Non-functional Analysis of Distributed Systems in Unreliable Environments Using Stochastic Object Based Graph Grammars

  • Odorico Machado Mendizabal
  • Fernando Luis Dotti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4178)


In unreliable environments, e.g. wireless networks, often there are messages lost, connection and process crashes, among other undesirable fault occurrences. Mechanisms to enhance the dependability of these systems can be employed, but with a performance cost. Analytical approaches are useful to predict performance and dependability values, guiding the system developer to adjust bounds for specific requirements in complex systems. In this paper we use non-functional analysis of Stochastic Object-Based Graph Grammars (SOBGG) models considering classical fault behaviors in distributed systems, allowing the developer to predict performance and dependability values for high performance and resilient systems. The specific contributions of this paper are: (i) revisit the notion of fault representation to allow non-functional analysis, more specifically, steady-state analysis; (ii) discuss the specification of rates associated to SOBGG rules, describing an adequate approach to distributed systems; (iii) show the suitability of the proposed techniques through their application to a case study.


Object-based graph grammars distributed systems fault-tolerance non-functional analysis dependability 


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  1. 1.
    Brenner, L., Fernandes, P., Sales, A.: The need for and the advantages of generalized tensor algebra for kronecker structured representations. International Journal of Simulation: Systems, Science & Technology 6(3-4), 52–60 (2005)Google Scholar
  2. 2.
    Chung, M.-Y., Ciardo, G., Donatelli, S., He, N., Plateau, B., Stewart, W.J., Sulaiman, E., Yu, J.: A comparison of structural formalisms for modeling large markov models. In: IPDPS. IEEE Computer Society, Los Alamitos (2004)Google Scholar
  3. 3.
    Cristian, F.: A rigorous approach to fault-tolerant programming. IEEE Trans. on Soft. Eng. 11(1), 23–31 (1985)CrossRefGoogle Scholar
  4. 4.
    Dotti, F.L., Mendizabal, O.M., Santos, O.M.: Verifying fault-tolerant distributed systems using object-based graph grammars. In: Maziero, C.A., Gabriel Silva, J., Andrade, A.M.S., de Assis Silva, F.M. (eds.) LADC 2005. LNCS, vol. 3747, pp. 80–100. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  5. 5.
    Dotti, F.L., Ribeiro, L.: Specification of mobile code systems using graph grammars. In: 4th International Conference on Formal Methods for Open Object-Based Distributed Systems. IFIP Conference Proceedings, vol. 177, pp. 45–63. Kluwer Academic Publishers, Dordrecht (2000)Google Scholar
  6. 6.
    Dotti, F.L., Ribeiro, L., Santos, O.M.: Specification and analysis of fault behaviours using graph grammars. In: Pfaltz, J.L., Nagl, M., Böhlen, B. (eds.) AGTIVE 2003. LNCS, vol. 3062, pp. 120–133. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Dotti, F.L., Santos, O.M., Rödel, E.T.: On use of formal specification to anayse fault behaviors of distributed systems. In: de Lemos, R., Weber, T.S., Camargo Jr., J.B. (eds.) LADC 2003. LNCS, vol. 2847, pp. 341–360. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    Ehrig, H.: Introduction to the algebraic theory of graph grammars. In: Ng, E.W., Ehrig, H., Rozenberg, G. (eds.) Graph Grammars 1978. LNCS, vol. 73, pp. 1–69. Springer, Heidelberg (1979)CrossRefGoogle Scholar
  9. 9.
    Falai, L., Bondavalli, A.: Experimental evaluation of the qos of failure detectors on wide area network. In: DSN 2005: Proceedings of the 2005 International Conference on Dependable Systems and Networks (DSN 2005), Washington, DC, pp. 624–633. IEEE Computer Society, Los Alamitos (2005)CrossRefGoogle Scholar
  10. 10.
    Fernandes, P., Plateau, B., Stewart, W.J.: Numerical evaluation of stochastic automata networks. In: Proceedings of the Third International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems, pp. 179–183 (1995)Google Scholar
  11. 11.
    Gärtner, F.C.: Fundamentals of fault-tolerant distributed computing in asynchronous environments. ACM Computing Surveys 31(1), 1–26 (1999)CrossRefGoogle Scholar
  12. 12.
    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)CrossRefGoogle Scholar
  13. 13.
    Hermanns, Herzog, Katoen: Process algebra for performance evaluation. TCS: Theoretical Computer Science 274 (2002)Google Scholar
  14. 14.
    Ajmone Marsan, M., Balbo, G., Conte, G., et al.: Modelling with Generalized Stochastic Petri Nets. Wiley series in parallel computing. Wiley, New York (1995)zbMATHGoogle Scholar
  15. 15.
    Mendizabal, O.M., Dotti, F.L., Ribeiro, L.: Stochastic Object-Based Graph Grammars. In: Proceedings of the Brazilian Symposium on Formal Methods (SBMF 2005), pp. 128–143 (2005),
  16. 16.
    Plateau, B.: On the stochastic structure of parallelism and synchronization models for distributed algorithms. In: SIGMETRICS, pp. 147–154 (1985)Google Scholar
  17. 17.
    Plateau, B., Atif, K.: Peps: a package for solving complex Markov models of parallel systems. In: Proceedings of the 4th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation (1988)Google Scholar
  18. 18.
    Santos, O.M., Dotti, F.L., Ribeiro, L.: Verifying object-based graph grammars. Eletronic Notes in Theoretical Computer Science 109, 125–136 (2004)CrossRefGoogle Scholar
  19. 19.
    Sergent, N., Défago, X., Schiper, A.: Impact of a failure detection mechanism on the performance of consensus. In: Proc. 8th IEEE Pacific Rim Symp. on Dependable Computing (PRDC 2001), Seoul, Korea (December 2001)Google Scholar
  20. 20.
    Stewart, W.J.: Introduction to the numerical solution of Markov chains. Princeton University Press, Princeton (1995)Google Scholar
  21. 21.
    Tanenbaum, A.S.: Computer Networks, 3rd edn. Prentice-Hall, Englewood Cliffs (1996)Google Scholar
  22. 22.
    Urbán, P., Défago, X., Schiper, A.: Contention-aware metrics for distributed algorithms: Comparison of atomic broadcast algorithms. In: Proc. 9th IEEE Int’l Conf. on Computer Communications and Networks (IC3N), pp. 582–589 (2000)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Odorico Machado Mendizabal
    • 1
  • Fernando Luis Dotti
    • 2
  1. 1.Faculdade de CiênciasUniversidade de LisboaLisboaPortugal
  2. 2.Faculdade de InformáticaPontifícia Universidade Católica do Rio Grande do SulPorto AlegreBrazil

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