Markovian testing and trace equivalences correspond to a coarser exact relation we call T-lumpability. While there exists an ordinary-lumpability-consistent aggregation algorithm, this is not the case with T-lumpability. Based on the axiomatization of Markovian testing and trace equivalences, we provide a sufficient condition for T-lumpability that can easily be embedded in the aggregation algorithm for ordinary lumpability, thus enhancing the potential for exact state space reduction. We also identify a class of systems --- those providing incremental services --- for which the resulting aggregation algorithm turns out to be useful.