Skip to main content
Springer Nature Link
Log in

A Precedence PEPA Model for Performance and Reliability Analysis

  • Conference paper
Formal Methods and Stochastic Models for Performance Evaluation (EPEW 2006)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 4054))

Included in the following conference series:

  • 328 Accesses

Abstract

We propose new techniques to simplify the computation of the cycle times and the absorption times for a large class of PEPA models. These techniques allow us to simplify the model description to reduce the number of states of the underlying Markov chain. The simplification processes are associated with stochastic comparisons of random variables. Thus the simplified models are stochastic bounds for the original ones.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Baccelli, F., Cohen, G., Olsder, G.J., Quadrat, J.P.: Synchronization and Linearity, an algebra for Discrete Event Systems. Wiley & Sons, Chichester (1992)

    MATH  Google Scholar 

  2. Baccelli, F., Liu, Z.: On the executions of parallel programs on multiprocessor systems - a queueing theory approach. JACM 37(2), 373–414 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  3. Baccelli, F., Liu, Z.: Comparison properties of stochastic decision free Petri nets, Inria Report 1433 (1991)

    Google Scholar 

  4. Barlow, R.E., Proschan, F.: Statistical Theory of Reliability and Life Testing (1981)

    Google Scholar 

  5. Ben Mamoun, M., Busic, A., Fourneau, J.M., Pekergin, N.: Increasing Convex Monotone Markov Chains: Theory, Algorithm and Applications (submitted)

    Google Scholar 

  6. Bobbio, A., Horvath, A., Scarpa, M., Telek, M.: Acyclic Discrete Phase type distributions; properties and a parameter estimation algorithm. Performance evaluation 54, 1–32 (2003)

    Article  Google Scholar 

  7. Bradley, J.T., Dingle, N., Gilmore, S.T., Knottenbelt, W.J.: Extracting Passage Time form PEPA models with the Hydra tool: a case study. In: UKPEW 2003 (2003)

    Google Scholar 

  8. Fourneau, J.M., Pekergin, N.: An algorithmic approach to stochastic bounds. In: Calzarossa, M.C., Tucci, S. (eds.) Performance 2002. LNCS, vol. 2459, pp. 64–88. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  9. Gilmore, S., Hillston, J., Kloul, L., Ribaudo, M.: PEPA nets: A structured performance modelling formalism. Performance Evaluation 54, 79–104 (2003)

    Article  Google Scholar 

  10. Hillston, J.: A compositional Approach to Performance Modelling, PhD Thesis, The University of Edinburgh (1994)

    Google Scholar 

  11. Hillston, J., Kloul, L.: An Efficient Kronecker Representation for PEPA Models. In: de Luca, L., Gilmore, S. (eds.) PROBMIV 2001, PAPM-PROBMIV 2001, and PAPM 2001. LNCS, vol. 2165, pp. 120–135. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  12. Pekergin, N.: Stochastic delay bounds on fair queueing algorithms. In: Proceedings of INFOCOM 1999, New York, pp. 1212–1220 (1999)

    Google Scholar 

  13. Pekergin, N., Vincent, J.M.: Stochastic Bounds on Execution Times of Parallel Programs. IEEE Transactions on Software Engineering 17(17) (October 1991)

    Google Scholar 

  14. Stoyan, D.: Comparison Methods for Queues and Other Stochastic Models. Wiley & Sons, New York (1983)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. PRiSM, Université de Versailles Saint-Quentin, 45 Av. des Etats Unis, 78000, Versailles, France

    Jean-Michel Fourneau & Leïla Kloul

Authors
  1. Jean-Michel Fourneau
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leïla Kloul
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università di Torino, Corso Svizzera 185, 10149, Torino, Italy

    András Horváth

  2. Department of Telecommunications, Technical University of Budapest, 1521, Budapest, Hungary

    Miklós Telek

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fourneau, JM., Kloul, L. (2006). A Precedence PEPA Model for Performance and Reliability Analysis. In: Horváth, A., Telek, M. (eds) Formal Methods and Stochastic Models for Performance Evaluation. EPEW 2006. Lecture Notes in Computer Science, vol 4054. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11777830_1

Download citation

  • DOI: https://doi.org/10.1007/11777830_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35362-1

  • Online ISBN: 978-3-540-35365-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics