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April  2016, 12(2): 667-685. doi: 10.3934/jimo.2016.12.667

Effect of energy-saving server scheduling on power consumption for large-scale data centers

Masataka Kato 1, , Hiroyuki Masuyama 1, , Shoji Kasahara 2, and  Yutaka Takahashi 1,

1. 

Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan
2. 

Graduate School of Information Science, Nara Institute of Science and Technology, 8916-5 Takayama, Ikoma, Nara 630-0192

Received  October 2014 Revised  March 2015 Published  June 2015

Large-scale data centers for cloud computing services consist of a number of commodity servers, resulting in a huge amount of power consumption. In order to save power consumption, BEEMR (Berkeley Energy Efficient MapReduce), a MapReduce workload manager, is proposed. In a BEEMR-based data center, servers are allocated to either of the interactive and batch zones. Arriving jobs of a small size begin to be processed immediately in the interactive zone, while large-sized jobs are queued and served simultaneously at every fixed service period in the batch zone. In this paper, we analyze the performance of BEEMR-type job scheduling. We consider two queueing models for the interactive and batch zones. The interactive zone is modeled as a single-server queueing system with processor-sharing (PS) service. In terms of the batch zone, we consider a queueing system with gated service in which arriving jobs are queued and begin to be served when a fixed service period starts. For these models, the time-average power consumption and the mean response time are derived. Numerical examples show that the power consumption is significantly affected by the allocation of servers to both zones, while the power consumption is insensitive to the length of the batch-service period.
Keywords: performance evaluation., energy-saving server scheduling, Data centers, queueing analysis, cloud computing.
Mathematics Subject Classification: Primary: 60K25, 60J27; Secondary: 68M2.
Citation: Masataka Kato, Hiroyuki Masuyama, Shoji Kasahara, Yutaka Takahashi. Effect of energy-saving server scheduling on power consumption for large-scale data centers. Journal of Industrial & Management Optimization, 2016, 12 (2) : 667-685. doi: 10.3934/jimo.2016.12.667
References:
[1]

S. Asmussen, Applied Probability and Queues,, $2^{nd}$ edition, (2003).   Google Scholar

[2]

K. E. Avrachenkov, U. Ayesta, P. Brown and R. Núñez-Queija, Discriminatory processor sharing revisited,, in Proc. IEEE INFOCOM'05, (2005), 784.  doi: 10.1109/INFCOM.2005.1498310.  Google Scholar

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L. A. Barroso and U. Hölzle, The Datacenter as a Computer: An Introduction to the Design of Warehouse-Scale Machines,, Morgan & Claypool, (2009).  doi: 10.2200/S00193ED1V01Y200905CAC006.  Google Scholar

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P. Bremaud, Markov Chains, Gibbs Fields, Monte Carlo Simulation, and Queues,, Springer, (1999).  doi: 10.1007/978-1-4757-3124-8.  Google Scholar

[5]

L. Breuer and D. Baum, An Introduction to Queueing Theory and Matrix-Analytic Methods,, Springer, (2005).   Google Scholar

[6]

R. Brown, E. Masanet, B. Nordman, W. Tschudi, A. Shehabi, J. Stanley, J. Koomey, D. Sartor, P. Chan, J. Loper, S. Capana, B. Hedman, R. Duff, E. Haines, D. Sass and A. Fanara, Report to congress on server and data center energy efficiency: Public law 109-431,, Lawrence Berkeley National Laboratory, (2007).   Google Scholar

[7]

Y. Chen, S. Alspaugh, D. Borthakur and R. Katz, Energy efficiency for large-scale MapReduce workloads with significant interactive analysis,, in Proc. The European Professional Society on Computer Systems 2012, (2012), 43.  doi: 10.1145/2168836.2168842.  Google Scholar

[8]

D. Gibson and E. Seneta, Monotone infinite stochastic matrices and their augmented truncations,, Stochastic Processes and their Applications, 24 (1987), 287.  doi: 10.1016/0304-4149(87)90019-6.  Google Scholar

[9]

H. Masuyama, Error bounds for augmented truncations of discrete-time block-monotone Markov chains under geometric drift conditions,, Accepted for publication in Advances in Applied Probability, ().  doi: 10.1239/aap/1427814582.  Google Scholar

[10]

