Abstract
Distributed systems with mobile components are naturally modelled by graph transformations. To formalise and predict properties such as performance or reliability of such systems, stochastic methods are required. Stochastic graph transformations allow the integrated modelling of these two concerns by associating with each rule and match a probability distribution governing the delay of its application. Depending on the nature of these distributions, different techniques for analysis are available, ranging from stochastic model checking for exponential distributions to simulation for systems with general distributions.
In this paper we explore further the second notion, adding a model of global time to avoid the overhead of frequent local clock updates. We also transfer the notion of stochastic graph transformation system from an algebraic to a general background, allowing an arbitrary graph transformation approach to be used for the underlying system. We present a correspondingly extended semantic model, simulation algorithm and tool. The concepts are justified and illustrated by an accident management scenario which requires a model of physical mobility and sophisticated transformation concepts.
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References
D’Argenio, P.R., Katoen, J.P.: Formal languages of labelled graphs. Computing 16, 113–137 (1976)
Nagl, M. (ed.): Building Tightly Integrated Software Development Environments: The IPSEN Approach. LNCS, vol. 1170. Springer, Heidelberg (1996)
Schürr, A.: Introduction to PROGRES, an attribute graph grammar based specification language. In: Nagl, M. (ed.) WG 1989. LNCS, vol. 411, pp. 151–165. Springer, Heidelberg (1990)
Heckel, R., Lajios, G., Menge, S.: Stochastic graph transformation systems. In: Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds.) ICGT 2004. LNCS, vol. 3256, pp. 210–225. Springer, Heidelberg (2004)
Heckel, R.: Stochastic analysis of graph transformation systems: A case study in P2P networks. In: Van Hung, D., Wirsing, M. (eds.) ICTAC 2005. LNCS, vol. 3722, pp. 53–69. Springer, Heidelberg (2005)
Kosiuczenko, P., Lajios, G.: Simulation of generalised semi-Markov processes based on graph transformation systems. Electr. Notes Theor. Comput. Sci. 175(4), 73–86 (2007)
Khan, A., Torrini, P., Heckel, R.: Model-based simulation of VoIP network reconfigurations using graph transformation systems. ECEASST 16, 1–20 (2008)
Bergmann, G., Ökrös, A., Ráth, I., Varró, D., Varró, G.: Incremental pattern matching in the VIATRA model transformation system. In: GRaMoT 2008: Proceedings of the Third International Workshop on Graph and Model Transformations, pp. 25–32. ACM, New York (2008)
Heckel, R., Lajios, G., Menge, S.: Stochastic graph transformation systems. Fundamenta Informaticae 74 (2006)
Cassandras, C.G., Lafortune, S.: Introduction to discrete event systems. Kluwer, Dordrecht (2008)
Marsan, M.A., Bobbio, A., Donatelli, S.: Petri nets in performance analysis: An introduction. In: Reisig, W., Rozenberg, G. (eds.) APN 1998. LNCS, vol. 1491, pp. 211–256. Springer, Heidelberg (1998)
Danos, V., Feret, J., Fontana, W., Krivine, J.: Scalable simulation of cellular signaling networks. In: Shao, Z. (ed.) APLAS 2007. LNCS, vol. 4807, pp. 139–157. Springer, Heidelberg (2007)
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. Journal of Physical Chemistry, 2340–2361 (1977)
Bradley, J.T., Dingle, N., Harrison, P.G., Knottenbelt, W.J.: Performance queries on semi-Markov stochastic Petri nets with an extended continuous stochastic logic. In: 10th International Workshop on Petri Nets and Performance Models, pp. 1063–1067 (2003)
Danos, V., Feret, J., Fontana, W., Harmer, R., Krivine, J.: Rule-based modelling, symmetries, refinements. In: Fisher, J. (ed.) FMSB 2008. LNCS (LNBI), vol. 5054, pp. 103–122. Springer, Heidelberg (2008)
Kumar, N., Koushik, S., Meseguer, J., Gul, A.: A rewriting based model for probabilistic distributed object systems. In: Najm, E., Nestmann, U., Stevens, P. (eds.) FMOODS 2003. LNCS, vol. 2884, pp. 32–46. Springer, Heidelberg (2003)
Gilmore, S., Hillston, J.: The PEPA workbench: a tool to support a process algebra-based approach to performance modelling. In: Haring, G., Kotsis, G. (eds.) TOOLS 1994. LNCS, vol. 794, pp. 353–368. Springer, Heidelberg (1994)
Priami, C.: Stochastic pi-calculus. The Computer Journal 38(7), 578–589 (1998)
Bradley, J.T.: Semi-Markov PEPA: modelling with generally distributed actions. International Simulation Journal 6(3-4), 43–51 (2005)
Priami, C.: Stochastic pi-calculus with general distributions. In: Proc. of the 4th Workshop on Process Algebras and Performance Modelling (PAPM 1996), CLUT, pp. 41–57 (1996)
Kreowski, H.J., Kuske, S.: On the interleaving semantics of transformation units - a step into GRACE. In: Cuny, J., Engels, G., Ehrig, H., Rozenberg, G. (eds.) Graph Grammars 1994. LNCS, vol. 1073, pp. 89–106. Springer, Heidelberg (1996)
Ehrig, H., Pfender, M., Schneider, H.: Graph grammars: an algebraic approach. In: 14th Annual IEEE Symposium on Switching and Automata Theory, pp. 167–180. IEEE, Los Alamitos (1973)
Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation (Monographs in Theoretical Computer Science. An EATCS Series). Springer, Heidelberg (2006)
D’Argenio, P.R., Katoen, J.P.: A theory of stochastic systems part I: Stochastic automata. Inf. Comput. 203(1), 1–38 (2005)
Nelson, R.: Probability, Stochastic processes, and queueing theory. Springer, Heidelberg (1995)
Varró, G., Varró, D.: Graph transformation with incremental updates. Electr. Notes Theor. Comput. Sci. 109, 71–83 (2004)
L’Ecuyer, P.L., Meliani, L., Vaucher, J.: SSJ: a framework for stochastic simulation in Java. In: Proceedings of the 2002 Winter Simulation Conference, pp. 234–242 (2002)
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Heckel, R., Torrini, P. (2010). Stochastic Modelling and Simulation of Mobile Systems. In: Engels, G., Lewerentz, C., Schäfer, W., Schürr, A., Westfechtel, B. (eds) Graph Transformations and Model-Driven Engineering. Lecture Notes in Computer Science, vol 5765. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17322-6_5
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DOI: https://doi.org/10.1007/978-3-642-17322-6_5
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