Iterative disaggregation for a class of lumpable discrete-time stochastic automata networks
Performance Evaluation
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Product Form Steady-State Distribution for Stochastic Automata Networks with Domino Synchronizations
EPEW '08 Proceedings of the 5th European Performance Engineering Workshop on Computer Performance Engineering
Stochastic Automata Networks with Master/Slave Synchronization: Product Form and Tensor
ASMTA '09 Proceedings of the 16th International Conference on Analytical and Stochastic Modeling Techniques and Applications
Queueing Systems: Theory and Applications
Convergence of multi-level iterative aggregation-disaggregation methods
Journal of Computational and Applied Mathematics
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Stochastic automata networks (SANs) have been developed and used in the last fifteen years as a modeling formalism for large systems that can be decomposed into loosely connected components. In this work, we extend the near complete decomposability concept of Markov chains (MCs) to SANs so that the inherent difficulty associated with solving the underlying MC can be forecasted and solution techniques based on this concept can be investigated. A straightforward approach to finding a nearly completely decomposable (NCD) partitioning of the MC underlying a SAN requires the computation of the nonzero elements of its global generator. This is not feasible for very large systems even in sparse matrix representation due to memory and execution time constraints. We devise an efficient decompositional solution algorithm to this problem that is based on analyzing the NCD structure of each component of a given SAN. Numerical results show that the given algorithm performs much better than the straightforward approach.