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An introduction to stochastic bin packing-based server consolidation with conflicts

Author

Listed:
  • John Martinovic

    (Technische Universität Dresden)

  • Markus Hähnel

    (Technische Universität Dresden)

  • Guntram Scheithauer

    (Technische Universität Dresden)

  • Waltenegus Dargie

    (Technische Universität Dresden)

Abstract

The energy consumption of large-scale data centers or server clusters is expected to grow significantly in the next couple of years contributing to up to 13% of the worldwide energy demand in 2030. As the involved processing units require a disproportional amount of energy when they are idle, underutilized, or overloaded, balancing the supply of and the demand for computing resources is a key issue to obtain energy-efficient server consolidations. Whereas traditional concepts mostly consider deterministic predictions of the future workloads or only aim at finding approximate solutions, in this article, we propose an exact approach to tackle the problem of assigning jobs with (not necessarily independent) stochastic characteristics to a minimal amount of servers subject to further practically relevant constraints. As a main contribution, the problem under consideration is reformulated as a stochastic bin packing problem with conflicts and modeled by an integer linear program. Finally, this new approach is tested on real-world instances obtained from a Google data center.

Suggested Citation

  • John Martinovic & Markus Hähnel & Guntram Scheithauer & Waltenegus Dargie, 2022. "An introduction to stochastic bin packing-based server consolidation with conflicts," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 296-331, July.
  • Handle: RePEc:spr:topjnl:v:30:y:2022:i:2:d:10.1007_s11750-021-00613-1
    DOI: 10.1007/s11750-021-00613-1
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    References listed on IDEAS

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    1. Valerio de Carvalho, J. M., 2002. "LP models for bin packing and cutting stock problems," European Journal of Operational Research, Elsevier, vol. 141(2), pages 253-273, September.
    2. Oró, Eduard & Depoorter, Victor & Garcia, Albert & Salom, Jaume, 2015. "Energy efficiency and renewable energy integration in data centres. Strategies and modelling review," Renewable and Sustainable Energy Reviews, Elsevier, vol. 42(C), pages 429-445.
    3. P. C. Gilmore & R. E. Gomory, 1961. "A Linear Programming Approach to the Cutting-Stock Problem," Operations Research, INFORMS, vol. 9(6), pages 849-859, December.
    4. John Martinovic & Markus Hähnel & Guntram Scheithauer & Waltenegus Dargie & Andreas Fischer, 2019. "Cutting stock problems with nondeterministic item lengths: a new approach to server consolidation," 4OR, Springer, vol. 17(2), pages 173-200, June.
    5. Martinovic, J. & Scheithauer, G. & Valério de Carvalho, J.M., 2018. "A comparative study of the arcflow model and the one-cut model for one-dimensional cutting stock problems," European Journal of Operational Research, Elsevier, vol. 266(2), pages 458-471.
    6. Maxime C. Cohen & Philipp W. Keller & Vahab Mirrokni & Morteza Zadimoghaddam, 2019. "Overcommitment in Cloud Services: Bin Packing with Chance Constraints," Management Science, INFORMS, vol. 65(7), pages 3255-3271, July.
    7. Fredrick S. Hillier, 1967. "Chance-Constrained Programming with 0-1 or Bounded Continuous Decision Variables," Management Science, INFORMS, vol. 14(1), pages 34-57, September.
    8. L. V. Kantorovich, 1960. "Mathematical Methods of Organizing and Planning Production," Management Science, INFORMS, vol. 6(4), pages 366-422, July.
    9. Nicola Jones, 2018. "How to stop data centres from gobbling up the world’s electricity," Nature, Nature, vol. 561(7722), pages 163-166, September.
    10. Maxence Delorme & Manuel Iori, 2020. "Enhanced Pseudo-polynomial Formulations for Bin Packing and Cutting Stock Problems," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 101-119, January.
    11. Guntram Scheithauer, 2018. "One-Dimensional Cutting Stock," International Series in Operations Research & Management Science, in: Introduction to Cutting and Packing Optimization, chapter 0, pages 73-122, Springer.
    12. John Martinovic & Markus Hähnel & Waltenegus Dargie & Guntram Scheithauer, 2020. "A Stochastic Bin Packing Approach for Server Consolidation with Conflicts," Operations Research Proceedings, in: Janis S. Neufeld & Udo Buscher & Rainer Lasch & Dominik Möst & Jörn Schönberger (ed.), Operations Research Proceedings 2019, pages 159-165, Springer.
    13. Harald Dyckhoff, 1981. "A New Linear Programming Approach to the Cutting Stock Problem," Operations Research, INFORMS, vol. 29(6), pages 1092-1104, December.
    14. Belov, G. & Scheithauer, G., 2006. "A branch-and-cut-and-price algorithm for one-dimensional stock cutting and two-dimensional two-stage cutting," European Journal of Operational Research, Elsevier, vol. 171(1), pages 85-106, May.
    15. Anders S. G. Andrae & Tomas Edler, 2015. "On Global Electricity Usage of Communication Technology: Trends to 2030," Challenges, MDPI, vol. 6(1), pages 1-41, April.
    16. Clautiaux, François & Hanafi, Saïd & Macedo, Rita & Voge, Marie-Émilie & Alves, Cláudio, 2017. "Iterative aggregation and disaggregation algorithm for pseudo-polynomial network flow models with side constraints," European Journal of Operational Research, Elsevier, vol. 258(2), pages 467-477.
    17. Guntram Scheithauer, 2018. "Introduction to Cutting and Packing Optimization," International Series in Operations Research and Management Science, Springer, number 978-3-319-64403-5, April.
    18. Delorme, Maxence & Iori, Manuel & Martello, Silvano, 2016. "Bin packing and cutting stock problems: Mathematical models and exact algorithms," European Journal of Operational Research, Elsevier, vol. 255(1), pages 1-20.
    19. Fabio Furini & Emiliano Traversi, 2019. "Theoretical and computational study of several linearisation techniques for binary quadratic problems," Annals of Operations Research, Springer, vol. 279(1), pages 387-411, August.
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