S. Pelley, D. Meisner, T. F. Wenisch and J. W. VanGilder, Understanding and abstracting total data center power,, in Proc. Workshop on Energy-Efficient Design 2009, (2009).   Google Scholar

[11]

M. Sakata, S. Noguchi and J. Oizumi, An analysis of the M/G/1 queue under round-robin scheduling,, Operations Research, 19 (1971), 371.   Google Scholar

[12]

C. Schwarts, R. Pries and P. Tran-Gia, A queuing analysis of an energy-saving mechanism in data centers,, in Proc. International Conference on Information Networking 2012, (2012), 70.  doi: 10.1109/ICOIN.2012.6164352.  Google Scholar

[13]

R. L. Tweedie, Truncation approximations of invariant measures for Markov chains,, Journal of Applied Probability, 35 (1998), 517.  doi: 10.1239/jap/1032265201.  Google Scholar

[14]

R. W. Wolff, Stochastic Modeling and the Theory of Queues,, Prentice-hall, (1989).   Google Scholar

show all references

References:
[1]

S. Asmussen, Applied Probability and Queues,, $2^{nd}$ edition, (2003).   Google Scholar

[2]

K. E. Avrachenkov, U. Ayesta, P. Brown and R. Núñez-Queija, Discriminatory processor sharing revisited,, in Proc. IEEE INFOCOM'05, (2005), 784.  doi: 10.1109/INFCOM.2005.1498310.  Google Scholar

[3]

L. A. Barroso and U. Hölzle, The Datacenter as a Computer: An Introduction to the Design of Warehouse-Scale Machines,, Morgan & Claypool, (2009).  doi: 10.2200/S00193ED1V01Y200905CAC006.  Google Scholar

[4]

P. Bremaud, Markov Chains, Gibbs Fields, Monte Carlo Simulation, and Queues,, Springer, (1999).  doi: 10.1007/978-1-4757-3124-8.  Google Scholar

[5]

L. Breuer and D. Baum, An Introduction to Queueing Theory and Matrix-Analytic Methods,, Springer, (2005).   Google Scholar

[6]

R. Brown, E. Masanet, B. Nordman, W. Tschudi, A. Shehabi, J. Stanley, J. Koomey, D. Sartor, P. Chan, J. Loper, S. Capana, B. Hedman, R. Duff, E. Haines, D. Sass and A. Fanara, Report to congress on server and data center energy efficiency: Public law 109-431,, Lawrence Berkeley National Laboratory, (2007).   Google Scholar

[7]

Y. Chen, S. Alspaugh, D. Borthakur and R. Katz, Energy efficiency for large-scale MapReduce workloads with significant interactive analysis,, in Proc. The European Professional Society on Computer Systems 2012, (2012), 43.  doi: 10.1145/2168836.2168842.  Google Scholar

[8]

D. Gibson and E. Seneta, Monotone infinite stochastic matrices and their augmented truncations,, Stochastic Processes and their Applications, 24 (1987), 287.  doi: 10.1016/0304-4149(87)90019-6.  Google Scholar

[9]

H. Masuyama, Error bounds for augmented truncations of discrete-time block-monotone Markov chains under geometric drift conditions,, Accepted for publication in Advances in Applied Probability, ().  doi: 10.1239/aap/1427814582.  Google Scholar

[10]

S. Pelley, D. Meisner, T. F. Wenisch and J. W. VanGilder, Understanding and abstracting total data center power,, in Proc. Workshop on Energy-Efficient Design 2009, (2009).   Google Scholar

[11]

M. Sakata, S. Noguchi and J. Oizumi, An analysis of the M/G/1 queue under round-robin scheduling,, Operations Research, 19 (1971), 371.   Google Scholar

[12]

C. Schwarts, R. Pries and P. Tran-Gia, A queuing analysis of an energy-saving mechanism in data centers,, in Proc. International Conference on Information Networking 2012, (2012), 70.  doi: 10.1109/ICOIN.2012.6164352.  Google Scholar

[13]

R. L. Tweedie, Truncation approximations of invariant measures for Markov chains,, Journal of Applied Probability, 35 (1998), 517.  doi: 10.1239/jap/1032265201.  Google Scholar

[14]

R. W. Wolff, Stochastic Modeling and the Theory of Queues,, Prentice-hall, (1989).   Google Scholar

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