@inproceedingsMuellner2012,
Author = {Müllner, Nils and Theel, Oliver and Fränzle, Martin},
Title = {Combining Decomposition and Reduction for State Space Analysis of a Self-Stabilizing System - Best Paper Award},
Journal = {Advanced Information Networking and Applications, International Conference on},
Year = {2012},
Pages = {936-943},
Month = {03},
Publisher = {IEEE Computer Society},
Series = {AINA'12},
Isbn = {1550-445X},
Organization = {IEEE Computer Society},
Doi = {http://doi.ieeecomputersociety.org/10.1109/AINA.2012.127},
Url = {http://www.computer.org/csdl/proceedings/aina/2012/4651/00/4651a936-abs.html},
School = {Universit\"at Oldenburg},
type = {inproceedings},
note = {Verifying fault tolerance properties of a distributed
system can be achieved by state space analysis via Markov chains. Yet, the power of such exact analytic methods is confined by exponential growth of the chain's state space in the size of the system m},
Abstract = {Verifying fault tolerance properties of a distributed
system can be achieved by state space analysis via Markov chains. Yet, the power of such exact analytic methods is confined by exponential growth of the chain's state space in the size of the system modeled. We propose a method that alleviates this limit. Lumping is a well known reduction technique that can be applied to a Markov chain to prune redundant information. We propose a system decomposition to employ lumping piecewise on the
considerably smaller Markov chains of the subsystems which are much more likely to be tractable. Recomposing the lumped Markov chains of the subsystems results in a state space that is likely to be considerably smaller. An example demonstrates how the limiting window availability (i.e. a fault tolerance property) can be computed for a system while exploiting the combination of lumping and decomposition.}
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