Exploiting Partial Symmetries for Markov Chain Aggregation

The technique presented in this paper allows the automatic construction of a lumped Markov chain for almost symmetrical Stochastic Well-formed Net (SWN) models. The starting point is the Extended Symbolic Reachability Graph (ESRG), which is a reduced representation of a SWN model reachability graph...

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Published inElectronic notes in theoretical computer science Vol. 39; no. 3; pp. 231 - 257
Main Authors Capra, L., Dutheillet, C., Franceschinis, G., Ilié, J-M.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 2000
Subjects
Extended Symbolic Reachability Graph
High-level Petri Nets
Lumpable Markov Chains
Symmetries
Lumpable Markov Chains
Extended Symbolic Reachability Graph
Symmetries
High-level Petri Nets
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Summary:The technique presented in this paper allows the automatic construction of a lumped Markov chain for almost symmetrical Stochastic Well-formed Net (SWN) models. The starting point is the Extended Symbolic Reachability Graph (ESRG), which is a reduced representation of a SWN model reachability graph (RG), based on the aggregation of states into classes. These classes may be used as aggregates for lumping the Continuous Time Markov Chain (CTMC) isomorphic to the model RG: however it is not always true that the lumpability condition is verified by this partition of states. In the paper we propose an algorithm that progressively refines the ESRG classes until a lumped Markov chain is obtained.
ISSN:1571-0661
1571-0661
DOI:10.1016/S1571-0661(05)80750-9