Weak Stochastic Comparisons for Performability Verification
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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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- 2.Baier, C., Haverkort, B., Hermanns, H., Katoen, J.P.: Model-Checking Algorithms for Continuous Markov Chains. IEEE Transactions on Software Engineering 29(6) (June 2003)Google Scholar
- 3.Ben Mamoun, M., Pekergin, N., Younès, S.: Model Checking of Continuous Time Markov Chains by Closed-Form Bounding Distributions. In: Qest 2006 (2006)Google Scholar
- 4.Castel-Taleb, H., Mokdad, L., Pekergin, N.: Model Checking of steady-state rewards using bounding aggregations. In: 2008 International Symposium on Performance Evaluation of Computer and Telecommunication Systems, SPECTS 2008, Edinburgh, UK, June 16-18 (2008)Google Scholar
- 5.Castel-Taleb, H., Pekergin, N.: Stochastic monotonicity in queueing networks (submitted)Google Scholar
- 8.Lindvall, T.: Lectures on the coupling method. Wiley series in Probability and Mathematical statistics (1992)Google Scholar
- 10.Massey, W.: Stochastic orderings for Markov processes on partially ordered spaces. Mathematics of Operations Research 12(2) (May 1987)Google Scholar
- 13.Remke, A., Haverkort, B.R.: CSL model checking algorithms for infinite-state structured Markov chainsGoogle Scholar
- 14.Stoyan, D.: Comparison methods for queues and other stochastics models. J. Wiley and son, Chichester (1976)Google Scholar
- 15.Younes, S.: Model Checking Stochastique par la méthode de comparaison stochastique, Thèse de doctorat de l’université de Versailles Saint Quentin (December 2008)Google Scholar