Componentwise bounds for nearly completely decomposable Markov chains using stochastic comparison and reordering
Date
2005
Authors
Pekergin, N.
Dayar T.
Alparslan, D. N.
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Source Title
European Journal of Operational Research
Print ISSN
0377-2217
1872-6860
1872-6860
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Publisher
Elsevier
Volume
165
Issue
3
Pages
810 - 825
Language
English
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Abstract
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. © 2004 Elsevier B.V. All rights reserved.
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Keywords
Aggregation , Markov processes , Near complete decomposability , Reorderings , Stochastic comparison , Algorithms , Eigenvalues and eigenfunctions , Linear equations , Markov processes , Matrix algebra , Poisson distribution , Probability , Problem solving , Queueing networks , Vectors , Markov modulated Poisson process (MMPP) , Near complete decomposability , Reordering , Stochastic comparison , Operations research