Deterministic and stochastic modeling of parallel garbage collection: towards real-time criteria
ISCA '87 Proceedings of the 14th annual international symposium on Computer architecture
The reduction of perturbed Markov generators: an algorithm exposing the role of transient states
Journal of the ACM (JACM)
A Decomposition Procedure for the Analysis of a Closed Fork/Join Queueing System
IEEE Transactions on Computers
Advances in Model Representations
PAPM-PROBMIV '01 Proceedings of the Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Performance Evaluation: Origins and Directions
Distributed PageRank computation based on iterative aggregation-disaggregation methods
Proceedings of the 14th ACM international conference on Information and knowledge management
Performance modelling and Markov chains
SFM'07 Proceedings of the 7th international conference on Formal methods for performance evaluation
Passage-time computation and aggregation strategies for large semi-Markov processes
Performance Evaluation
Network performance engineering
Triangular and skew-symmetric splitting method for numerical solutions of Markov chains
Computers & Mathematics with Applications
A new parallel block aggregated algorithm for solving Markov chains
The Journal of Supercomputing
A new parallel algorithm for solving large-scale Markov chains
The Journal of Supercomputing
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Iterative aggregation/disaggregation methods provide an efficient approach for computing the stationary probability vector of nearly uncoupled (also known as nearly completely decomposable) Markov chains. Three such methods that have appeared in the literature recently are considered and their similarities and differences are outlined. Specifically, it is shown that the method of Takahashi corresponds to a modified block Gauss-Seidel step and aggregation, whereas that of Vantilborgh corresponds to a modified block Jacobi step and aggregation. The third method, that of Koury et al., is equivalent to a standard block Gauss-Seidel step and iteration. For each of these methods, a lemma is established, which shows that the unique fixed point of the iterative scheme is the left eigenvector corresponding to the dominant unit eigenvalue of the stochastic transition probability matrix. In addition, conditions are established for the convergence of the first two of these methods; convergence conditions for the third having already been established by Stewart et al. All three methods are shown to have the same asymptotic rate of convergence.