Skip to main content
SpringerLink
Log in

Towards Non-Stationary Grid Models

  • Published:
Journal of Grid Computing Aims and scope Submit manuscript

Abstract

Despite intense research on Grid scheduling, differentiated quality of service remains an open question, and no consensus has emerged on the most promising strategy. The difficulties of experimentation might be one of the root causes of this stalling. An alternative to experimenting on real, large, and complex data is to look for well-founded and parsimonious representations, which may also contribute to the a-priori knowledge required for operational Autonomics. The goal of this paper is thus to explore explanatory and generative models rather than predictive ones. As a test case, we address the following issue: is it possible to exhibit and validate consistent models of the Grid workload? Most existing work on modeling the dynamics of Grid behavior describes Grids as complex systems, but assumes a steady-state system (technically stationarity) and concludes to some form of long-range dependence (slowly decaying correlation) in the associated time-series. But the physical (economic and sociologic) processes governing the Grid behavior dispel the stationarity hypothesis. This paper considers an appealing different class of models: a sequence of stationary processes separated by breakpoints. The model selection question is now defined as identifying the breakpoints and fitting the processes in each segment. Experimenting with data from the EGEE/EGI Grid, we found that a non-stationary model can consistently be identified from empirical data, and that limiting the range of models to piecewise affine (autoregressive) time series is sufficiently powerful. We propose and experiment a validation methodology that empirically addresses the current lack of theoretical results concerning the quality of the estimated model parameters. Finally, we present a bootstrapping strategy for building more robust models from the limited samples at hand.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Beran, J.: Statistics for Long-Memory Processes, vol. 61 of Monographs on Statistics and Applied Probability. Chapman and Hall, New York (1994)

    MATH  Google Scholar 

  2. Bhattacharya, R.N., Gupta, V.K., Waymire, E.: The Hurst effect under trends. J. Appl. Probab. 20(3), 649–662 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  3. Breiman L.: Bagging predictors. Mach. Learn. 24(2), 123–140 (1996)

    MathSciNet  MATH  Google Scholar 

  4. Brevik, J., Nurmi, D., Wolski, R.: Predicting bounds on queuing delay in space-shared computing environments. In: IISWC, pp. 213–224 (2006)

  5. Burns, P.J.: Robustness of the Ljung-Box Test and its Rank Equivalent (2002). Available at SSRN: http://ssrn.com/abstract=443560 or doi:10.2139/ssrn.443560

  6. Davis, R.A., Lee, T., Rodriguez-Yam, G.: Structural break estimation for nonstationary time series models. J. Am. Stat. Assoc. 101, 229–239 (2006)

    MathSciNet  Google Scholar 

  7. Diebold, F.X., Inoue, A.: Long memory and regime switching. J. Econom. 105(1), 131–159 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  8. Dinda, P.A., O’Hallaron, D.R.: Host load prediction using linear models. Cluster Comput. 3(4), 265–280 (2000)

    Article  Google Scholar 

  9. Downey A.B.: Using queue time predictions for processor allocation. In: IPPS’97, JSSPP’97, pp. 35–57 (1997)

  10. Efron, B.: Bootstrap. Another look at jackknife. Ann. Stat. 7(1), 1–26 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  11. Elteto, T., Germain Renaud, C., Bondon, P., Sebag, M.: Discovering piecewise linear models of Grid workload. In: 10th IEEE/ACM Int. Symp. on Cluster, Cloud and Grid Computing, pp. 474–484 (2010)

  12. Germain-Renaud, C., et al.: The Grid observatory. In: 11th IEEE/ACM Int. Symp. on Cluster, Cloud and Grid Computing (2011)

  13. Laure, E., et al.: Programming the Grid with gLite. Comput. Methods Sci. Technol. 12(1), 33–45 (2006)

    Google Scholar 

  14. Gagliardi, F., et al.: Building an infrastructure for scientific Grid computing: status and goals of the EGEE project. Philos. Trans. R. Soc. A 1833, 1729–1742 (2005)

    Article  Google Scholar 

  15. Lassnig, M., et al.: Identification, modelling and prediction of non-periodic bursts in workloads. In: 10th IEEE/ACM Int. Symp. on Cluster, Cloud and Grid Computing, pp. 485–494 (2010)

  16. Andreozzi, S., et al.: Glue schema specification, V1.3. Technical report, Open Grid Forum (2008)

  17. Fearnhead, P.: Exact Bayesian curve fitting and signal segmentation. IEEE Trans. Signal Process. 53(6), 2160–2166 (2005)

