Weak stochastic comparisons for performability verification

Abstract : The probabilistic model checking provides a precise formalism for the performance and reliability verification of telecommunication systems modeled by Markov chains. We study a queueing system similar to a Jackson network except that queues have a finite capacity. We propose to study in this paper (state and path) formulas from the Continuous Stochastic Logic (CSL), in order to verify performability properties. Unfortunately, transient and stationary analysis is very complex for multidimensional Markov processes. So we propose to use the stochastic comparisons in the sense of weak orderings to define bounding processes. Bounding processes are represented by independent M/M/1 queues for which transient and stationary distributions can be computed as the product of probability distributions of each queue. We use the increasing set method, and we develop an intuitive formalism based on events to establish weak stochastic comparisons
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Contributor : Médiathèque Télécom Sudparis & Institut Mines-Télécom Business School <>
Submitted on : Wednesday, September 21, 2016 - 2:29:48 PM
Last modification on : Tuesday, January 22, 2019 - 2:32:06 PM

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Hind Castel-Taleb, Nihal Pekergin. Weak stochastic comparisons for performability verification. ASMTA 2009 : 16th International Conference on Analytical and Stochastic Modeling Techniques and Applications , Jun 2009, Madrid, Spain. pp.294 - 308, ⟨10.1007/978-3-642-02205-0_21⟩. ⟨hal-01369734⟩



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