Advertisement

Discrete Event Dynamic Systems

, Volume 29, Issue 4, pp 567–606 | Cite as

Optimal energy-efficient policies for data centers through sensitivity-based optimization

  • Jing-Yu Ma
  • Li XiaEmail author
  • Quan-Lin Li
Article
  • 33 Downloads

Abstract

In this paper, we propose a novel dynamic decision method by applying the sensitivity-based optimization theory to find the optimal energy-efficient policy of a data center with two groups of heterogeneous servers. Servers in Group 1 always work at high energy consumption, while servers in Group 2 may either work at high energy consumption or sleep at low energy consumption. An energy-efficient control policy determines the switch between work and sleep states of servers in Group 2 in a dynamic way. Since servers in Group 1 are always working with high priority to jobs, a transfer rule is proposed to migrate the jobs in Group 2 to idle servers in Group 1. To find the optimal energy-efficient policy, we set up a policy-based Poisson equation, and provide explicit expressions for its unique solution of performance potentials by means of the RG-factorization. Based on this, we characterize monotonicity and optimality of the long-run average profit with respect to the policies under different service prices. We prove that the bang-bang control is always optimal for this optimization problem, i.e., we should either keep all servers sleep or turn on the servers such that the number of working servers equals that of waiting jobs in Group 2. As an easy adoption of policy forms, we further study the threshold-type policy and obtain a necessary condition of the optimal threshold policy. We hope the methodology and results derived in this paper can shed light to the study of more general energy-efficient data centers.

Keywords

Queueing Data center Energy-efficient policies Sensitivity-based optimization Markov decision process 

Notes

Acknowledgments

Li Xia was supported by the National Key Research and Development Program of China (2016YFB0901900, 2017YFC0704100), the National Natural Science Foundation of China under grant No. 61573206 and No. 11931018, the National 111 International Collaboration Project (B06002), and Tsinghua-Tencent Cooperation Research Project.

Quan-Lin Li was supported by the National Natural Science Foundation of China under grant No. 71932002, No. 71671158 and No. 71471160, and by the Natural Science Foundation of Hebei province under grant No. G2017203277.

References

  1. Barroso LA, Hölzle U (2007) The case for energy-proportional computing. Computer 40(12):33–37Google Scholar
  2. Benini L, Bogliolo A, De Micheli G (2000) A survey of design techniques for system-level dynamic power management. IEEE Trans Very Large Scale Integr VLSI Syst 8(3):299–316Google Scholar
  3. Becker R, Zilberstein S, Lesser V (2004) Decentralized Markov decision processes with event-driven interactions. In: Proceedings of the 3rd international joint conference on autonomous agents and multiagent systems, vol 1, 302–309Google Scholar
  4. Bell C E (1980) Optimal operation of an M/M/2 queue with removable servers. Oper Res 28(5):1189– 1204MathSciNetzbMATHGoogle Scholar
  5. Bodenstein C, Schryen G, Neumann D (2012) Energy-aware workload management models for operation cost reduction in data centers. Eur J Oper Res 222 (1):157–167Google Scholar
  6. Cao XR (2007) Stochastic learning and optimization—A sensitivity-based approach. Springer, New YorkzbMATHGoogle Scholar
  7. Chen X, Wardi Y, Yalamanchili S (2018) Instruction-throughput regulation in computer processors with data-center applications. Discrete Event Dynamic Systems: Theory and Applications 28(1):127–158MathSciNetzbMATHGoogle Scholar
  8. De Napoli C, Forestiero A, Lagana D, Lupi G, Mastroianni C, Spataro L (2016) Business scenarios for geographically distributed data centers. RT-ICAR-CS-16-03Google Scholar
  9. Engel Y, Etzion O (2011) Towards proactive event-driven computing. In: Proceedings of the 5th ACM international conference on distributed event-based system, pp 125–136Google Scholar
  10. Gandhi A (2013) Dynamic server provisioning for data center power management. Ph.D. Thesis, School of Computer Science Carnegie Mellon University, Pittsburgh, USAGoogle Scholar
  11. Gandhi A, Doroudi S, Harchol-Balter M, Scheller-Wolf A (2014) Exact analysis of the M/M/k/setup class of Markov chains via recursive renewal reward. Queueing Systems 77(2):177–209MathSciNetzbMATHGoogle Scholar
  12. Gandhi A, Gupta V, Harchol-Balter M, Kozuch M A (2010a) Optimality analysis of energy-performance trade-off for server farm management. Perform Eval 67 (11):1155–1171Google Scholar
  13. Gandhi A, Harchol-Balter M (2013) M/G/k with staggered setup. Oper Res Lett 41(4):317–320MathSciNetzbMATHGoogle Scholar
  14. Gandhi A, Harchol-Balter M, Adan I (2010b) Server farms with setup costs. Perform Eval 67(11):1123– 1138Google Scholar
  15. Gandhi A, Harchol-Balter M, Kozuch MA (2012) Are sleep states effective in data centers? In: 2012 international green computing conference (IGCC), pp 1–10Google Scholar
  16. Gebrehiwot M E, Aalto S, Lassila P (2016) Optimal energy-aware control policies for FIFO servers. Perform Eval 103:41–59zbMATHGoogle Scholar
  17. Gebrehiwot M E, Aalto S, Lassila P (2016) Energy-performance trade-off for processor sharing queues with setup delay. Oper Res Lett 44(1):101–106MathSciNetzbMATHGoogle Scholar
  18. Gebrehiwot M E, Aalto S, Lassila P (2017) Energy-aware SRPT server with batch arrivals: Analysis and optimization. Perform Eval 115:92–107zbMATHGoogle Scholar
  19. Hassin R, Shaki Y Y, Yovel U (2015) Optimal service-capacity allocation in a loss system. Nav Res Logist 62(2):81–97MathSciNetzbMATHGoogle Scholar
  20. Hipp S K, Holzbaur U D (1988) Decision processes with monotone hysteretic policies. Oper Res 36(4):585–588MathSciNetzbMATHGoogle Scholar
  21. Huang L, Neely M J (2013) Utility optimal scheduling in energy-harvesting networks. IEEE/ACM Trans Netw 21(4):1117–1130Google Scholar
  22. Hong K S, Lee C (2013) Integrated pricing and capacity decision for a telecommunication service provider. Multimed Tools Appl 64(2):389–406Google Scholar
  23. Hunter J J (1982) Generalized inverses and their application to applied probability problems. Linear Algebra Appl 45:157–198MathSciNetzbMATHGoogle Scholar
  24. Kamitsos I, Andrew L, Kim H, Chiang M (2010) Optimal sleep patterns for serving delay-tolerant jobs. In: Poceedings of the 1st international conference on energy-efficient computing and networking, pp 31–40Google Scholar
  25. Kamitsos I, Andrew L, Kim H, Ha S (2012) Better energy-delay tradeoff via server resource pooling. In: The 2012 international conference on computing, networking and communications, pp 611–616Google Scholar
  26. Kamitsos I, Ha S, Andrew L, Bawa J, Butnariu D, Kim H, Chiang M (2017) Optimal sleeping: models and experiments for energy-delay tradeoff. International Journal of Systems Science: Operations & Logistics 4(4):356–371Google Scholar
  27. Kliazovich D, Bouvry P, Khan S U (2012) GreenCloud: a packet-level simulator of energy-aware cloud computing data centers. J Supercomput 62(3):1263–1283Google Scholar
  28. Koole G (1998) Structural results for the control of queueing systems using event-based dynamic programming. Queueing Systems 30(3–4):323–339MathSciNetzbMATHGoogle Scholar
  29. Kuehn P J, Mashaly M E (2015) Automatic energy efficiency management of data center resources by load-dependent server activation and sleep modes. Ad Hoc Netw 25 (Part B):497–504Google Scholar
  30. Li QL (2010) Constructive computation in stochastic models with applications: The RG-factorizations. SpringerGoogle Scholar
  31. Li Q L, Cao J (2004) Two types of RG-factorizations of quasi-birth-and-death processes and their applications to stochastic integral functionals. Stoch Model 20 (3):299–340MathSciNetzbMATHGoogle Scholar
  32. Li QL, Ma JY, Xie MZ, Xia L (2017) Group-server queues. In: International conference on queueing theory and network applications, pp 49–72Google Scholar
  33. Lu F V, Serfozo R F (1984) M/M/1 queueing decision processes with monotone hysteretic optimal policies. Oper Res 32(5):1116–1132MathSciNetzbMATHGoogle Scholar
  34. Ma J Y, Li Q L, Xia L (2019) Optimal asynchronous dynamic policies in energy-efficient data centers. arXiv:1901.03371, pp 1–63
  35. Maccio V J, Down D G (2015) On optimal policies for energy-aware servers. Perform Eval 90:36–52Google Scholar
  36. Maccio V J, Down D G (2018) Structural properties and exact analysis of energy-aware multiserver queueing systems with setup times. Perform Eval 121:48–66Google Scholar
  37. Maccio VJ, Down DG (2018) Asymptotic performance of energy-aware multiserver queueing systems with setup times. In: 2018 annual american control conference, pp 6266–6272Google Scholar
  38. Mazzucco M, Dyachuk D, Deters R (2010) Maximizing cloud providers revenues via energy aware allocation policies. In: IEEE international conference on cloud computing, pp 131–138Google Scholar
  39. Mitrani I (2011) Service center trade-offs between customer impatience and power consumption. Perform Eval 68(11):1222–1231Google Scholar
  40. Mitrani I (2013) Managing performance and power consumption in a server farm. Ann Oper Res 202(1):121–134MathSciNetzbMATHGoogle Scholar
  41. Natural Resources Defense Council (2016) Environmental issues [Online]. Available: https://www.nrdc.org/resources/americas-data-centers-consuming-and-wasting-growing-amounts-energy
  42. Phung-Duc T (2015) Multiserver queues with finite capacity and setup time. In: International conference on analytical and stochastic modeling techniques and applications, Springer, pp 173–187Google Scholar
  43. Phung-Duc T (2017) Exact solutions for M/M/c/setup queues. Telecommun Syst 64(2):309–324Google Scholar
  44. Phung-Duc T, Ren Y, Chen JC, Yu ZW (2016) Design and analysis of deadline and budget constrained autoscaling (DBCA) algorithm for 5G mobile networks. In: 2016 IEEE international conference on cloud computing technology and science (CloudCom), pp 94–101Google Scholar
  45. Puterman ML (2014) Markov decision processes: discrete stochastic dynamic programming. John Wiley & SonsGoogle Scholar
  46. Qiu Q, Pedram M (1999) Dynamic power management based on continuous-time Markov decision processes. In: Proceedings of the 36th annual ACM/IEEE design automation conference, pp 555– 561Google Scholar