    Article  MathSciNet  Google Scholar 

  18. Granger, C.W.J., Hyung, N.: Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns. J. Empir. Finance 11(3), 399–421 (2004)

    Article  Google Scholar 

  19. Granger, C.W.J., Joyeux, R.: An introduction to long-memory time series models and fractional differencing. J. Time Ser. Anal. 1(1), 15–29 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  20. Hosking, J.R.M.: Fractional differencing. Biometrika 68(1), 165–176 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  21. Huebscher, M.C., McCann, J.A.: A survey of autonomic computing: degrees, models, and applications. ACM Comput. Surv. 40, 7,1–7,28 (2008)

    Article  Google Scholar 

  22. Gott, R., III.: Implications of the copernican principle for our future prospects. Nature 363, 315–319 (1993)

    Article  Google Scholar 

  23. Ilijašić, L., Saitta, L.: Characterization of a computational Grid as a complex system. In: Procs. of GMAC ’09, pp. 9–18 (2009)

  24. Jha, S., Parashar, M., Rana, O.: Investigating autonomic behaviours in Grid-basedcomputational science applications. In: Proceedings of GMAC’09, pp. 29–38 (2009)

  25. Kitagawa, G., Akaike, H.: A procedure for the modeling of non-stationary time series. Ann. Inst. Stat. Math. 30(1), 351–363 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  26. Lagana, A., et al.: COMPCHEM: Progress towards gems a Grid empowered molecular simulator and beyond. Journal of Grid Computing 8, 571–586 (2010)

    Article  Google Scholar 

  27. Lee, B.-D., Schopf., J. M.: Run-time prediction of parallel applications on shared environments. In: CLUSTER, pp. 487–491 (2003)

  28. Lee, T.-W., Yang, Y.: Bagging binary and quantile predictors for times series. J. Econom. 135(1–2), 465–497 (2006)

    Article  MathSciNet  Google Scholar 

  29. Li, H., Muskulus, M.: Analysis and modeling of job arrivals in a production Grid. SIGMETRICS Perform. Eval. Rev. 34(4), 59–70 (2007)

    Article  Google Scholar 

  30. Lingrand, D., Glatard, T., Montagnat, J.: Modeling the latency on production Grids with respect to the execution context. Parallel Comput. 35, 493–511 (2009)

    Article  Google Scholar 

  31. Macias, M., Rana, O., Smith, G., Guitart, J., Torres, J.: Maximising revenue in Grid markets using an economically enhanced resource manager. Concurrency and Computation: Practice and Experience 22(14), 1990–2011 (2008)

    Article  Google Scholar 

  32. Meng, J., Chakradhar, S.T., Raghunathan, A.: Best-effort parallel execution framework for recognition and mining applications. In: IPDPS, pp. 1–12 (2009)

  33. Mi, N., Casale, G., Cherkasova, L., Smirni, E.: Injecting realistic burstiness to a traditional client-server benchmark. In: Proceedings of ICAC ’09, pp. 149–158 (2009)

  34. Minh, T.N., Wolters, L., Epema D.: A realistic integrated model of parallel system workloads. In: 10th IEEE/ACM Int. Symp. on Cluster, Cloud and Grid Computing, pp. 464–473 (2010)

  35. Mutz, A., Wolski, R., Brevik, J.: Eliciting honest value information in a batch-queue environment. In: Proceedings of GRID ’07, pp. 291–297 (2007)

  36. Nadeem, F., Yousaf, M.M., Prodan, R., Fahringer, T.: Soft benchmarks-based application performance prediction using a minimum training set. In: e-science’06 (2006)

  37. Special issue: EGEE applications and supporting Grid technologies. Journal of Grid Computing 8(3) (2010)

  38. Perez, J., Germain-Renaud, C., Kégl, B., Loomis, C.: Utility-based reinformcement learning for reactive Grids. In: The 5th IEEE ICAC Autonomic Computing (2008)

  39. Perez, J., Germain-Renaud, C., Kégl, B., Loomis, C.: Multi-objective reinforcement learning for responsive Grids. Journal of Grid Computing 8(3), 473–492 (2010)

    Article  Google Scholar 

  40. Pugliese, A., Talia, D., Yahyapour, R.: Modeling and supporting Grid scheduling. Journal of Grid Computing 6(2), 195–213 (2008)

