Combining Decomposition and Reduction for State Space Analysis of a Self-Stabilizing System - Best Paper Award

Müllner, Nils and Theel, Oliver and Fränzle, Martin
Advanced Information Networking and Applications, International Conference on
Verifying fault tolerance properties of a distributedsystem 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 theconsiderably 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.
03 / 2012
IEEE Computer Society
IEEE Computer Society
Modeling, Verification and Control of complex Systems: From Foundations to Power Network Appliances