Abstract
To formalize, measure, and predict availability properties, stochastic concepts are required. Reconfiguration and communication in mobile and distributed environments, where due to the high volatility of network connections reasoning on such properties is most important, is best described by graph transformation systems.
Consequently, in this paper we introduce stochastic graph transformation systems, following the outline of stochastic Petri nets. Besides the basic definition and a motivating example, we discuss the analysis of properties expressed in continuous stochastic logic including an experimental tool chain.
Research funded in part by Deutsche Forschungsgemeinschaft, grant DO 263/8-1 [Algebraische Eigenschaften stochastischer Relationen] and by European Community’s Human Potential Programme under contract HPRN-CT-2002-00275, [SegraVis].
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References
The attributed graph grammar system, http://tfs.cs.tu-berlin.de/agg/
Anderson, W.G.: Continuous-Time Markov Chains. Springer, Heidelberg (1991)
Andrade, L., Baldan, P., Baumeister, H.: AGILE: Software architecture for mobility. In: Wirsing, M., Pattinson, D., Hennicker, R. (eds.) WADT 2003. LNCS, vol. 2755, pp. 1–33. Springer, Heidelberg (2003)
Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P.: Model checking continuous-time markov chains by transient analysis. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 358–372. Springer, Heidelberg (2000)
Bause, F., Kritzinger, P.S.: Stochastic Petri Nets, 2nd edn. Vieweg Verlag (2002)
Brinksma, E., Hermanns, H.: Process algebra and markov chains. In: Brinksma, E., Hermanns, H., Katoen, J.-P. (eds.) EEF School 2000 and FMPA 2000. LNCS, vol. 2090, pp. 183–231. Springer, Heidelberg (2001)
Corradini, A., Ehrig, H., Löwe, M., Montanari, U., Rossi, F.: Note on standard representation of graphs and graph derivations. Technical Report 92-25, FB13 (1992)
Corradini, A., Montanari, U., Rossi, F.: Graph processes. Fundamenta Informaticae 26(3,4), 241–266 (1996)
Corradini, A., Ribeiro, L., Dotti, F.L.: A graph transformation view on the specification of applications using mobile code. In: Taentzer, G., Baresi, L., Pezze, M., Zaroliagis, C. (eds.) Proceedings 2nd Int. Workshop on Graph Transformation and Visual Modeling Technique (GT-VMT 2001). Elect. Notes in Th. Comput. Sci., vol. 50.3, Elsevier Science, Amsterdam (2001)
D’Argenio, P.R.: Algebras and Automata for Timed and Stochastic Systems. IPA Dissertation Series 1999-10, CTIT PhD-Thesis Series 99-25, University of Twente (November 1999)
Diederich, J., Wolf, L., Zitterbart, M.: A mobile differentiated services QoS model. In: Proceedings of the 3rd Workshop on Applications and Services in Wireless Networks (2003)
Ehrig, H., Pfender, M., Schneider, H.J.: Graph grammars: an algebraic approach. In: 14th Annual IEEE Symposium on Switching and Automata Theory, pp. 167–180. IEEE, Los Alamitos (1973)
Gadducci, F., Montanari, U.: A concurrent graph semantics for mobile ambients. In: Brooks, S., Mislove, M. (eds.) Proc. Mathematical Foundations of Programming Semantics, Aarhus. Elect. Notes in Th. Comput. Sci., vol. 45, Elsevier Science, Amsterdam (2001)
Guo, P., Heckel, R.: Conceptual modelling of styles for mobile systems: A layered approach based on graph transformation. In: Proc. IFIP TC8 Working Conference on Mobile Information Systems, Oslo, Norway (2004) (to appear)
Habel, A., Heckel, R., Taentzer, G.: Graph grammars with negative application conditions. Fundamenta Informaticae 26(3,4), 287–313 (1996)
Hirsch, D., Montanari, U.: Consistent transformations for software architecture styles of distributed systems. In: Stefanescu, G. (ed.) Workshop on Distributed Systems. ENTCS, vol. 28 (1999)
Kwiatkowska, M., Norman, G., Parker, D.: PRISM: Probabilistic symbolic model checker. In: Field, T., Harrison, P.G., Bradley, J., Harder, U. (eds.) TOOLS 2002. LNCS, vol. 2324, pp. 200–204. Springer, Heidelberg (2002)
Conte, G., Donatelli, S., Ajmone-Marsan, M., Balbo, G., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets. Wiley Series in Parallel Computing. John Wiley and Sons, Chichester (1995)
Norris, J.R.: Markov Chains. Cambridge University Press, Cambridge (1997)
Rensink, A.: The GROOVE simulator: A tool for state space generation. In: Pfaltz, J.L., Nagl, M., Böhlen, B. (eds.) AGTIVE 2003. LNCS, vol. 3062, pp. 479–485. Springer, Heidelberg (2004)
Schmidt, Á., Varró, D.: CheckVML: A tool for model checking visual modeling languages. In: Stevens, P., Whittle, J., Booch, G. (eds.) UML 2003. LNCS, vol. 2863, pp. 92–95. Springer, Heidelberg (2003)
Schürr, A.: PROGRES: a VHL-language based on graph grammars. In: Ehrig, H., Kreowski, H.-J., Rozenberg, G. (eds.) Graph Grammars 1990. LNCS, vol. 532, pp. 641–659. Springer, Heidelberg (1991)
Stewart, W.: Introduction to the Numerical Solution of Markov Chains. Princeton University Press, Princeton (1994)
Taentzer, G.: Hierarchically distributed graph transformation. In: LNCSWil, pp. 304–320 (1996)
Varró, D.: Automated formal verification of visual modeling languages by model checking. Journal of Software and Systems Modelling (2003); Accepted to the Special Issue on Graph Transformation and Visual Modelling Techniques
Yu, O.T.W., Leung, V.C.M.: Adaptive resource allocation for prioritized call admission over an ATM-based wireless PCN. IEEE Journal on Selected Areas in Communications 15, 1208–1224 (1997)
Zonoozi, M., Dassanayake, P.: User mobility modeling and characterization of mobility patterns. IEEE Journal on Selected Areas in Communications 15, 1239–1252 (1997)
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Heckel, R., Lajios, G., Menge, S. (2004). Stochastic Graph Transformation Systems. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds) Graph Transformations. ICGT 2004. Lecture Notes in Computer Science, vol 3256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30203-2_16
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DOI: https://doi.org/10.1007/978-3-540-30203-2_16
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