Numerical methods in Markov chain modeling
Operations Research
Iterative aggregation/disaggregation techniques for nearly uncoupled markov chains
Journal of the ACM (JACM)
Comparison of Partitioning Techniques for Two-Level Iterative Solvers on Large, Sparse Markov Chains
SIAM Journal on Scientific Computing
A parallel solver for large-scale Markov chains
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
A New Iterative Method for Solving Large-Scale Markov Chains
MMB '95 Proceedings of the 8th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation: Quantitative Evaluation of Computing and Communication Systems
A new parallel block aggregated algorithm for solving Markov chains
The Journal of Supercomputing
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In this paper, we propose a new parallel sparse iterative method (PPSIA) for computing the stationary distribution of large-scale Markov chains. The PPSIA method is based on Markov chain state isolation and aggregation techniques. The parallel method conserves as much as possible the benefits of aggregation, and Gauss---Seidel effects contained in the sequential algorithm (SIA) using a pipelined technique. Both SIA and PPSIA exploit sparse matrix representation in order to solve large-scale Markov chains. Some Markov chains have been tested to compare the performance of SIA, PPSIA algorithms with other techniques such as the power method, and the generalized minimal residual GMRES method. In all the tested models, PPSIA outperforms the other methods and shows a super-linear speed-up.