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Estimation of the throughput for some stochastic resources sharing systems

  • Matthieu Brilman
  • Jean-Marc Vincent
Workshop 19 Performance Evaluation
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1124)

Abstract

We present in this paper a stochastic model for a class of resources sharing systems, on which we define a performance parameter: γ This parameter can be seen as the inverse of the asymptotic throughput of the system. We then present an upper-bound and a lower-bound for γ These bounds are simply deduced from the conflict graph of the system. We finally show how they can lead to a good estimation of γ for some large systems.

Keywords

Parallel Systems Synchronization Shared Resources (max, +) Systems Stochastic Processes 

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References

  1. 1.
    M. Brilman. Modélisation et évaluation de performances de systèmes de ressources partagées. PhD thesis, Université Joseph Fourrier, 1996.Google Scholar
  2. 2.
    M. Brilman and J-M. Vincent. Dynamics of synchronized parallel systems. March 1995. Submitted to Stochastic Models.Google Scholar
  3. 3.
    M. Brilman and J-M. Vincent. On the estimation of the throughput for a class of stochastic resources sharing systems. November 1995. Submitted to Mathematics of Operations Research.Google Scholar
  4. 4.
    G.H. Golub and C.F. Van Loan. Matrix Computations. Hopkins University Press, 1987.Google Scholar
  5. 5.
    J. Mairesse. Products of Irreducible Random Matrices in the (Max,+) Algebra-Part1. Technical Report 1939, INRIA, June 1993.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Matthieu Brilman
    • 1
  • Jean-Marc Vincent
    • 1
  1. 1.LMC-IMAGGrenoble Cedex 9France

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