A Tighter Analysis of Work Stealing

  • Marc Tchiboukdjian
  • Nicolas Gast
  • Denis Trystram
  • Jean-Louis Roch
  • Julien Bernard
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6507)


Classical list scheduling is a very popular and efficient technique for scheduling jobs in parallel platforms. However, with the increasing number of processors, the cost for managing a single centralized list becomes prohibitive. The objective of this work is to study the extra cost that must be paid when the list is distributed among the processors. We present a general methodology for computing the expected makespan based on the analysis of an adequate potential function which represents the load unbalance between the local lists. A bound on the deviation from the mean is also derived. Then, we apply this technique to show that the expected makespan for scheduling W unit independent tasks on m processors is equal to W/m with an additional term in 3.65log2 W. Moreover, simulations show that our bound is very close to the exact value, approximately 50% off. This new analysis also enables to study the influence of the initial repartition of tasks and the reduction of the number of steals when several thieves can simultaneously steal work in the same processor’s list.


Markov Decision Process List Schedule Independent Task Precedence Graph Load Unbalance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Graham, R.L.: Bounds on multiprocessing timing anomalies. SIAM Journal on Applied Mathematics 17, 416–429 (1969)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Hoffmann, R., Korch, M., Rauber, T.: Performance evaluation of task pools based on hardware synchronization. In: Proc. of Supercomputing (2004)Google Scholar
  3. 3.
    Frigo, M., Leiserson, C.E., Randall, K.H.: The implementation of the Cilk-5 multithreaded language. In: Proceedings of PLDI (1998)Google Scholar
  4. 4.
    Robison, A., Voss, M., Kukanov, A.: Optimization via reflection on work stealing in TBB. In: Proceedings of IPDPS, pp. 1–8 (2008)Google Scholar
  5. 5.
    Gautier, T., Besseron, X., Pigeon, L.: KAAPI: A thread scheduling runtime system for data flow computations on cluster of multi-processors. In: Proceedings of PASCO, pp. 15–23 (2007)Google Scholar
  6. 6.
    Blumofe, R.D., Leiserson, C.E.: Scheduling multithreaded computations by work stealing. Journal of the ACM 46(5), 720–748 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Arora, N.S., Blumofe, R.D., Plaxton, C.G.: Thread scheduling for multiprogrammed multiprocessors. Theory of Computing Systems 34(2), 115–144 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Berenbrink, P., Friedetzky, T., Goldberg, L.A.: The natural work-stealing algorithm is stable. SIAM Journal of Computing 32(5), 1260–1279 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Mitzenmacher, M.: Analyses of load stealing models based on differential equations. In: Proceedings of SPAA, pp. 212–221 (1998)Google Scholar
  10. 10.
    Hendler, D., Shavit, N.: Non-blocking steal-half work queues. In: Proceedings of PODC (2002)Google Scholar
  11. 11.
    Gast, N., Gaujal, B.: A Mean Field Model of Work Stealing in Large-Scale Systems. In: Proceedings of SIGMETRICS (2010)Google Scholar
  12. 12.
    Berenbrink, P., Friedetzky, T., Goldberg, L.A., Goldberg, P.W., Hu, Z., Martin, R.: Distributed selfish load balancing. SIAM Journal on Computing 37(4) (2007)Google Scholar
  13. 13.
    Traoré, D., Roch, J.L., Maillard, N., Gautier, T., Bernard, J.: Deque-free work-optimal parallel STL algorithms. In: Luque, E., Margalef, T., Benítez, D. (eds.) Euro-Par 2008. LNCS, vol. 5168, pp. 887–897. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  14. 14.
    Puterman, M.L.: Markov Decision Processes : Discrete Stochastic Dynamic Programming. Wiley, Chichester (2005)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Marc Tchiboukdjian
    • 1
  • Nicolas Gast
    • 1
  • Denis Trystram
    • 1
  • Jean-Louis Roch
    • 1
  • Julien Bernard
    • 2
  1. 1.Grenoble UniversityFrance
  2. 2.Université de Franche-ComtéFrance

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