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An algorithm approach to bounding aggregations of multidimensional Markov chains

Abstract : We analyze transient and stationary behaviors of multidimensional Markov chains defined on large state spaces. In this paper, we apply stochastic comparisons on partially ordered state which could be very interesting for performance evaluation of computer networks. We propose an algorithm for bounding aggregations in order to derive upper and lower performance measure bounds on a reduced state space. We study different queueing networks with rejection in order to compute blocking probability and end to end mean delay bounds. Parametric aggregation schemes are studied in order to propose an attractive solution: given a performance measure threshold, we vary the parameter values to obtain a trade-off between the accuracy of bounds and the computation complexity.
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Contributor : Médiathèque Télécom Sudparis & Institut Mines-Télécom Business School <>
Submitted on : Wednesday, April 3, 2013 - 3:31:04 PM
Last modification on : Friday, January 8, 2021 - 11:22:05 AM

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Hind Castel-Taleb, Lynda Mokdad, Nihal Pekergin. An algorithm approach to bounding aggregations of multidimensional Markov chains. Theoretical Computer Science, Elsevier, 2012, 452, pp.12-20. ⟨10.1016/j.tcs.2012.05.030⟩. ⟨hal-00807451⟩



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