Abstract
In this work, we propose two high-level formalisms, Markov Decision Petri Nets (MDPNs) and Markov Decision Well-formed Nets (MDWNs), useful for the modeling and analysis of distributed systems with probabilistic and non deterministic features: these formalisms allow a high level representation of Markov Decision Processes. The main advantages of both formalisms are: a macroscopic point of view of the alternation between the probabilistic and the non deterministic behaviour of the system and a syntactical way to define the switch between the two behaviours. Furthermore, MDWNs enable the modeller to specify in a concise way similar components. We have also adapted the technique of the symbolic reachability graph, originally designed for Well-formed Nets, producing a reduced Markov decision process w.r.t. the original one, on which the analysis may be performed more efficiently. Our new formalisms and analysis methods are already implemented and partially integrated in the GreatSPN tool, so we also describe some experimental results.
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Alur, R., Henzinger, T.: Reactive modules. Formal Methods in System Design 15(1), 7–48 (1999)
Beccuti, M., Franceschinis, G., Haddad, S.: Markov Decision Petri Net and Markov Decision Well-formed Net formalisms. Technical Report TR-INF-2007-02-01, Dipartimento di Informatica, Università del Piemonte Orientale (2007) http://www.di.unipmn.it/Tecnical-R
Bianco, A., de Alfaro, L.: Model checking of probabilistic and nondeterministic systems. In: Thiagarajan, P.S. (ed.) Foundations of Software Technology and Theoretical Computer Science. LNCS, vol. 1026, pp. 499–513. Springer, Heidelberg (1995)
Chiola, G., Dutheillet, C., Franceschinis, G., Haddad, S.: Stochastic well-formed coloured nets for symmetric modelling applications. IEEE Transactions on Computers 42(11), 1343–1360 (November 1993)
Chiola, G., Dutheillet, C., Franceschinis, G., Haddad, S.: A symbolic reachability graph for coloured Petri nets. Theoretical Computer Science 176(1–2), 39–65 (1997)
Chiola, G., Franceschinis, G., Gaeta, R., Ribaudo, M.: GreatSPN 1.7: Graphical editor and analyzer for timed and stochastic petri nets. Performance Evaluation, special issue on Performance Modeling Tools 24(1-2), 47–68 (November 1995)
de Alfaro, L.: Temporal logics for the specification of performance and reliability. In: Reischuk, R., Morvan, M. (eds.) STACS 97. LNCS, vol. 1200, pp. 165–176. Springer, Heidelberg (1997)
de Alfaro, L.: Stochastic transition systems. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 423–438. Springer, Heidelberg (1998)
Demaille, K., Peyronnet, S., Sigoure, B.: Modeling of sensor networks using XRM. In: 2nd International Symposium on Leveraging Applications of Formal Methods, Verification and Validation, Paphos, Cyprus (2006)
Garavel, H., Hermanns, H.: On combining functional verification and performance evaluation using CADP. In: FME 2002. LNCS, vol. 2391, pp. 10–429. Springer, Heidelberg (2000)
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 and ETAPS 2006. LNCS, vol. 3920, pp. 441–444. Springer, Heidelberg (2006)
Ajmone Marsan, M., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets. Wiley Series in Parallel Computing. John Wiley and Sons, New york (1995) http://www.di.unito.it/~greatspn
Puterman, M.L.: Markov Decision Processes. In: Discrete Stochastic Dynamic Programming, Wiley, Chichester (2005)
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Beccuti, M., Franceschinis, G., Haddad, S. (2007). Markov Decision Petri Net and Markov Decision Well-Formed Net Formalisms. In: Kleijn, J., Yakovlev, A. (eds) Petri Nets and Other Models of Concurrency – ICATPN 2007. ICATPN 2007. Lecture Notes in Computer Science, vol 4546. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73094-1_6
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DOI: https://doi.org/10.1007/978-3-540-73094-1_6
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