Obtaining Optimal Thresholds for Processors with Speed-Scaling
Pages 135 - 155
Abstract
In this research we consider a processor that can operate at multiple speeds and suggest a strategy for optimal speed-scaling. While higher speeds improve latency, they also draw a lot of power. Thus we adopt a threshold-based policy that uses higher speeds under higher workload conditions, and vice versa. However, it is unclear how to select "optimal" thresholds. For that we use a stochastic fluid-flow model with varying processing speeds based on fluid level.First, given a set of thresholds, we develop an approach based on spectral expansion by modeling the evolution of the fluid queue as a semi-Markov process (SMP) and analyzing its performance. While there are techniques based on matrix-analytic methods and forward-backward decomposition, we show that they are not nearly as fast as the spectral-expansion SMP-based approach. Using the performance measures obtained from the SMP model, we suggest an algorithm for selecting the thresholds so that power consumption is minimized, while satisfying a quality-of-service constraint. We illustrate our results using a numerical example.
References
[1]
V. Aggarwal, N. Gautam, S.R.T. Kumara, M. Greaves, Stochastic fluid flow models for determining optimal switching thresholds with an application to agent task scheduling, Performance Evaluation, 59 (2004) 19-46.
[2]
S. Ahn, V. Ramaswami, Efficient algorithms for transient analysis of stochastic fluid flow models, Journal of Applied Probability, 42 (2005) 531-549.
[3]
D. Anick, D. Mitra, M.M. Sondhi, Stochastic theory of a data handling system with multiple sources, Bell System Technical Journal, 61 (1982) 1871-1894.
[4]
Y. Chen, A. Das, W. Qin, A. Sivasubramaniam, Q. Wang, N. Gautam, Managing server energy and operational costs in hosting centers, SIGMETRICS Perform. Eval. Rev., 33 (June 2005) 303-314.
[5]
A. da, Silva Soares, G. Latouche, Matrix-analytic methods for fluid queues with finite buffers, Performance Evaluation, 63 (May 2006) 295-314.
[6]
A. da, Silva Soares, G. Latouche, Fluid queues with level dependent evolution, European Journal of Operational Research, 196 (August 2009) 1041-1048.
[7]
A.I. Elwalid, D. Mitra, Analysis, approximations and admission control of a multi-service multiplexing system with priorities, in: Proc. IEEE INFOCOM, vol. 2, Apr 1995, pp. 463-472.
[8]
N. Gautam, V.G. Kulkarni, Z. Palmowski, T. Rolski, Bounds for fluid models driven by semi-markov inputs, Probability in Engineering and Informational Sciences, 13 (1999) 429-475.
[9]
L. Huang, T.T. Lee, Generalized pollaczek-khinchin formula for markov channels, IEEE Transactions on Communications, 61 (August 2013) 3530-3540.
[10]
H.E. Kankaya, N. Akar, Solving multi-regime feedback fluid queues, Stochastic Models, 24 (2008) 425-450.
[11]
V.G. Kulkarni, Modeling and analysis of stochastic systems, CRC Press, 1996.
[12]
V.G. Kulkarni, Fluid models for single buffer systems, Frontiers in queueing: Models and applications in science and engineering, 321 (1997) 338.
[13]
V.G. Kulkarni, N. Gautam, Admission control of multi-class traffic with service priorities in high speed networks, Queueing systems: Theory and Applications, 27 (1997) 79-97.
[14]
S.R. Mahabhashyam, N. Gautam, S.R.T. Kumara, Resource-sharing queueing systems with fluid-flow traffic, Operations Research, 56 (May 2008) 728-744.
[15]
R. Malhotra, M. Mandjes, W. Scheinhardt, J. van den Berg, A feedback fluid queue with two congestion control thresholds, Mathematical Methods of Operations Research, 70 (2009) 149-169.
[16]
Revolutionizing Data Center Efficiency. Uptime Institute Symposium. http://uptimeinstitute.org/content/view/168/57
[17]
A. Narayanan, V.G. Kulkarni, First passage times in fluid models with an application to two-priority fluid systems, in: IEEE International Computer Performance and Dependability Symposium, 1996.
[18]
M. O'Reilly, Multi-stage stochastic fluid models for congestion control, European Journal of Operations Research (2013).
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Published: 05 January 2015
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