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Semi-numerical Solution of Stochastic Process Algebra Models

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Formal Methods for Real-Time and Probabilistic Systems (ARTS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1601))

Abstract

A solution method for solving Markov chains for a class of stochastic process algebra terms is presented. The solution technique is based on a reformulation of the underlying continuous-time Markov chain (CTMC) in terms of semi-Markov processes. For the reformulation only local information about the processes running in parallel is needed, and it is therefore never necessary to generate the complete global state space of the CTMC. The method works for a fixed number of sequential processes running in parallel and which all synchronize on the same global set of actions. The behaviour of the processes is expressed by the embedded Markov chain of a semi-Markov process and by distribution functions (exponomials) which describe the times between synchronizations. The solution method is exact, hence, the state space explosion problem for this class of processes has been solved. A distributed implementation of the solution technique is straightforward.

An earlier version of this paper has been presented on the PAPM’ 98 workshop [1] in Nice, France.

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References

  1. Henrik Bohnenkamp and Boudewijn Haverkort. Semi-numerical solution of stochastic process algebra models. In Priami [16], pages 71–84.

    Google Scholar 

  2. Henrik Bohnenkamp and Boudewijn Haverkort. Stochastic event structures for the decomposition of stochastic process algebra models. Submitted for presentation at the PAPM’ 99 workshop, Feb 1999.

    Google Scholar 

  3. Stephen D. Brookes, C. A. R. Hoare, and A. W. Roscoe. A theory of communicating sequential processes. Journal of the ACM, 31(3):560–599, July 1984.

    Article  MathSciNet  MATH  Google Scholar 

  4. Erhan Çinlar. Introduction to Stochastic Processes. Prentice Hall, Inc., Englewood Cliffs, New Jersey, 1975.

    MATH  Google Scholar 

  5. Ricardo Fricks, Miklós Telek, Antonio Puliafito, and Kishor Trivedi. Markov renewal theory applied to performability evaluation. Technical Report TR-96/11, The Center for Advanced Computing and Communication, North Carolina State University, Raleigh, NC, USA, 1996. http://www.ece.ncsu.edu/cacc/tech_reports/abs/abs9611.html.

    Google Scholar 

  6. H. Hermanns and J.-P. Katoen. Automated compositional Markov chain generation for a plain-old telephone system. Science of Computer Programming, Oct 1998. accepted for publication.

    Google Scholar 

  7. Holger Hermanns. Interactive Markov chains. PhD thesis, Universität Erlangen-Nürnberg, Germany, 1998.

    MATH  Google Scholar 

  8. Holger Hermanns and Michael Rettelbach. Syntax, Semantics, Equivalences, and Axioms for MTIPP. In Michael Rettelbach, editors. Proceedings of the 2nd workshop on process algebras and performance modelling. FAU Erlangen-Nürnberg, 1994 Herzog and Rettelbach [9].

    Google Scholar 

  9. Ulrich Herzog and Michael Rettelbach, editors. Proceedings of the 2nd workshop on process algebras and performance modelling. FAU Erlangen-Nürnberg, 1994.

    Google Scholar 

  10. Jane Hillston. A Compositional Approach to Performance Modelling. PhD thesis, University of Edinburgh, 1994.

    Google Scholar 

  11. Jane Hillston. The nature of synchronization. In Michael Rettelbach, editors. Proceedings of the 2nd workshop on process algebras and performance modelling. FAU Erlangen-Nürnberg, 1994 Herzog and Rettelbach [9], pages 51–70.

    Google Scholar 

  12. Jane Hillston. Exploiting structure in solution: Decomposing composed models. In Priami [16], pages 1–15.

    Google Scholar 

  13. Ronald A. Howard. Dynamic Probabilistic Systems., volume 2: Semimarkov and Decision Processes. John Wiley & Sons, Inc., New York, London, Syndney, Toronto, 1971.

    MATH  Google Scholar 

  14. Vidyadhar G. Kulkarni. Modeling and Analysis of Stochastic Systems. Chapman & Hall, London, Glasgow, Weinheim, 1995.

    MATH  Google Scholar 

  15. Raymond Marie, Andrew L. Reibman, and Kishor S. Trivedi. Transient analysis of acyclic Markov chains. Performance Evaluation, 7:175–194, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  16. Corrado Priami, editor. Proceedings of the sixth workshop on process algebras and performance modelling. Universita Degli Studi di Verona, 1998.

    Google Scholar 

  17. A. V. Ramesh and K. Trivedi. Semi-numerical transient analysis of Markov models. In Proceedings of the 33rd ACM Southeast Conference, pages 13–23, 1995.

    Google Scholar 

  18. Michael Rettelbach. Stochastische Prozessalgebren mit zeitlosen Aktivitäten und probabilistischen Verzweigungen. PhD thesis, Friedrich-Alexander-Universität Erlangen-Nürnberg, April 1996.

    Google Scholar 

  19. Robin A. Sahner, Kishor S. Trivedi, and Antonio Puliafito. Performance and Reliability Analysis of Computer Systems. An Example-Based Approach Using the SHARPE Software Package. Kluwer Academic Publishers, Boston, London, Dordrecht, 1996.

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratory for Performance Evaluation and Distributed Systems Department of Computer Science, RWTH Aachen, Aachen, Germany

    Henrik C. Bohnenkamp & Boudewijn R. Haverkort

Authors
  1. Henrik C. Bohnenkamp
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  2. Boudewijn R. Haverkort
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Editor information

Editors and Affiliations

  1. Lehrstuhl für Informatik, University of Erlangen-Nürnberg, Martensstr. 3, D-91058, Erlangen, Germany

    Joost-Pieter Katoen

  2. Formal Methods and Tools Group, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Joost-Pieter Katoen

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© 1999 Springer-Verlag Berlin Heidelberg

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Bohnenkamp, H.C., Haverkort, B.R. (1999). Semi-numerical Solution of Stochastic Process Algebra Models. In: Katoen, JP. (eds) Formal Methods for Real-Time and Probabilistic Systems. ARTS 1999. Lecture Notes in Computer Science, vol 1601. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48778-6_14

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  • DOI: https://doi.org/10.1007/3-540-48778-6_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66010-1

  • Online ISBN: 978-3-540-48778-4

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