Skip to main content
SpringerLink
Log in

Optimal Threshold Policies for Robust Data Center Control

  • Published:
Journal of Shanghai Jiaotong University (Science) Aims and scope Submit manuscript

Abstract

With the simultaneous rise of energy costs and demand for cloud computing, efficient control of data centers becomes crucial. In the data center control problem, one needs to plan at every time step how many servers to switch on or off in order to meet stochastic job arrivals while trying to minimize electricity consumption. This problem becomes particularly challenging when servers can be of various types and jobs from different classes can only be served by certain types of server, as it is often the case in real data centers. We model this problem as a robust Markov decision process (i.e., the transition function is not assumed to be known precisely). We give sufficient conditions (which seem to be reasonable and satisfied in practice) guaranteeing that an optimal threshold policy exists. This property can then be exploited in the design of an efficient solving method, which we provide. Finally, we present some experimental results demonstrating the practicability of our approach and compare with a previous related approach based on model predictive control.

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.

Similar content being viewed by others

References

  1. KAPLAN J M, FOREST W, KINDLER N. Revolutionizing data center energy efficiency [R]. Chicago: McKinsey & Company, 2008.

    Google Scholar 

  2. MASTROLEON L, BAMBOS N, KOZYRAKIS C, et al. Automatic power management schemes for Internet servers and data centers [C]//Global Telecommunications Conference, 2005. Missouri: IEEE, 2005: 1–5.

    Google Scholar 

  3. PAROLINI L, SINOPOLI B, KROGH B H. Reducing data center energy consumption via coordinated cooling and load management [C]//Proceedings of the Conference on Power Aware Computing and Systems. [s.l.]: USENIX Association, 2008: 1–5.

    Google Scholar 

  4. PAROLINI L, SINOPOLI B, KROGH B H, et al. A cyber-physical systems approach to data center modeling and control for energy efficiency [J]. Proceedings of the IEEE, 2011, 100(1): 254–268.

    Article  Google Scholar 

  5. YIN X, SINOPOLI B. Adaptive robust optimization for coordinated capacity and load control in data centers [C]// the International Conference on Decision and Control. [s.l.]: IEEE, 2014: 5674–5679.

    Google Scholar 

  6. FEINBERG E, ZHANG X. Optimizing cloud utilization via switching decisions [J]. Performance Evaluation Review, 2014, 41(4): 57–60.

    Article  Google Scholar 

  7. LUBIN B, KEPHART J O, DAS R, et al. Expressive power-based resource allocation for data centers [C]//International Joint Conference on Artificial Intelligence. Pasadena, California: Morgan Kaufmann Publishers Inc., 2009: 1451–1456.

    Google Scholar 

  8. BOD’IK P. Automating datacenter operations using machine learning [D]. Berkeley: University of California, Berkeley, 2010.

    Google Scholar 

  9. GAO J. Machine learning applications for data center optimization [EB/OL]. (2014-10-27) [2017-09-25]. https://www.cse.iitk.ac.in/users/cs300/2014/home/~ratnesh/cs300A/techpaper-review/5A.pdf.

    Google Scholar 

  10. GHASEMI M, LUBIN B. Modeling multi-attribute demand for sustainable cloud computing with copulae [C]//International Conference on Artificial Intelligence. Buenos Aires, Argentina: AAAI Press, 2015: 2596–2602.

    Google Scholar 

  11. HORDIJK A, SCHOUTEN F V D D. On the optimality of (s, S)-policies in continuous review inventory models [J]. SIAM Journal on Applied Mathematics, 1986, 46(5): 912–929.

    Article  MathSciNet  MATH  Google Scholar 

  12. KALIN D. On the optimality of (_, s)-policies [J]. Mathematics of Operations Research, 1980, 5(2): 293–307.

    Article  MathSciNet  MATH  Google Scholar 

  13. HYON E, JEAN-MARIE A. Scheduling services in a queueing system with impatience and setup costs [J]. The Computer Journal, 2012, 55(5): 553–563.

    Article  Google Scholar 

  14. FOX M, LONG D, MAGAZZENI D. Automatic construction of efficient multiple battery usage policies [C]//International Joint Conference on Artificial Intelligence. Freiburg: AAAI Press, 2011: 2620–2625.

