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Exploiting Structure in Solution: Decomposing Compositional Models

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Abstract

Since their introduction in the early 1990s, compositionality has been reported as one of the major attractions of stochastic process algebras. The benefits that compositionality provides for model construction are readily apparent and have been demonstrated in numerous case studies. Early research on the compositionality of the languages focused on how the inherent structure could be used, in conjunction with equivalence relations, for model simplification and aggregation. In this chapter we consider how far we have been able to take advantage of compositionality when it comes to solving the Markov process underlying a Markovian process algebra model.

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References

  1. A. Aldini, M. Bernardo, and R. Gorrieri. An algebraic model for evaluating the performance of an ATM switch with explicit rate marking. In J. Hillston and M. Silva, editors, Proc. of 7th Int. Workshop on Process Algebra and Performance Modelling (PAPM’99), pages 119–138. Prensas Universitarias de Zaragoza, September 1999.

    Google Scholar 

  2. H.H. Ammar and S.M. Rezaul Islam. Time Scale Decomposition of a Class of Generalized Stochastic Petri Net Models. IEEE Transactions on Software Engineering, 15(6):809–820, June 1989.

    Article  Google Scholar 

  3. F. Baskett, K.M. Chandy, R.R. Muntz, and F.G. Palacios. Open, Closed and Mixed Networks of Queues with Different Classes of Customers. Journal of the ACM, 22(2):248–260, April 1975.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Bernardo and R. Gorrieri. A Tutorial on EMPA: A Theory of Concurrent Processes with Nondeterminism, Priorities, Probabilities and Time. Theoretical Computer Science, 202(1-2):1–54, July 1998.

    Article  MATH  MathSciNet  Google Scholar 

  5. M. Bhabuta, P.G. Harrison, and K. Kanani. Detecting reversibility in Markovian Process Algebra. In Performance Engineering of Computer and Telecommunications Systems, Liverpool John Moores University, September 1995. Springer-Verlag.

    Google Scholar 

  6. A. Blakemore and S. Tripathi. Automated Time Scale Decomposition of SPNs. In Proc. of 5th International Workshop on Petri Nets and Performance Models (PNPM’ 93), Toulouse, 1993.

    Google Scholar 

  7. H. Bohnenkamp and B. Haverkort. Decomposition Methods for the Solution of Stochastic Process Algebra Models: a Proposal. In E. Brinksma and A. Nymeyer, editors, Proc. of 5th Process Algebra and Performance Modelling Workshop, 1997.

    Google Scholar 

  8. H. Bohnenkamp and B. Haverkort. Semi-Numerical Solution of Stochastic Process Algebra Models. In C. Priami, editor, Proc. of 6th Process Algebra and Performance Modelling Workshop, 1998.

    Google Scholar 

  9. H. Bohnenkamp and B. Haverkort. Stochastic event structures for the decomposition of stochastic process algebra models. In J. Hillston and M. Silva, editors, Proc. of 7th Int. Workshop on Process Algebra and Performance Modelling (PAPM’99), pages 119–138. Prensas Universitarias de Zaragoza, September 1999.

    Google Scholar 

  10. R.J. Boucherie. A Characterisation of Independence for Competing Markov Chains with Applications to Stochastic Petri Nets. IEEE Transactions on Software Engineering, 20(7):536–544, July 1994.

    Article  Google Scholar 

  11. R.J. Boucherie and M. Sereno. On the Traffic Equations of Batch Routing Queueing Networks and Stochastic Petri Nets. Technical report, European Research Consortium for Informatics and Mathematics, 1994.

    Google Scholar 

  12. P. Buchholz. Compositional Analysis of a Markovian Process Algebra. In U. Herzog and M. Rettelbach, editors, Proc. of 2nd Process Algebra and Performance Modelling Workshop, 1994.

    Google Scholar 

  13. G. Ciardo and K.S. Trivedi. A Decomposition Approach for Stochastic Petri Net Models. Performance Evaluation, 1992.

    Google Scholar 

  14. G. Clark. An Extended Weak Isomorphism for Model Simplification. In E. Brinksma and A. Nymeyer, editors, Proc. of 5th Process Algebra and Performance Modelling Workshop, 1997.

    Google Scholar 

  15. G. Clark. Stochastic Process Algebra Structure for Insensitivity. In J. Hillston and M. Silva, editors, Proc. of 7th Int. Workshop on Process Algebra and Performance Modelling (PAPM’99), pages 63–82. Prensas Universitarias de Zaragoza, September 1999.

    Google Scholar 

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

    Google Scholar 

  17. G. Clark and J. Hillston. Product form solution for an insensitive stochastic process algebra structure. Performance Evaluation, 2001. To appear.

    Google Scholar 

  18. P.J. Courtois. Decomposability: Queueing and Computer System Applications. ACM Series. Academic Press, New York, 1977.

    MATH  Google Scholar 

  19. P. D’Argenio, J-P. Katoen, and E. Brinksma. General Purpose Discrete Event Simulation Using Spades. In C. Priami, editor, Proc. of 6th Process Algebra and Performance Modelling Workshop, 1998.

