Advertisement

Programming and Computer Software

, Volume 40, Issue 5, pp 229–249 | Cite as

Performance analysis of concurrent systems in algebra dtsiPBC

  • I. V. Tarasyuk
  • H. Macià
  • V. Valero
Article

Abstract

Petri box calculus PBC is a well-known algebra of concurrent processes with a Petri net semantics. In the paper, an extension of PBC with discrete stochastic time and immediate multiactions, which is referred to as discrete time stochastic and immediate PBC (dtsiPBC), is considered. Performance analysis methods for concurrent and distributed systems with random time delays are investigated in the framework of the new stochastic process algebra. It is demonstrated that the performance evaluation is possible not only via the underlying semi-Markov chains of the dtsiPBC expressions but also with the use of the underlying discrete time Markov chains, and the latter analysis technique is more optimal.

Keywords

stochastic process algebras stochastic Petri nets Petri box calculus discrete time immediate multiactions semantics transition systems dtsi-boxes performance analysis Markov chains 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hermanns, H. and Rettelbach, M., Syntax, semantics, equivalences and axioms for MTIPP, Proc. of the 2nd Workshop on Process Algebras and Performance Modelling (PAPM’94), Regensberg, 1994, pp. 71–88.Google Scholar
  2. 2.
    Hillston, J., A Compositional Approach to Performance Modelling, Cambridge (UK): Cambridge Univ. Press, UK, 1996.CrossRefGoogle Scholar
  3. 3.
    Bernardo, M. and Gorrieri, R., A tutorial on EMPA: a theory of concurrent processes with nondeterminism, priorities, probabilities and time, Theor. Comput. Sci., 1998, vol. 202, pp. 1–54.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Best, E., Devillers, R., and Hall, J.G., The box calculus: a new causal algebra with multi-label communication, Lect. Notes Comp. Sci., 1992, vol. 609. pp. 21–69.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Best, E. and Koutny, M., A refined view of the box algebra, Lect. Notes Comp. Sci., 1995, vol. 935, pp. 1–20.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Best, E., Devillers, R., and Koutny, M., Petri Net Algebra, EATCS Monographs on Theoretical Comp. Sci., Springer, 2001.CrossRefGoogle Scholar
  7. 7.
    Milner, R.A.J., Communication and Concurrency, Upper Saddle River, NJ: Prentice-Hall, 1989.zbMATHGoogle Scholar
  8. 8.
    Macià, H., Valero, V., and de Frutos, D., sPBC: a Markovian extension of finite Petri box calculus, Proc. of the 9th IEEE Int. Workshop on Petri Nets and Performance Models (PNPM’01), Aachen: IEEE Comput. Society, 2001. pp. 207–216.CrossRefGoogle Scholar
  9. 9.
    Macià, H., Valero, V., Cazorla, D., and Cuartero, F., Introducing the iteration in sPBC, Lect. Notes Comp. Sci., 2004, vol. 3235, pp. 292–308.CrossRefGoogle Scholar
  10. 10.
    Macià, H., Valero, V., Cuartero, F., and Ruiz, M.C., sPBC: a Markovian extension of Petri box calculus with immediate multiactions, Fundamenta Informaticae, 2008, vol. 87, nos. 3–4, pp. 367–406.MathSciNetzbMATHGoogle Scholar
  11. 11.
    Tarasyuk, I.V., Discrete time stochastic Petri box calculus. Oldenburg, Germany, 2005 (Berichte aus dem Department für Informatik. Carl von Ossietzky Univ. Oldenburg. no. 3/05).Google Scholar
  12. 12.
    Tarasyuk, I.V., Stochastic Petri box calculus with discrete time, Fundamenta Informaticae, 2007, vol. 76, nos. 1–2, pp. 189–218.MathSciNetzbMATHGoogle Scholar
  13. 13.
