Stochastic Well-Formed Colored Nets and Symmetric Modeling Applications
IEEE Transactions on Computers
PNPM '01 Proceedings of the 9th international Workshop on Petri Nets and Performance Models (PNPM'01)
Optimal state-space lumping in Markov chains
Information Processing Letters
Detecting and Exploiting Symmetry in Discrete-state Markov Models
PRDC '06 Proceedings of the 12th Pacific Rim International Symposium on Dependable Computing
A symbolic algorithm for optimal Markov chain lumping
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
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A model-based evaluation of a system's design often considers to what degree components need to be available multiple times in order to reach a desired level of availability, reliability or dependability. Multiple components of the same kind then lead to models with regular structures. In stochastic models, especially Markovian models, such regularities have been studied for a long time and are used to establish lumpability results that help to achieve a significant state space reduction and alleviate the effects of the infamous state space explosion problem. In this paper, we introduce a new procedure to identify and reduce Markovian models that are built in a compositional manner based on sharing state variables. This procedure can also detect symmetries based on reflection in spatial models where state variables can commute. The results extend existing work of Obal, McQuinn, and Sanders and will contribute to Möbius, a multi-paradigm, multi-solution framework for the model-based dependability and performance assessment of systems.