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Abstract

Peps is a software package for solving very large Markov models expressed as Stochastic Automata Networks (San). The San formalism defines a compact storage scheme for the transition matrix of the Markov chain and it uses tensor algebra to handle the basic vector matrix multiplications. Among the diverse application areas to which Peps may be applied, we cite the areas of computer and communication performance modeling, distributed and parallel systems and finite capacity queueing networks. This paper presents the numerical techniques included in version 2003 of the Peps software, the basics of its interface and three practical examples.

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References

  1. Ajmone-Marsan, M., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets. John-Wiley, New York (1995)

    Google Scholar 

  2. Atif, K., Plateau, B.: Stochatic Automata Networks for Modeling Parallel Systems. IEEE Transactions on Software Engineering 17(10), 1093–1108 (1991)

    Article  MathSciNet  Google Scholar 

  3. Benoit, A., Plateau, B., Stewart, W.J.: Memory-efficient Kronecker algorithms with applications to the modelling of parallel systems. To appear in PMEOPDS 2003 (2003)

    Google Scholar 

  4. Ciardo, G.F., Miner, A.S.: A Data Structure for the Efficient Kronecker Solution of GSPNs. In: Proc. 8th International Workshop on Petri Nets and Performance Evaluation (1999)

    Google Scholar 

  5. Donnatelli, S.: Superposed Stochastic Automata: a Class of Stochastic Petri Nets with Parallel Solution and Distributed State Space. Performance Evaluation 18, 21–36 (1993)

    Article  MathSciNet  Google Scholar 

  6. Fernandes, P.: Méthodes Numériques pour la Solution de Systèmes Markoviens à Grand Espace d’Etats. Thèse de doctorat, Institut National Polytechnique de Grenoble, France (1998)

    Google Scholar 

  7. Fernandes, P., Plateau, B., Stewart, W.J.: Efficient Descriptor-Vector Multiplication in Stochastic Automata Networks. Journal of the ACM 45(3), 381–414 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  8. Fourneau, J., Plateau, B.: A Methodology for Solving Markov Models of Parallel Systems. Journal of Parallel and Distributed Computing 12, 370–387 (1991)

    Article  Google Scholar 

  9. Gelenbe, E., Pujolle, G.: Introduction to Queueing Networks. John Wiley, Chichester (1997)

    Google Scholar 

  10. Hillston, J.: A Compositional Approach for Performance Modelling. Ph.D. Thesis, University of Edinburg, United Kingdom (1994)

    Google Scholar 

  11. Muppala, J.K., Ciardo, G.F., Trivedi, K.S.: Stochastic Reward Nets for Reliability Prediction. Communications in Reliability, Maintainability and Serviceability 1(2), 9–20 (1994)

    Google Scholar 

  12. Plateau, B.: De l’Evaluation du Parellélisme et de la Synchronisation. Thèse de Doctorat d’Etat, Paris-Sud, Orsay, France (1984)

    Google Scholar 

  13. Plateau, B.: On the Stochastic Structure of Parallelism and Synchronization Models for Distributed Algorithms. In: Proc. ACM Sigmetrics Conference on Measurement and Modeling of Computer Systems, Austin, Texas (1985)

    Google Scholar 

  14. Plateau, B., Fourneau, J.M., Lee, K.: PEPS: A Package for Solving Complex Markov Models of Parallel Systems. In: Puigjaner, R., Potier, D. (eds.) Modelling Techniques and Tools for Computer Performance Evaluation (1988)

    Google Scholar 

  15. Peps team. Peps, Software Tool. On-line document (2003), available at http://www-apache.imag.fr/software/peps (visited February 14, 2003)

  16. Saad, Y.: Iterative Methods for Sparse Linear Systems. PWS Publishing Company (1995)

    Google Scholar 

  17. Sanders, W.H., Meyer, J.F.: An Unified Approach for Specifying Measures of Performance, Dependability, and Performability. Dependable Computing for Critical Applications 4, 215–238 (1991)

    Google Scholar 

  18. Stewart, W.J.: Marca: Markov Chain Analyzer. IEEE Computer Repository No. R76 232 (1976)

    Google Scholar 

  19. Stewart, W.J.: Introduction to the Numerical Solution of Markov Chains. Princeton University Press, Princeton (1994)

    MATH  Google Scholar 

  20. Sun Microsystems The JIT Compiler Interface Specification. On-line document, available at http://java.sun.com/docs/jit_interface.html (visited February 14, 2003)

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© 2003 Springer-Verlag Berlin Heidelberg

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Benoit, A., Brenner, L., Fernandes, P., Plateau, B., Stewart, W.J. (2003). The Peps Software Tool. In: Kemper, P., Sanders, W.H. (eds) Computer Performance Evaluation. Modelling Techniques and Tools. TOOLS 2003. Lecture Notes in Computer Science, vol 2794. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45232-4_7

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  • DOI: https://doi.org/10.1007/978-3-540-45232-4_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40814-7

  • Online ISBN: 978-3-540-45232-4

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