A decomposition approach for stochastic reward net models
Performance Evaluation
Asynchronous two-stage iterative methods
Numerische Mathematik
On generating a hierarchy for GSPN analysis
ACM SIGMETRICS Performance Evaluation Review - Special issue on Stochastic Petri Nets
Structured analysis approaches for large Markov chains
Applied Numerical Mathematics
Comparison of Partitioning Techniques for Two-Level Iterative Solvers on Large, Sparse Markov Chains
SIAM Journal on Scientific Computing
Hierarchical Structuring of Superposed GSPNs
IEEE Transactions on Software Engineering
A Toolbox for the Analysis of Discrete Event Dynamic Systems
CAV '99 Proceedings of the 11th International Conference on Computer Aided Verification
INFORMS Journal on Computing
Extracting state-based performance metrics using asynchronous iterative techniques
Performance Evaluation
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Very large systems of linear equations arise from numerous fields of application, e.g. analysis of continuous time Markov chains yields homogeneous, singular systems with millions of unknowns. Despite the availability of high computational power sophisticated solution methods like distributed iterative methods combined with space-efficient matrix representations are necessary to make the solution of such systems feasible. In this paper we combine block-structured matrices represented by Kronecker operators [3,4] with synchronous and asynchronous two-stage iterative methods [11] using the PVM message-passing tool. We describe, how these methods profit from the proposed matrix representation, how these methods perform in wide-spread local area networks and what difficulties arise from this setting.