On solving stochastic coupling matrices arising in iterative aggregation/disaggregation methods

Iterative aggregation/disaggregation (IAD) methods are powerful tools for solving Markov chain models whose transition probability matrices are nearly completely decomposable (NCD). Such models arise frequently during the performance and reliability analysis of computer and telecommunication systems...

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Bibliographic Details
Main Authors: Stewart, W.J., Touzene, A.
Format: Conference Proceeding
Language:English
Subjects:
Computer errors
Computer science
Distributed decision making
Iterative methods
Matrix decomposition
Performance analysis
Power system modeling
Power system reliability
Stochastic processes
Telecommunication computing
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Summary:Iterative aggregation/disaggregation (IAD) methods are powerful tools for solving Markov chain models whose transition probability matrices are nearly completely decomposable (NCD). Such models arise frequently during the performance and reliability analysis of computer and telecommunication systems. IAD methods require the solution of a stochastic coupling matrix whose elements denote transition probabilities among blocks. The coupling matrices are often large and in NCD models necessarily have diagonal elements close to one and small off-diagonal elements. This makes their solution by either iterative or direct methods rather difficult. We propose a modification of the coupling matrix that allows us to accurate and efficiently compute its stationary probability vector.< >
DOI:10.1109/MASCOT.1994.284413