    Tarasyuk, I.V., Iteration in discrete time stochastic Petri box calculus, Bulletin of the Novosibirsk Computing Center, Series Comp. Sci., IIS Special Issue, 2006, vol. 24, pp. 129–148.zbMATHGoogle Scholar
  14. 14.
    Tarasyuk, I.V., Macià, H., and Valero, V., Discrete time stochastic Petri box calculus with immediate multi-actions, Technical Report, Department of Computer Systems, High School of Information Engineering, Univ. of Castilla-La Mancha. no. DIAB-10-03-1.Google Scholar
  15. 15.
    Tarasyuk, I.V., Macià, H., Valero, V., Discrete time stochastic Petri box calculus with immediate multiactions dtsiPBC, in Electronic Notes in Theoretical Computer Science, Elsevier, 2013, vol. 296, pp. 229–252.CrossRefGoogle Scholar
  16. 16.
    Molloy, M.K., Discrete time stochastic Petri nets, IEEE Trans. Software Eng., 1985, vol. 11, no. 4. pp. 417–423.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Ross, S.M., Stochastic Processes, New York: Wiley, 1996.zbMATHGoogle Scholar
  18. 18.
    Bernardo, M. and Bravetti, M., Reward based congruences: can we aggregate more?, Lect. Notes Comp. Sci., 2001, vol. 2165, pp. 136–151.MathSciNetCrossRefGoogle Scholar
  19. 19.
    Balbo, G., Introduction to generalized stochastic Petri nets, Lect. Notes Comp. Sci., 2007, vol. 4486. pp. 83–131.CrossRefGoogle Scholar
  20. 20.
    van Glabbeek, R.J., Smolka, S.A., and Steffen, B., Reactive, generative, and stratified models of probabilistic processes, Information Computation, 1995, vol. 121, no. 1, pp. 59–80.CrossRefzbMATHGoogle Scholar
  21. 21.
    Zimmermann, A., Freiheit, J., and Hommel, G., Discrete time stochastic Petri nets for modeling and evaluation of real-time systems, Proc. of the 9th Int. Workshop on Parallel and Distributed Real Time Systems (WPDRTS’01), San Francisco, 2001, pp. 282–286.Google Scholar
  22. 22.
    Zijal, R., Ciardo, G., and Hommel, G., Discrete deterministic and stochastic Petri nets, Proc. of the 9th ITG/GI Professional Meeting “Messung, Modellierung und Bewertung von Rechen- und Kommunikationssystemen”(MMB’97), VDE-Verlag, Berlin, 1997, pp. 103–117.Google Scholar
  23. 23.
    Buchholz P. and Tarasyuk, I.V., Net and algebraic approaches to probabilistic modeling, Joint Novosibirsk Computing Center and Institute of Informatics Systems Bulletin, Series Comp. Sci., Novosibirsk, 2001, vol. 15, pp. 31–64.zbMATHGoogle Scholar
  24. 24.
    Haverkort, B.R., Markovian models for performance and dependability evaluation, Lect. Notes Comp. Sci., 2001, vol. 2090, pp. 38–83.CrossRefGoogle Scholar
  25. 25.
    van Glabbeek, R.J., The linear time — branching time spectrum II: the semantics of sequential systems with silent moves (extended abstract), Lect. Notes Comp. Sci., 1993, vol. 715, pp. 66–81.CrossRefGoogle Scholar
  26. 26.
    Mudge, T.N. and Al-Sadoun, H.B., A semi-Markov model for the performance of multiple-bus systems, IEEE Trans. Computers, 1985, vol. C-34, no. 10, pp. 934–942.CrossRefGoogle Scholar
  27. 27.
    Katoen, J.-P., Quantitative and qualitative extensions of event structures, Ph. D. Thesis, Enschede, The Netherlands, 1996, (CTIT Ph. D.-thesis series. Centre for Telematics and Information Technology, University of Twente, no. 96-09).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.A. P. Ershov Institute of Informatics Systems, Siberian DivisionRussian Academy of SciencesNovosibirskRussia
  2. 2.High School of Information EngineeringUniversity of Castilla-La ManchaAlbaceteSpain

Personalised recommendations