Componentwise bounds for nearly completely decomposable Markov chains using stochastic comparison and reordering

This paper presents an improved version of a componentwise bounding algorithm for the state probability vector of nearly completely decomposable Markov chains, and on an application it provides the first numerical results with the type of algorithm discussed. The given two-level algorithm uses aggre...

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Bibliographic Details
Published in:European journal of operational research 2005-09, Vol.165 (3), p.810-825
Main Authors: Pekergin, Nihal, Dayar, Tuğrul, Alparslan, Denizhan N.
Format: Article
Language:English
Subjects:
Aggregation
Algorithms
Applied sciences
Exact sciences and technology
Markov analysis
Markov processes
Mathematics
Near complete decomposability
Operational research and scientific management
Operational research. Management science
Operations research
Optimization. Search problems
Probability and statistics
Probability theory and stochastic processes
Reorderings
Sciences and techniques of general use
Stochastic comparison
Studies
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Summary:This paper presents an improved version of a componentwise bounding algorithm for the state probability vector of nearly completely decomposable Markov chains, and on an application it provides the first numerical results with the type of algorithm discussed. The given two-level algorithm uses aggregation and stochastic comparison with the strong stochastic (st) order. In order to improve accuracy, it employs reordering of states and a better componentwise probability bounding algorithm given st upper- and lower-bounding probability vectors. Results in sparse storage show that there are cases in which the given algorithm proves to be useful.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2001.09.001