Browsing by Subject "Reorderings"

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    Componentwise bounds for nearly completely decomposable Markov chains using stochastic comparison and reordering
    (Elsevier, 2005) Pekergin, N.; Dayar T.; Alparslan, D. N.
    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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    Stochastic comparison on nearly completely decomposable Markov chains
    (2000) Alparslan, Denizhan N.
    This thesis presents an improved version of a componentwise bounding algorithm for the steady state probability vector of nearly completely decomposable Markov chains. 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. A thorough analysis of the algorithm is implemented in sparse storage and its implementation details are given. Numerical results on an application of wireless Asynchronous Transfer Mode network show that there are cases in which the given algorithm proves to be useful in computing bounds on the performance measures of the system. An improvement in the algorithm that must be considered to obtain better bounds on performance measures is also presented at the end.