Abstract
We propose to perform statistical probabilistic model checking by using perfect simulation in order to verify steady-state and time unbounded until formulas over Markov chains. The model checking of probabilistic models by statistical methods has received increased attention in the last years since it provides an interesting alternative to numerical model checking which is poorly scalable with the increasing model size. In previous statistical model checking works, unbounded until formulas could not be efficiently verified, and steady-state formulas had not been considered due to the burn-in time problem to detect the steady-state. Perfect simulation is an extension of Markov Chain Monte Carlo (MCMC) methods that allows us to obtain exact steady-state samples of the underlying Markov chain, and thus it avoids the burn-in time problem to detect the steady-state. Therefore we suggest to verify time unbounded until and steady-state dependability properties for large Markov chains through statistical model checking by combining perfect simulation and statistical hypothesis testing.
This work is supported by a french research project, ANR-06-SETI-002.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
El Rabih, D., Pekergin, N.: Statistical model checking for steady state dependability verification. In: WIP paper in proceedings of 2nd International conference on Dependability. DEPEND 2009, IEEE CS proceedings, Athens, Greece (2009)
Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Model Checking Continuous Time Markov Chains. ACM Trans. on Comp. Logic 1(1), 162–170 (2000)
Baier, C., Haverkort, B., Hermanns, H., Katoen, J.P.: Model-Checking Algorithms for Continuous-Time Markov Chains. IEEE Trans. Software Eng. 29(6), 524–541 (2003)
Glasserman, P., Yao, D.: Monotone Structure in Discrete-Event Systems. John Wiley & Sons, Chichester (1994)
Hansson, H., Jonsson, B.: A logic for reasonning about time and reliability. Formal Aspects Compt. 6, 512–535 (1994)
Hinton, A., Kwiatkowska, M., Norman, G., Parker, D.: PRISM: A tool for automatic verification of probabilistic systems. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 441–444. Springer, Heidelberg (2006)
Keshav, S.: An Engineering approach to computer networking. Addison Wesley, Reading (1997)
Propp, J.G., Wilson, D.B.: Exact sampling with coupled Markov chains and applications to statistical mechanics. Random Structures and Algorithms 9(1 and 2), 223–252 (1996)
Sen, K., Viswanathan, M., Agha, G.: On Statistical Model Checking of Stochastic Systems. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 266–280. Springer, Heidelberg (2005)
Vincent, J.M., Marchand, C.: On the exact simulation of functionals of stationary Markov chains. Linear Algebra and its Applications 386, 285–310 (2004)
Vincent, J.-M., Vienne, J.: Perfect simulation of index based routing networks. Performance Evaluation Review 34(2), 24–25 (2006)
Vincent, J.-M., Vienne, J.: PSI2 a Software Tool for the Perfect Simulation of Finite Queuing Networks. In: QEST, Edinburgh (September 2007)
Fernandes, P., Vincent, J.-M., Webber, T.: Perfect Simulation of Stochastic Automata Networks. In: Al-Begain, K., Heindl, A., Telek, M. (eds.) ASMTA 2008. LNCS, vol. 5055, pp. 249–263. Springer, Heidelberg (2008)
Busic, A., Gaujal, B., Vincent, J.-M.: Perfect simulation and non-monotone (Markovian) systems. In: Proceedings of 3rd International Conference on Performance Evaluation Methodologies and Tools, VALUETOOLS 2008, Athens, Greece (October 2008)
Younes, H.L.S., Simmons, R.G.: Probabilistic verification of discrete event systems using acceptance sampling. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 223–235. Springer, Heidelberg (2002)
Younes, H.L., Kwiatkowska, M., Norman, G., Parker, D.: Numerical vs. statistical probabilistic model checking. Software Tools for Technology Transfer 8(3), 216–228 (2006)
Younes, H.L.S.: Error Control for Probabilistic Model Checking. In: Emerson, E.A., Namjoshi, K.S. (eds.) VMCAI 2006. LNCS, vol. 3855, pp. 142–156. Springer, Heidelberg (2006)
Younes, H.L.S., Simmons, R.G.: Statistical probabilistic model checking with a focus on time-bounded properties. Information and Computation 204(9), 1368–1409 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
El Rabih, D., Pekergin, N. (2009). Statistical Model Checking Using Perfect Simulation. In: Liu, Z., Ravn, A.P. (eds) Automated Technology for Verification and Analysis. ATVA 2009. Lecture Notes in Computer Science, vol 5799. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04761-9_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-04761-9_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04760-2
Online ISBN: 978-3-642-04761-9
eBook Packages: Computer ScienceComputer Science (R0)