Componentwise bounds for nearly completely decomposable Markov chains using stochastic comparison and reordering
Author
Pekergin, N.
Dayar T.
Alparslan, D. N.
Date
2005Source Title
European Journal of Operational Research
Print ISSN
0377-2217 1872-6860
Publisher
Elsevier
Volume
165
Issue
3
Pages
810 - 825
Language
English
Type
ArticleItem Usage Stats
133
views
views
76
downloads
downloads
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.
Keywords
AggregationMarkov 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