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Lumping matrix diagram representations of Markov models

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3 Author(s)
S. Derisavi ; Coordinated Sci. Lab., Illinois Univ., Urbana, IL, USA ; P. Kemper ; W. H. Sanders

Continuous-time Markov chains (CTMCs) have been used successfully to model the dependability and performability of many systems. Matrix diagrams (MDs) are known to be a space-efficient, symbolic representation of large CTMCs. In this paper, we identify local conditions for exact and ordinary lumpings that allow us to lump MD representations of Markov models in a compositional manner. We propose a lumping algorithm for CTMCs that are represented as MDs that is based on partition refinement, is applied to each level of an MD directly, and results in an MD representation of the lumped CTMC. Our compositional lumping approach is complementary to other known model-level lumping approaches for matrix diagrams. The approach has been implemented, and we demonstrate its efficiency and benefits by evaluating an example model of a tandem multi-processor system with load balancing and failure and repair operations.

Published in:

2005 International Conference on Dependable Systems and Networks (DSN'05)

Date of Conference:

28 June-1 July 2005