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Analysis of an M/M/1 queue with vacations and impatience timers which depend on the server's states
Effect of energy-saving server scheduling on power consumption for large-scale data centers
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 |
References:
[1] |
S. Asmussen, Applied Probability and Queues, $2^{nd}$ edition, Springer, New York, 2003. |
[2] |
K. E. Avrachenkov, U. Ayesta, P. Brown and R. Núñez-Queija, Discriminatory processor sharing revisited, in Proc. IEEE INFOCOM'05, (2005), 784-795.
doi: 10.1109/INFCOM.2005.1498310. |
[3] |
L. A. Barroso and U. Hölzle, The Datacenter as a Computer: An Introduction to the Design of Warehouse-Scale Machines, Morgan & Claypool, California, 2009.
doi: 10.2200/S00193ED1V01Y200905CAC006. |
[4] |
P. Bremaud, Markov Chains, Gibbs Fields, Monte Carlo Simulation, and Queues, Springer, New York, 1999.
doi: 10.1007/978-1-4757-3124-8. |
[5] |
L. Breuer and D. Baum, An Introduction to Queueing Theory and Matrix-Analytic Methods, Springer, New York, 2005. |
[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, LBNL-363E, 2007. |
[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), 43-56.
doi: 10.1145/2168836.2168842. |
[8] |
D. Gibson and E. Seneta, Monotone infinite stochastic matrices and their augmented truncations, Stochastic Processes and their Applications, 24 (1987), 287-292.
doi: 10.1016/0304-4149(87)90019-6. |
[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, available online at: http://infosys.sys.i.kyoto-u.ac.jp/~masuyama/papers/ap14504.pdf.
doi: 10.1239/aap/1427814582. |
[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). |
[11] |
M. Sakata, S. Noguchi and J. Oizumi, An analysis of the M/G/1 queue under round-robin scheduling, Operations Research, 19 (1971), 371-385. |
[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), 70-75.
doi: 10.1109/ICOIN.2012.6164352. |
[13] |
R. L. Tweedie, Truncation approximations of invariant measures for Markov chains, Journal of Applied Probability, 35 (1998), 517-536.
doi: 10.1239/jap/1032265201. |
[14] |
R. W. Wolff, Stochastic Modeling and the Theory of Queues, Prentice-hall, Englewood Cliffs, NJ, 1989. |
show all references
References:
[1] |
S. Asmussen, Applied Probability and Queues, $2^{nd}$ edition, Springer, New York, 2003. |
[2] |
K. E. Avrachenkov, U. Ayesta, P. Brown and R. Núñez-Queija, Discriminatory processor sharing revisited, in Proc. IEEE INFOCOM'05, (2005), 784-795.
doi: 10.1109/INFCOM.2005.1498310. |
[3] |
L. A. Barroso and U. Hölzle, The Datacenter as a Computer: An Introduction to the Design of Warehouse-Scale Machines, Morgan & Claypool, California, 2009.
doi: 10.2200/S00193ED1V01Y200905CAC006. |
[4] |
P. Bremaud, Markov Chains, Gibbs Fields, Monte Carlo Simulation, and Queues, Springer, New York, 1999.
doi: 10.1007/978-1-4757-3124-8. |
[5] |
L. Breuer and D. Baum, An Introduction to Queueing Theory and Matrix-Analytic Methods, Springer, New York, 2005. |
[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, LBNL-363E, 2007. |
[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), 43-56.
doi: 10.1145/2168836.2168842. |
[8] |
D. Gibson and E. Seneta, Monotone infinite stochastic matrices and their augmented truncations, Stochastic Processes and their Applications, 24 (1987), 287-292.
doi: 10.1016/0304-4149(87)90019-6. |
[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, available online at: http://infosys.sys.i.kyoto-u.ac.jp/~masuyama/papers/ap14504.pdf.
doi: 10.1239/aap/1427814582. |
[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). |
[11] |
M. Sakata, S. Noguchi and J. Oizumi, An analysis of the M/G/1 queue under round-robin scheduling, Operations Research, 19 (1971), 371-385. |
[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), 70-75.
doi: 10.1109/ICOIN.2012.6164352. |
[13] |
R. L. Tweedie, Truncation approximations of invariant measures for Markov chains, Journal of Applied Probability, 35 (1998), 517-536.
doi: 10.1239/jap/1032265201. |
[14] |
R. W. Wolff, Stochastic Modeling and the Theory of Queues, Prentice-hall, Englewood Cliffs, NJ, 1989. |
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