    Google Scholar 

  20. S. Donatelli and M. Sereno. On the Product Form Solution for Stochastic Petri Nets. In Application and Theory of Petri Nets, pages 154–172. Springer Verlag, 1992.

    Google Scholar 

  21. J-M. Fourneau, L. Kloul, and F. Valois. Performance Modelling of Hierarchical Cellular Networks using PEPA. In J. Hillston and M. Silva, editors, Proc. of 7th Int. Workshop on Process Algebra and Performance Modelling (PAPM’99), pages 139–154. Prensas Universitarias de Zaragoza, September 1999.

    Google Scholar 

  22. 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, Proceedings of the Seventh International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, volume 794 of LNCS, pages 353–368. Springer-Verlag, 1994.

    Google Scholar 

  23. S. Gilmore, J. Hillston, R. Holton, and M. Rettelbach. Specifications in Stochastic Process Algebra for a Robot Control Problem. International Journal of Production Research, December 1995.

    Google Scholar 

  24. S. Gilmore, J. Hillston, and L. Recalde. Elementary structural analysis for PEPA. Technical Report ECS-LFCS-97-377, Laboratory for Foundations of Computer Science, Department of Computer Science, The University of Edinburgh, 1997.

    Google Scholar 

  25. P. Harrison and J. Hillston. Exploiting Quasi-reversible Structures in Markovian Process Algebra Models. The Computer Journal, 38(6), 1995.Special Issue: Proc. of 3rd Process Algebra and Performance Modelling Workshop.

    Google Scholar 

  26. W. Henderson, D. Lucic, and P.G. Taylor. A Net level Performance Analysis of Stochastic Petri Nets. Journal of the Australian Mathematical Society, Series B, 31:176–187, 1989.

    MATH  MathSciNet  Google Scholar 

  27. W. Henderson and P.G. Taylor. Embedded Processes in Stochastic Petri Nets. IEEE Transactions on Software Engineering, 17(2):108–116, February 1991.

    Article  MathSciNet  Google Scholar 

  28. H. Hermanns and M. Rettelbach. Towards a Superset of Basic LOTOS for Performance Prediction. In M. Ribaudo, editor, Proc. of 6th Process Algebra and Performance Modelling Workshop, 1996.

    Google Scholar 

  29. H. Hermanns and M.L. Rettelbach. Syntax, Semantics, Equivalences and Axioms for MTIPP. In U. Herzog and M. Rettelbach, editors, Proc. of 2nd Process Algebra and Performance Modelling Workshop, 1994.

    Google Scholar 

  30. U. Herzog. Formal description, time and performance analysis: A framework. Technical Report 15/90, IMMD VII, Friedrich-Alexander-Universität, Erlangen-Nürnberg, Germany, September 1990.

    Google Scholar 

  31. J. Hillston. The Nature of Synchronisation. In U. Herzog and M. Rettelbach, editors, Proc. of 2nd Process Algebra and Performance Modelling Workshop, 1994.

    Google Scholar 

  32. J. Hillston. Compositional Markovian Modelling Using a Process Algebra. In W.J. Stewart, editor, Numerical Solution of Markov Chains. Kluwer, 1995.

    Google Scholar 

  33. J. Hillston. A Compositional Approach to Performance Modelling. Distinguished Dissertations in Computer Science. Cambridge University Press, 1996.

    Google Scholar 

  34. J. Hillston. A Class of PEPA Models Exhibiting Product Form Solution. Technical Report ECS-LFCS-98-382, LFCS, Dept. of Computer Science, University of Edinburgh, February 1998.

    Google Scholar 

  35. J. Hillston, H. Hermanns, U. Herzog, V. Mertsiotakis, and M. Rettelbach. Integrating Qualitative and Quantitative Modelling with Stochastic Process Algebras. Technical report, IMMD VII, Universität Erlangen-Nürnberg, May 1994.

    Google Scholar 

  36. J. Hillston and L. Kloul. An Efficient Kronecker Representation for PEPA Models. Submitted for publication, 2000.

    Google Scholar 

  37. J. Hillston and V. Mertsiotakis. A Simple Time Scale Decomposition Technique for Stochastic Process Algebras. The Computer Journal, 38(6), 1995. Special Issue: Proc. of 3rd Process Algebra and Performance Modelling Workshop.

    Google Scholar 

  38. J. Hillston and N. Thomas. A Syntactical Analysis of Reversible PEPA Models. In Proc. of 6th Process Algebra and Performance Modelling Workshop, Nice, France, September 1998. University of Verona.

    Google Scholar 

  39. J. Hillston and N. Thomas. Product Form Solution for a class of PEPA Models. Performance Evaluation, 35:171–192, 1999.

    Article  MATH  Google Scholar 

  40. J. Hillston and J. Tomasik. Amalgamation of transition sequences in the PEPA formalism. In Proc. of ICALP Workshops 2000 (PAPM). Carleton Scientific Press, 2000.

