Strong and weak stochastic bounds for multidimensional Markov chains

Abstract : We study queueing networks similar to Jackson networks, modelled by a multidimensional Markov chain. The performance analysis may be very difficult or intractable, if there is no specific solution form. We explain how stochastic comparisons of Markov chains can be used to overcome this problem. We build new queueing which are easier to analyse and providing stochastic bounds (upper or lower) for the original model. In this paper, we propose different queueing systems in the sense of the strong and weak stochastic ordering for a general queueing network model in order to compute performance measure bounds as blocking probabilities. We discuss the accuracy of the bounds under different input parameter values
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Journal articles
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https://hal.archives-ouvertes.fr/hal-01260059
Contributor : Médiathèque Télécom Sudparis & Institut Mines-Télécom Business School <>
Submitted on : Thursday, January 21, 2016 - 2:37:01 PM
Last modification on : Thursday, February 7, 2019 - 3:55:20 PM

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Hind Castel-Taleb, Nihal Pekergin. Strong and weak stochastic bounds for multidimensional Markov chains. International Journal of Critical Computer-Based Systems, Inderscience, 2014, 5 (1/2), pp.148 - 168. ⟨10.1504/IJCCBS.2014.059592⟩. ⟨hal-01260059⟩

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