  47. Qiu Q, Qu Q, Pedram M (2001) Stochastic modeling of a power-managed system-construction and optimization. IEEE Trans Comput Aided Des Integr Circuits Syst 20(10):1200–1217Google Scholar
  48. Ren Y, Phung-Duc T, Chen JC, Yu ZW (2016) Dynamic auto scaling algorithm (DASA) for 5G mobile networks. In: 2016 IEEE global communications conference (GLOBECOM), pp 1–6Google Scholar
  49. Ren Y, Phung-Duc T, Liu YK, Chen JC, Lin YH (2018) ASA: Adaptive VNF scaling algorithm for 5G mobile networks. In: 2018 IEEE 7th international conference on cloud networking (CloudNet), pp 1–4Google Scholar
  50. Schwartz C, Pries R, Tran-Gia P (2012) A queuing analysis of an energy-saving mechanism in data centers. In: The international conference on information network (ICOIN), pp 70–75Google Scholar
  51. Shehabi A, Smith S, Sartor D et al (2016) United States data center energy usage report. Lawrence Berkely LabGoogle Scholar
  52. Šimunić T, Benini L, Glynn P, De Micheli G (2001) Event-driven power management. IEEE Trans Comput Aided Des Integr Circuits Syst 20(7):840–857Google Scholar
  53. Tan Y, Lu Y, Xia C H (2012) Provisioning for large scale loss network systems with applications in cloud computing. ACM Sigmetrics Performance Evaluation Review 40(3):83–85Google Scholar
  54. van der Laan D (2018) Assigning multiple job types to parallel specialized servers. Discrete Event Dyn Syst 28(4):471–507MathSciNetzbMATHGoogle Scholar
  55. Xia L (2014) Service rate control of closed Jackson networks from game theoretic perspective. Eur J Oper Res 237(2):546–554MathSciNetzbMATHGoogle Scholar
  56. Xia L (2014) Event-based optimization of admission control in open queueing networks. Discrete Event Dynamic Systems: Theory and Applications 24(2):133–151MathSciNetzbMATHGoogle Scholar
  57. Xia L, Cao X R (2012) Performance optimization of queueing systems with perturbation realization. Eur J Oper Res 218(2):293–304MathSciNetzbMATHGoogle Scholar
  58. Xia L, Chen S (2018) Dynamic pricing control for open queueing networks. IEEE Trans Autom Control 63(10):3290–3300MathSciNetzbMATHGoogle Scholar
  59. Xia L, He Q M, Alfa A S (2017) Optimal control of state-dependent service rates in a MAP/M/1 queue. IEEE Trans Autom Control 62(10):4965–4979MathSciNetzbMATHGoogle Scholar
  60. Xia L, Jia Q S (2015) Parameterized Markov decision process and its application to service rate control. Automatica 54:29–35MathSciNetzbMATHGoogle Scholar
  61. Xia L, Jia Q S, Cao X R (2014) A tutorial on event-based optimization——A new optimization framework. Discrete Event Dynamic Systems: Theory and Applications 24(2):103–132MathSciNetzbMATHGoogle Scholar
  62. Xia L, Miller D, Zhou Z, Bambos N (2017) Service rate control of tandem queues with power constraints. IEEE Trans Autom Control 62(10):5111–5123MathSciNetzbMATHGoogle Scholar
  63. Xia L, Shihada B (2013) Max-min optimality of service rate control in closed queueing networks. IEEE Trans Autom Control 58(4):1051–1056MathSciNetzbMATHGoogle Scholar
  64. Xia L, Shihada B (2015) A Jackson network model and threshold policy for joint optimization of energy and delay in multi-hop wireless networks. Eur J Oper Res 242 (3):778–787MathSciNetzbMATHGoogle Scholar
  65. Yadin M, Naor P (1963) Queueing systems with a removable service station. J Oper Res Soc 14(4):393– 405Google Scholar
  66. Yang J, Zhang S, Wu X, Ran Y, Xi H (2017) Online learning-based server provisioning for electricity cost reduction in data center. IEEE Trans Control Syst Technol 25(3):1044–1051Google Scholar
  67. Yao Y, Huang L, Sharma A B, Golubchik L, Neely M J (2014) Power cost reduction in distributed data centers: A two-time-scale approach for delay tolerant workloads. IEEE Trans Parallel Distrib Syst 25(1):200–211Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Economics and ManagementYanshan UniversityQinhuangdaoChina
  2. 2.Business SchoolSun Yat-Sen UniversityGuangzhouChina
  3. 3.School of Economics and ManagementBeijing University of TechnologyBeijingChina

Personalised recommendations