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

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      Author
      Pekergin, N.
      Dayar T.
      Alparslan, D. N.
      Date
      2005
      Source Title
      European Journal of Operational Research
      Print ISSN
      0377-2217
       
      1872-6860
       
      Publisher
      Elsevier
      Volume
      165
      Issue
      3
      Pages
      810 - 825
      Language
      English
      Type
      Article
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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.
      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
      Permalink
      http://hdl.handle.net/11693/23983
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.ejor.2001.09.001
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