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Exploiting Modal Logic to Express Performance Measures

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Book cover Computer Performance Evaluation.Modelling Techniques and Tools (TOOLS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1786))

Abstract

Stochastic process algebras such as PEPA provide ample support for the component-based construction of models. Tools compute the numerical solution of these models; however, the stochastic process algebra methodology has lacked support for the specification and calculation of complex performance measures. In this paper we present a stochastic modal logic which can aid the construction of a reward structure over the model. We discuss its relationship to the underlying theory of PEPA. We also present a performance specification language which supports high level reasoning about PEPA models, and allows queries about their equilibrium behaviour. The meaning of the specification language has its foundations in the stochastic modal logic. We describe the implementation of the logic within the PEPA Workbench and a case study is presented to illustrate the approach.

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References

  1. P. G. Harrison and N. M. Patel. Performance Modelling of Communication Networks and Computer Architectures. International Computer Science Series. Addison-Wesley, 1993.

    Google Scholar 

  2. M. Ajmone Marsan, G. Balbo, G. Conte, S. Donatelli, and G. Franceschinis. Modelling with Generalized Stochastic Petri Nets. John Wiley, 1995.

    Google Scholar 

  3. J.F. Meyer, A. Movaghar, and W.H. Sanders. Stochastic activity networks: Structure, behavior and application. In Proc of Int. Workshop on Timed Petri Nets, pages 106–115, Torino, Italy, 1985. IEEE Computer Society Press.

    Google Scholar 

  4. J. Hillston. A Compositional Approach to Performance Modelling. Cambridge University Press, 1996.

    Google Scholar 

  5. N. Götz, U. Herzog, and M. Rettelbach. Multiprocessor and Distributed System Design: The Integration of Functional Specification and Performance Analysis using Stochastic Process Algebras. In Performance’93, 1993.

    Google Scholar 

  6. M. Bernardo and R. Gorrieri. A tutorial on EMPA: A theory of concurrent processes with nondeterminism, priorities, probabilities and time. Theoretical Computer Science, 201:1–54, July 1998.

    Article  MathSciNet  Google Scholar 

  7. R. A. Howard. Dynamic Probabilistic Systems, volume II: Semi-Markov and Decision Processes, chapter 13, pages 851–915. John Wiley & Sons, New York, 1971.

    Google Scholar 

  8. J. Bryans, H. Bowman, and J. Derrick. Analysis of a Multimedia Stream using Stochastic Process Algebra. In C. Priami, editor, Proc. of 6th Int. Workshop on Process Algebras and Performance Modelling, pages 51–69, Nice, France, September 1998.

    Google Scholar 

  9. H. Hansson and B. Jonsson. A logic for reasoning about time and reliability. Formal Aspects of Computing, 6(5):512–535, 1994.

    Article  MATH  Google Scholar 

  10. M. Huth and M. Kwiatkowska. Quantitative analysis and model checking. In Proceedings, Twelth Annual IEEE Symposium on Logic in Computer Science, pages 111–122, Warsaw, Poland, 29 June–2 July 1997. IEEE Computer Society Press.

    Google Scholar 

  11. V. Hartonas-Garmhausen. Probabilistic Symbolic Model Checking with Engineering Models and Applications. PhD thesis, Carnegie Mellon University, 1998.

    Google Scholar 

  12. L. de Alfaro. How to specify and verify the long-run average behavior of probabilistic systems. In LICS: IEEE Symposium on Logic in Computer Science, 1998.

    Google Scholar 

  13. S. Gilmore and J. Hillston. The PEPA Workbench: A Tool to Support a Process Algebra-based Approach to Performance Modelling. In G. Haring and G. Kotsis, editors, Proc. of 7th Conf. on Mod. Techniques and Tools for Computer Perf. Eval., volume 794 of LNCS, pages 353–368, 1994.

    Google Scholar 

  14. G. Clark. Formalising the Specification of Rewards with PEPA. In Proc. of 4th Process Algebras and Performance Modelling Workshop, pages 139–160, July 1996.

    Google Scholar 

  15. G. Clark, S. Gilmore, and J. Hillston. Specifying performance measures for PEPA. In J.P. Katoen, editor, Proc. of 5th Int. AMAST Workshop on Real-Time and Probabilistic Systems, volume 1601 of LNCS, pages 211–227, Bamberg, Germany, 1999. Springer-Verlag.

    Google Scholar 

  16. S. Gilmore, J. Hillston, and M. Ribaudo. An efficient algorithm for aggregating PEPA models. To appear in IEEE Transactions on Software Engineering, 2000.

    Google Scholar 

  17. G. Clark, S. Gilmore, J. Hillston, and N. Thomas. Experiences with the PEPA Performance Modelling Tools. IEE Proceedings—Software, 146(1):11–19, February 1999. Special issue of papers from 14th UK Performance Engineering Workshop.

    Google Scholar 

  18. K. G. Larsen and A. Skou. Bisimulation through probabilistic testing. Information and Computation, 94(1):1–28, September 1991.

    Article  MATH  MathSciNet  Google Scholar 

  19. M. Hennessy and R. Milner. Algebraic laws for nondeterminism and concurrency. Journal of the ACM, 32(1):137–161, January 1985.

    Article  MATH  MathSciNet  Google Scholar 

  20. G. Clark. Techniques for the Construction and Analysis of Algebraic Performance Models. PhD thesis, The University of Edinburgh, 2000.

    Google Scholar 

  21. M. Bernardo. An Algebra-Based Method to Associate Rewards with EMPA Terms. In P. Degano, R. Gorrieri, and A. Marchetti Spaccamela, editors, 24th Int. Colloquium on Automata, Languages and Programming, volume 1256 of LNCS, pages 358–368, Bologna, Italy, July 1997. Springer-Verlag.

    Google Scholar 

  22. C. Baier, J.-P. Katoen, and H. Hermanns. Approximate symbolic model checking of continuous time Markov chains. In Proceedings of CONCUR’99, volume 1664 of LNCS, pages 146–162, 1999.

    Google Scholar 

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Clark, G., Gilmore, S., Hillston, J., Ribaudo, M. (2000). Exploiting Modal Logic to Express Performance Measures. In: Haverkort, B.R., Bohnenkamp, H.C., Smith, C.U. (eds) Computer Performance Evaluation.Modelling Techniques and Tools. TOOLS 2000. Lecture Notes in Computer Science, vol 1786. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46429-8_18

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  • DOI: https://doi.org/10.1007/3-540-46429-8_18

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  • Print ISBN: 978-3-540-67260-9

  • Online ISBN: 978-3-540-46429-7

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