    Google Scholar 

  15. PETRIK M, WU X. Optimal threshold control for energy arbitrage with degradable battery storage [C]//Conference on Uncertainty in Artificial Intelligence. Amsterdam: AUAI Press, 2015: 692–701.

    Google Scholar 

  16. ERSEGHE T, ZANELLA A, CODEMO C. Markov decision processes with threshold based piecewise linear optimal policies [J]. IEEE Wireless Communication Letters, 2013, 2(4): 459–462.

    Article  Google Scholar 

  17. KOOLE G. Monotonicity in Markov reward and decision chains: Theory and applications [J]. Foundations & Trends® in Stochastic Systems, 2007, 1(1):1–76.

    Article  MathSciNet  MATH  Google Scholar 

  18. VEINOTT A. Optimal policy for a multi-product, dynamic, nonstationary inventory problem [J]. Management science, 1965, 12(3): 206–222.

    Article  MathSciNet  MATH  Google Scholar 

  19. JUAN D C, LI L, PENG H K, et al. Beyond Poisson: Modeling inter-arrival time of requests in a datacenter [C]//Pacific-Asia Conference on Knowledge Discovery and Data Mining. China, Taiwan: Springer, 2014: 198–209.

    Chapter  Google Scholar 

  20. GIVAN R, LEACH S M, DEAN T. Bounded parameter Markov decision processes [J]. Artificial Intelligence, 2000, 122(1/2): 71–109.

    Article  MathSciNet  MATH  Google Scholar 

  21. NILIM A, GHAOUI L E. Robustness in Markov decision problems with uncertain transition matrices [C]//Advances in Neural Information Processing Systems 16 (NIPS 2003). Vancouver and Whistler, British Columbia: NIPS, 2003: 1–8.

    Google Scholar 

  22. PUTERMAN M L. Markov decision processes: Discrete stochastic dynamic programming [M]. America: John Wiley & Sons, 1994: 1–353.

    MATH  Google Scholar 

  23. LITTMAN M L, DEAN T L, KAELBLING L P. On the complexity of solving Markov decision problems [C]//11th Conference on Uncertainty in Artificial Intelligence. San Francisco: Morgan Kaufmann Publishers, 1995: 394–402.

    Google Scholar 

  24. Index of /other/pageviews/2015/ [EB/OL]. (2016-12-30) [2017-09-25]. https://dumps.wikimedia.org/other/ pageviews/2015/

  25. SUROVIK D A, SCHEERES D J. Heuristic search and receding-horizon planning in complex spacecraft orbit domains [C]//Proceeding of the 25th International Joint Conference on Artificial Intelligence. Jerusalem, Israel: AAAI Press, 2015: 291–295.

    Google Scholar 

  26. WIERING M, OTTERLO M V. Reinforcement Learning: State-of-the-Art [M]. Germany: Springer Publishing Company, Incorporated, 2012: 1–650.

    Book  Google Scholar 

  27. HADOUX E, BEYNIER A, WENG P. Solving hidden-semi-Markov-mode Markov decision problems [C]//International Conference on Scalable Uncertainty Management. New York: Springer-Verlag. 2014: 176–189.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. SYSU-CMU Joint Institute of Engineering, School of Electronics and Information Technology, Sun Yat-sen University, Guangzhou, 510275, China

    Paul Weng

  2. SYSU-CMU Joint Research Institute, Shunde 528300, Guangdong, China

    Paul Weng

  3. Department of Electrical & Computer Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213, USA

    Zeqi Qiu  (邱泽麒), John Costanzo, Xiaoqi Yin  (阴小骐) & Bruno Sinopoli

Authors
  1. Paul Weng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zeqi Qiu  (邱泽麒)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. John Costanzo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiaoqi Yin  (阴小骐)
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Bruno Sinopoli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Paul Weng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Weng, P., Qiu, Z., Costanzo, J. et al. Optimal Threshold Policies for Robust Data Center Control. J. Shanghai Jiaotong Univ. (Sci.) 23, 52–60 (2018). https://doi.org/10.1007/s12204-018-1909-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12204-018-1909-x

Key words

CLC number

Search

Navigation