    Article  Google Scholar 

  41. Raman, R., Livny, M., Solomon, M.: Matchmaking: distributed resource management for high throughput computing. In: Procs 7th IEEE Int. Symp. on High Performance Distributed Computing, pp. 140–147 (1998)

  42. Rish, I., Das, R., Tesauro, G., Kephart, J.: Autonomic computing: a new challenge for machine learning. ECML/PKDD tutorial, available online at www.ecmlpkdd2006.org/tutorials.html (2006)

  43. Rissanen, J.: Stochastic Complexity in Statistical Inquiry. World Scientific, Singapore (1989)

    MATH  Google Scholar 

  44. Rogers, E.: Diffusion of Innovations. Free Press, New York (1983)

    Google Scholar 

  45. Skaug, H.J., Tjostheim, D.: Testing for serial independence using measures of distance between densities. In: Robinson, P.M., Rosenblatt, M. (eds.) Athens Conference on Applied Probability and Time Series. Springer Lecture Notes in Statistics, vol. 115 (1996)

  46. Smith, W., Taylor, V.E., Foster, I.T.: Using run-time predictions to estimate queue wait times and improve scheduler performance. In: IPPS/SPDP ’99, JSSPP’99, pp. 202–219 (1999)

  47. Sonmez, O., Yigitbasi, N., Iosup, A., Epema, D.: Trace-based evaluation of job runtime and queue wait time predictions in Grids. In: Proceedings of HPDC ’09 (2009)

  48. Sutton, R.S., Barto, A.G., Williams, R.J.: Reinforcement learning is direct adaptive optimal control. In: American Control Conference, pp. 2143–2146 (1992)

  49. Taqqu, M.S., Teverovsky, V.: Robustness of Whittle-type estimators for time series with long-range dependence. Commun. Stat. Stoch. Models 13(4), 723–757 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  50. Tesauro, G., Jong, N.K., Das, R., Bennani, M.N.: On the use of hybrid reinforcement learning for autonomic resource allocation. Cluster Comput. 10(3), 287–299 (2007)

    Article  Google Scholar 

  51. Tesauro, G.: Reinforcement learning in autonomic computing: a manifesto and case studies. IEEE Int. Comput. 11, 22–30 (2007)

    Article  Google Scholar 

  52. Teverovsky, V., Taqqu, M.: Testing for long-range dependence in the presence of shifting means or a slowly declining trend, using a variance-type estimator. J. Time Ser. Anal. 18(3), 279–304 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  53. Thain, D., Bent, J., Arpaci-Dusseau, A., Arpaci-Dusseau, R., Livny, M.: Gathering at the well: creating communities for Grid i/o. In: Proc. of Supercomputing (2001)

  54. Wolski, R., Spring, N.T., Hayes, J.: Predicting the cpu availability of time-shared unix systems on the computational Grid. Cluster Comput. 3(4), 293–301 (2000)

    Article  Google Scholar 

  55. Yang, L., Schopf, J.M., Foster, I.: Conservative scheduling: using predicted variance to improve scheduling decisions in dynamic environments. In: SC ’03: Proceedings of the 2003 ACM/IEEE conference on Supercomputing, p. 31 (2003)

  56. Yao, Y.-C.: Estimating the number of change-points via Schwarz’ criterion. Stat. Probab. Lett. 6(3), 181–189 (1988)

    Article  MATH  Google Scholar 

  57. Zhang, X., Furtlehner, C., Perez, J., Germain-Renaud, C., Sebag, M.: Toward autonomic Grids: analyzing the job flow with affinity streaming. In: Proc. of the 15th ACM SIGKDD, pp. 987–996 (2009)

Download references

Author information

Authors and Affiliations

  1. University Paris-Sud, INRIA-Saclay and CNRS, Orsay, France

    Tamás Éltető, Cécile Germain-Renaud & Michèle Sebag

  2. Laboratoire des Signaux et Systèmes, Supelec, CNRS, Gif Sur Yvette Cedex, France

    Pascal Bondon

Authors
  1. Tamás Éltető
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cécile Germain-Renaud
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pascal Bondon
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Michèle Sebag
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Cécile Germain-Renaud.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Éltető, T., Germain-Renaud, C., Bondon, P. et al. Towards Non-Stationary Grid Models. J Grid Computing 9, 423–440 (2011). https://doi.org/10.1007/s10723-011-9194-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10723-011-9194-z

Keywords

Search

Navigation