Optimality, fairness, and robustness in speed scaling designs

This work examines fundamental tradeoffs incurred by a speed scaler seeking to minimize the sum of expected response time and energy use per job. We prove that a popular speed scaler is 2-competitive for this objective and no "natural" speed scaler can do better. Additionally, we prove that energy-proportional speed scaling works well for both Shortest Remaining Processing Time (SRPT) and Processor Sharing (PS) and we show that under both SRPT and PS, gated-static speed scaling is nearly optimal when the mean workload is known, but that dynamic speed scaling provides robustness against uncertain workloads. Finally, we prove that speed scaling magnifies unfairness under SRPT but that PS remains fair under speed scaling. These results show that these speed scalers can achieve any two, but only two, of optimality, fairness, and robustness.

[1]  R. Tarjan Amortized Computational Complexity , 1985 .

[2]  G. J. A. Stern,et al.  Queueing Systems, Volume 2: Computer Applications , 1976 .

[3]  Lachlan L. H. Andrew,et al.  Power-aware speed scaling in processor sharing systems: Optimality and robustness , 2012, Perform. Evaluation.

[4]  Jeff Edmonds,et al.  Scheduling in the dark , 1999, STOC '99.

[5]  Minghong Lin,et al.  Heavy-traffic analysis of mean response time under Shortest Remaining Processing Time , 2011, Perform. Evaluation.

[6]  Kirk Pruhs,et al.  Improved Bounds for Speed Scaling in Devices Obeying the Cube-Root Rule , 2009, ICALP.

[7]  Stephen V. Hanly,et al.  Congestion measures in DS-CDMA networks , 1999, IEEE Trans. Commun..

[8]  Kirk Pruhs,et al.  Speed scaling for weighted flow time , 2007, SODA '07.

[9]  Adam Wierman,et al.  Fairness and classifications , 2007, PERV.

[10]  Lachlan L. H. Andrew,et al.  Power-Aware Speed Scaling in Processor Sharing Systems , 2009, IEEE INFOCOM 2009.

[11]  Adam Wierman,et al.  Classifying scheduling policies with respect to unfairness in an M/GI/1 , 2003, SIGMETRICS '03.

[12]  Karam S. Chatha,et al.  Approximation algorithm for the temperature-aware scheduling problem , 2007, 2007 IEEE/ACM International Conference on Computer-Aided Design.

[13]  Nikhil Bansal,et al.  Scheduling for Speed Bounded Processors , 2008, ICALP.

[14]  R. Núñez Queija,et al.  TCP as an Implementation of Age-Based Scheduling: Fairness and Performance , 2006, Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on Computer Communications.

[15]  W. Sandmann,et al.  A discrimination frequency based queueing fairness measure with regard to job seniority and service requirement , 2005, Next Generation Internet Networks, 2005.

[16]  Anthony Unwin,et al.  Reversibility and Stochastic Networks , 1980 .

[17]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[18]  Luiz André Barroso,et al.  The Case for Energy-Proportional Computing , 2007, Computer.

[19]  James R. Bradley Optimal control of a dual service rate M/M/1 production-inventory model , 2005, Eur. J. Oper. Res..

[20]  Adam Wierman,et al.  Asymptotic convergence of scheduling policies with respect to slowdown , 2002, Perform. Evaluation.

[21]  Robert B. Cooper,et al.  Queueing systems, volume II: computer applications : By Leonard Kleinrock. Wiley-Interscience, New York, 1976, xx + 549 pp. , 1977 .

[22]  David P. Bunde Power-aware scheduling for makespan and flow , 2006, SPAA '06.

[23]  Kirk Pruhs,et al.  Nonclairvoyant Speed Scaling for Flow and Energy , 2010, Algorithmica.

[24]  Paschalis Tsiaflakis,et al.  Fair greening for DSL broadband access , 2010, PERV.

[25]  Susanne Albers,et al.  Energy-efficient algorithms for flow time minimization , 2006, STACS.

[26]  Guillaume Urvoy-Keller,et al.  Analysis of LAS scheduling for job size distributions with high variance , 2003, SIGMETRICS '03.

[27]  T. B. Crabill Optimal Control of a Service Facility with Variable Exponential Service Times and Constant Arrival Rate , 1972 .

[28]  Benjamin Avi-Itzhak,et al.  A resource allocation queueing fairness measure: properties and bounds , 2007, Queueing Syst. Theory Appl..

[29]  R. Weber,et al.  Optimal control of service rates in networks of queues , 1987, Advances in Applied Probability.

[30]  Prudence W. H. Wong,et al.  Speed Scaling Functions for Flow Time Scheduling Based on Active Job Count , 2008, ESA.

[31]  M. Meerschaert Regular Variation in R k , 1988 .

[32]  J. Michael Harrison,et al.  Dynamic Control of a Queue with Adjustable Service Rate , 2001, Oper. Res..

[33]  F. Frances Yao,et al.  A scheduling model for reduced CPU energy , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[34]  Kirk Pruhs,et al.  Getting the best response for your erg , 2004, TALG.