Stochastic Simulation of Graph Transformation Systems

  • Paolo Torrini
  • Reiko Heckel
  • István Ráth
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6013)

Abstract

Stochastic graph transformation systems (SGTS) [1] support integrated modelling of architectural reconfiguration and non-functional aspects such as performance and reliability. In its simplest form a SGTS is a graph transformation system (GTS) where each rule name is associated with a rate of an exponential distribution governing the delay of its application. However, this approach has its limitations. Model checking with explicit states does not scale well to models with large state space. Since performance and reliability properties often depend on the behaviour of large populations of entities (network nodes, processes, services, etc.), this limitation is significant. Also, exponential distributions do not always provide the best abstraction. For example, the time it takes to make a phone call or transmit a message is more likely to follow a normal distribution.

References

  1. 1.
    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)CrossRefGoogle Scholar
  2. 2.
    Khan, A., Torrini, P., Heckel, R.: Model-based simulation of VoIP network reconfigurations using graph transformation systems. In: Corradini, A., Tuosto, E. (eds.) ICGT 2008. El. Com. EASST, vol. 16, pp. 1–20 (2008)Google Scholar
  3. 3.
    Bergmann, G., Ökrös, A., Ráth, I., Varró, D., Varró, G.: Incremental pattern matching in the Viatra model transformation system. In: GRaMoT 2008, pp. 25–32. ACM, New York (2008)CrossRefGoogle Scholar
  4. 4.
    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)CrossRefGoogle Scholar
  5. 5.
    D’Argenio, P.R., Katoen, J.P.: A theory of stochastic systems part I: Stochastic automata. Inf. Comput. 203(1), 1–38 (2005)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Paolo Torrini
    • 1
  • Reiko Heckel
    • 1
  • István Ráth
    • 2
  1. 1.Department of Computer ScienceUniversity of Leicester 
  2. 2.Department of Measurement and Information SystemsBudapest University of Technology and Economics 

Personalised recommendations