    Google Scholar 

  41. D.R.W. Holton. A PEPA Specification of an Industrial Production Cell. The Computer Journal, 38(6), 1995. Special Issue: Proc. of 3rd Process Algebra and Performance Modelling Workshop.

    Google Scholar 

  42. J.R. Jackson. Jobshop-like Queueing Systems. Management Science, 10: 131–142, 1963.

    Article  Google Scholar 

  43. H. Jungnitz. Approximation Methods for Stochastic Petri Nets. PhD thesis, Rensselaer Polytechnic Institute, May 1992.

    Google Scholar 

  44. F. Kelly. Reversibility and Stochastic Processes. Wiley, 1979.

    Google Scholar 

  45. A.A. Lazar and T.G. Robertazzi. Markovian Petri Net Protocols with Product Form Solution. Performance Evaluation, 12(1):67–77, January 1991.

    Article  MathSciNet  Google Scholar 

  46. V. Mertsiotakis. Time Scale Decomposition of Stochastic Process Algebra Models. In E. Brinksma and A. Nymeyer, editors, Proc. of 5th Process Algebra and Performance Modelling Workshop, 1997.

    Google Scholar 

  47. V. Mertsiotakis. Approximate Analysis Methods for Stochastic Process Algebras. PhD thesis, Universität Erlangen-Nürnberg, Martensstraße 3, 91058 Erlangen, September 1998.

    Google Scholar 

  48. V. Mertsiotakis and M. Silva. A Throughput Approximation Algorithm for Decision Free Processes. In M. Ribaudo, editor, Proc. of 6th Process Algebra and Performance Modelling Workshop, 1996.

    Google Scholar 

  49. V. Mertsiotakis and M. Silva. A Throughput Approximation Algorithm for Decision Free Processes. In M. Ribaudo, editor, Proc. of 7th International Workshop on Petri Nets and Performance Models, 1996.

    Google Scholar 

  50. I. Mitrani and N. Thomas. Routing Among Different Nodes Where Servers Break Down Without Losing Jobs. In F. Baccelli, A. Jean-Marie, and I. Mitrani, editors, Quantitative Methods in Parallel Systems, pages 248–261. Springer, 1995.

    Google Scholar 

  51. I. Mitrani and P.E. Wright. Routing in the Presence of Breakdowns. Performance Evaluation, 20:151–164, 1994.

    Article  Google Scholar 

  52. M.K. Molloy. Performance Analysis using Stochastic Petri Nets. IEEE Transactions on Computers, 31(9):913–917, September 1982.

    Article  Google Scholar 

  53. B. Plateau. On the Stochastic Structure of Parallelism and Synchronisation Models for Distributed Algorithms. In Proc. ACM Sigmetrics Conference on Measurement and Modelling of Computer Systems, 1985.

    Google Scholar 

  54. B. Plateau, J.M. Fourneau, and K.H. Lee. PEPS: A Package for Solving Complex Markov Models of Parallel Systems. In Proc. of the 4th International Conference on Modelling Techniques and Tools for Computer Performance Evaluation, 1988.

    Google Scholar 

  55. M.L. Rettelbach and M. Siegle. Compositional Minimal Semantics for the Stochastic Process Algebra TIPP. In U. Herzog and M. Rettelbach, editors, Proc. of 2nd Process Algebra and Performance Modelling Workshop, 1994.

    Google Scholar 

  56. M. Sereno. Towards a Product Form Solution of Stochastic Process Algebras. The Computer Journal, 38(6), 1995. Special Issue: Proc. of 3rd Process Algebra and Performance Modelling Workshop.

    Google Scholar 

  57. M. Sereno. Performance Models for Discrete Event Systems with Synchronisations, volume II, chapter Product form and Petri nets, pages 637–660. Kronos, 1998.

    Google Scholar 

  58. W.J. Stewart, K. Arif, and B. Plateau. The numerical solution of Stochastic Automata Networks. European Journal of Operation Research, 86(3):503–525, 1995.

    Article  MATH  Google Scholar 

  59. N. Thomas and J. Bradley. Approximating variance in non-product form decomposed models. In Proc. of ICALP Workshops 2000 (PAPM), pages 607–619. Carleton Scientific Press, 2000.

    Google Scholar 

  60. N. Thomas and S. Gilmore. Applying Quasi-Separability to Markovian Process Algebra. In Proc. of 6th Process Algebra and Performance Modelling Workshop, Nice, France, September 1998. University of Verona.

    Google Scholar 

  61. J. Tomasik and J. Hillston. Transforming PEPA Models to Obtain Product Form Bounds. Technical report, Division of Informatics, University of Edinburgh, 2000.

    Google Scholar 

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Hillston, J. (2001). Exploiting Structure in Solution: Decomposing Compositional Models. In: Brinksma, E., Hermanns, H., Katoen, JP. (eds) Lectures on Formal Methods and PerformanceAnalysis. EEF School 2000. Lecture Notes in Computer Science, vol 2090. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44667-2_8

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  • DOI: https://doi.org/10.1007/3-540-44667-2_8

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