Perfect Sampling of Load Sharing Policies in Large Scale Distributed Systems

  • Gaël Gorgo
  • Jean-Marc Vincent
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6148)

Abstract

This article presents a performance evaluation method for the dimensioning of load sharing policies in high performance distributed systems such as clusters and grids. Even for moderate system size, the corresponding Markovian models are not tractable neither analytically nor numerically. We propose a modelling framework and a simulation kernel which provides an unbiased sampling of the stationary distribution. As needed by the Propp & Wilson algorithm, we prove that events of load sharing systems preserve partial ordering on the state space (monotone events) that guarantees the simulation efficiency. This has been tested on large scale models (about 1000 nodes) in the Ψ2 simulation framework and applied for the comparison between work sharing and work stealing policies performances and for the optimisation of parameters such as the control rate and the probing depth.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Béguin, M., Gray, L., Ycart, B.: The load transfer model. The Annals of Applied Probability 8(2), 337–353 (1998)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Benaïm, M., Le Boudec, J.Y.: A class of mean field interaction models for computer and communication systems. Performance Evaluation 65(11-12), 823–838 (2008)CrossRefGoogle Scholar
  3. 3.
    Blumofe, R.D., Leiserson, C.E.: Scheduling multithreaded computations by work stealing. Journal of the ACM 46(5), 720–748 (1999)MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Burton, F.W., Sleep, M.R.: Executing functional programs on a virtual tree of processors. In: Functional Programming Languages and Computer Architecture, pp. 187–194 (1981)Google Scholar
  5. 5.
    Bušić, A., Gaujal, B., Vincent, J.M.: Perfect simulation and non-monotone markovian systems. In: ValueTools 2008: Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools, pp. 1–10 (2008)Google Scholar
  6. 6.
    Dandamudi, S.P., Kwok, M., Lo, C.: A comparative study of adaptive and hierarchical load sharing policies for distributed systems. In: Computers and Their Applications, pp. 136–141 (1998)Google Scholar
  7. 7.
    Eager, D.L., Lazowska, E.D., Zahorjan, J.: Adaptive load sharing in homogeneous distributed systems. IEEE Transaction on Software Engineering 12(5), 662–675 (1986)Google Scholar
  8. 8.
    Eager, D.L., Lazowska, E.D., Zahorjan, J.: A comparison of receiver-initiated and sender-initiated adaptive load sharing. Performance Evaluation 6(1), 53–68 (1986)CrossRefGoogle Scholar
  9. 9.
    Halstead, R.H.: Implementation of multilisp: Lisp on a multiprocessor. In: LISP and Functional Programming, pp. 9–17 (1984)Google Scholar
  10. 10.
    Karatza, H.D., Hilzer, R.C.: Parallel and distributed systems: load sharing in heterogeneous distributed systems. In: Winter Simulation Conference, pp. 489–496 (2002)Google Scholar
  11. 11.
    Lo, M., Dandamudi, S.P.: Performance of hierarchical load sharing in heterogeneous distributed systems. In: Parallel and Distributed Computing and Systems, pp. 370–377 (1996)Google Scholar
  12. 12.
    Mirchandaney, R., Towsley, D., Stankovic, J.A.: Adaptive load sharing in heterogeneous distributed systems. Journal of Parallel and Distributed Computating 9(4), 331–346 (1990)CrossRefGoogle Scholar
  13. 13.
    Mitzenmacher, M.: Analyses of load stealing models based on differential equations. In: Symposium on Parallel Algorithms and Architectures, pp. 212–221 (1998)Google Scholar
  14. 14.
    Propp, J.G., Wilson, D.B.: Exact sampling with coupled markov chains and applications to statistical mechanics. Random Structures and Algorithms 9(1-2), 223–252 (1996)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Squillante, M.S., Nelson, R.D.: Analysis of task migration in shared-memory multiprocessor scheduling. Performance Evaluation Review 19(1), 143–155 (1991)CrossRefGoogle Scholar
  16. 16.
    Vincent, J.M.: Perfect simulation of queueing networks with blocking and rejection. In: Symposium on Applications and the Internet Workshops, pp. 268–271 (2005)Google Scholar
  17. 17.
    Vincent, J.M., Vienne, J.: Perfect simulation of index based routing queueing networks. Performance Evaluation Review 34(2), 24–25 (2006)CrossRefGoogle Scholar
  18. 18.
    Vincent, J.M., Vienne, J.: Psi2 a software tool for the perfect simulation of finite queueing networks. In: QEST (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Gaël Gorgo
    • 1
  • Jean-Marc Vincent
    • 2
  1. 1.MESCAL Project, BullMontbonnotFrance
  2. 2.MESCAL ProjectUniversity of GrenobleMontbonnotFrance

Personalised recommendations