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International Conference on Information Technologies and Mathematical Modelling

ITMM 2015: Information Technologies and Mathematical Modelling - Queueing Theory and Applications pp 28–40Cite as

Mean-Field Analysis for Heterogeneous Work Stealing Models

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 564))

Abstract

In this paper, we provide a simple framework for applying the mean-field theory to dealing with a heterogeneous work stealing model of M clusters, each of which consists of N same servers and operates under two types of work stealing schemes: One within a cluster, and another between any two clusters. We first set up an infinite-dimensional system of mean-field equations, which is related to the M clusters. Then we use the martingale limit theory to prove the asymptotic independence of this heterogeneous work stealing model. Finally, we analyze and compute the fixed point, which can give performance analysis of this heterogeneous stealing model.

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References

  1. Anselmi, J., Gaujal, B.: Performance evaluation of a work stealing algorithm for streaming applications. In: Abdelzaher, T., Raynal, M., Santoro, N. (eds.) OPODIS 2009. LNCS, vol. 5923, pp. 1–12. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  2. Benaim, M., Le Boudec, J.Y.: A class of mean field interaction models for computer and communication systems. Perform. Eval. 65(11), 823–838 (2008)

    Article  Google Scholar 

  3. Berenbrink, P., Friedetzky, T., Goldberg, L.: The natural work-stealing algorithm is stable. SIAM J. Comput. 32(5), 1260–1279 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Blumofe, R.D., Leiserson, C.E.: Scheduling multithreaded computations by work stealing. J. ACM 46(5), 720–748 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  5. Blumofe, R.D., Papadopoulos, D.: The performance of work stealing in multiprogrammed environments. ACM SIGMETRICS Perform. Eval. Rev. 26(1), 266–267 (1998)

    Article  Google Scholar 

  6. Darling, R.W.R., Norris, J.R.: Structure of large random hypergraphs. Ann. Appl. Probab. 15(1), 125–152 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Gast, N., Gaujal, B.: A mean field model of work stealing in large-scale systems. ACM SIGMETRICS Perform. Eval. Rev. 38(1), 13–24 (2010)

    Article  Google Scholar 

  8. Harchol-Balter, M., Li, C., Osogami, T., Scheller-Wolf, A., Squillante, M.S.: Analysis of task assignment with cycle stealing under central queue. In: The 23rd International Conference of IEEE on Distributed Computing Systems, pp. 628–637 (2003)

    Google Scholar 

  9. Hendler, D., Shavit, N.: Non-blocking steal-half work queues. In: Proceedings of the Twenty-First Annual Symposium on Principles of Distributed Computing, ACM, pp. 280–289 (2002)

    Google Scholar 

  10. Li, Q.L.: Nonlinear Markov processes in big networks, pp. 1–23 (2015). arXiv:1504.07974

  11. Li, Q.L., Dai, G., Lui, J.C.S., Wang, Y.: The mean-field computation in a supermarket model with server multiple vacations. Discrete Event Dyn. Syst. 24(4), 473–522 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  12. Li, Q.L., Lui, J.C.S.: Block-structured supermarket models. Discrete Event Dynamic Systems, 1–36, 29 June 2014

    Google Scholar 

  13. Lu, Y., Xie, Q., Kliot, G., Geller, A., Larus, J.R., Greenberg, A.: Join-Idle-Queue: a novel load balancing algorithm for dynamically scalable web services. Perform. Eval. 68(11), 1056–1071 (2011)

    Article  Google Scholar 

  14. Minnebo, W., Van Houdt, B.: A fair comparison of pull and push strategies in large distributed networks. IEEE/ACM Trans. Netw. 22(3), 996–1006 (2014)

    Article  Google Scholar 

  15. Mitzenmacher, M.D.: The power of two choices in randomized load balancing. Ph.D. thesis, Department of Computer Science, University of California at Berkeley, USA (1996)

    Google Scholar 

  16. Mitzenmacher, M.D.: Analyses of load stealing models based in di erential equations. In: The 10th ACM Symposium on Parallel Algorithms and Architectures, pp. 212–221 (1998)

    Google Scholar 

  17. Osogami, T., Harchol-Balter, M., Scheller-Wolf, A.: Analysis of cycle stealing with switching cost. J. ACM 31(1), 184–195 (2003)

    Google Scholar 

  18. Rogers, L.C.G., Williams, D.: Diffusions, Markov Processes, and Martingales 2: Itô Calculus. Wiley, New York (1987)

    MATH  Google Scholar 

  19. Squillante, M.S.: Stochastic analysis of multiserver systems. ACM SIGMETRICS Perform. Eval. Rev. 34(4), 44–51 (2007)

    Article  Google Scholar 

  20. Squillante, M.S., Nelson, R.: Analysis of task migration in shared-memory multiprocessor scheduling. J. ACM 19(1), 143–155 (1991)

    Google Scholar 

  21. Vvedenskaya, N.D., Dobrushin, R.L., Karpelevich, F.I.: Queueing system with selection of the shortest of two queues: an asymptotic approach. Probl. Inf. Transmissions 32(1), 20–34 (1996)

    MATH  Google Scholar 

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Acknowledgement

This work is partly supported by the National Natural Science Foundation of China under grant (#71271187, #71471160), and the Fostering Plan of Innovation Team and Leading Talent in Hebei Universities under grant (# LJRC027).

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Authors and Affiliations

  1. School of Economics and Management Sciences, Yanshan University, Qinhuangdao, China

    Quan-Lin Li & Feifei Yang

Authors
  1. Quan-Lin Li
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  2. Feifei Yang
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Corresponding author

Correspondence to Quan-Lin Li .

Editor information

Editors and Affiliations

  1. Applied Mathematics and Computer Science, Belarusian State University, Minsk, Russia

    Alexander Dudin

  2. Tomsk State University, Tomsk, Russia

    Anatoly Nazarov

  3. Kemerovo State University, Anzhero-Sudzhensk, Russia

    Rafael Yakupov

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Li, QL., Yang, F. (2015). Mean-Field Analysis for Heterogeneous Work Stealing Models. In: Dudin, A., Nazarov, A., Yakupov, R. (eds) Information Technologies and Mathematical Modelling - Queueing Theory and Applications. ITMM 2015. Communications in Computer and Information Science, vol 564. Springer, Cham. https://doi.org/10.1007/978-3-319-25861-4_3

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  • DOI: https://doi.org/10.1007/978-3-319-25861-4_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25860-7

  • Online ISBN: 978-3-319-25861-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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