1. Improving Dynamic Voltage Scaling Algorithms with PACE Jacob R. LorchAlan Jay Smith University of California Berkeley June 18, 2001 To make the most of limited energy, pace yourself.

2. Improving Dynamic Voltage Scaling Algorithms with PACE Outline The role of dynamic voltage scaling in energy management The importance of deadlines in voltage scheduling Why a fundamental accepted principle about optimal voltage scheduling is wrong The optimal formula for improving voltage scheduling algorithms (the PACE approach) Practically applying the optimal formula using statistical modeling Results: PACE reduces CPU energy consumption by as much as 49% with no impact on performance

3. Improving Dynamic Voltage Scaling Algorithms with PACE Dynamic voltage scaling (DVS) for energy management Energy management is important –Limits on battery life and weight –Battery technology advancing slowly –High electricity prices Dynamic voltage scaling (DVS) –The ability to quickly and efficiently change the supply voltage of the CPU without rebooting –Starting to appear on commercial CPU’s (Transmeta, AMD, etc.) –Trades off power consumption for performance because lower voltages necessitate lower speeds –Energy consumption per cycle is CV 2, and maximum speed is roughly proportional to voltage, so CPU energy is roughly proportional to speed squared When is lower energy worth the lower speed?

4. Improving Dynamic Voltage Scaling Algorithms with PACE Scheduling Goals: Deadline-Based Applicable scenarios –The CPU is working on one or more tasks, each with a deadline. –As long as each task completes by its deadline, performance is considered equivalent. –The deadline may be soft, i.e., the CPU may not need to complete the task by then with probability 100%. Examples –CD/DVD player that does not buffer frames –User-interface events such as key presses and mouse operations: very common in traditional notebook computer use Goals –Complete as many tasks by deadline as possible –Minimize delay: time taken beyond deadlines –Minimize energy consumption Various algorithms exist (Weiser, Pering, Grunwald, etc.)

5. Improving Dynamic Voltage Scaling Algorithms with PACE Model CPU –Some minimum speed m and maximum speed M; can take any value in between –Energy consumption per cycle proportional to speed squared. Tasks –Known deadline D –Unknown work requirement W (number of CPU cycles needed) –Completion time depends on speed used –Effective completion time is the completion time or D, whichever is larger Reflects the fact that tasks completing by their deadlines might as well have completed at their deadlines –Excess is the amount of work left over after deadline –Delay is the time spent after deadline doing excess work –One task at a time

6. Improving Dynamic Voltage Scaling Algorithms with PACE Speed Schedules for Tasks with Deadlines A speed schedule has a pre-deadline part and post-deadline part. A schedule has a certain number of pre-deadline cycles (PDC) –Deadline missed if W > PDC. –Excess will be W – PDC. Two schedules are performance equivalent if, no matter what W is, the task will have the same effective completion time for both schedules. If two schedules have equal PDC’s and identical post-deadline parts, they are performance equivalent. We can improve a DVS algorithm by replacing its speed schedule with a performance-equivalent one with lower expected energy consumption. Pre-deadline partPost-deadline part PDC = 9,500,000 cycles for both schedules

7. Improving Dynamic Voltage Scaling Algorithms with PACE A Constant Speed Is Not Ideal When W is known, the ideal schedule uses a fixed speed, since power is a concave-up function of speed. However, generally W is unknown. In this case, a constant- speed schedule is not always ideal. Intuition: The task may be long or short; if we run slowly at first, we may never get to the high-energy late part. Example using 50 ms deadline –Work requirement is 5 Mc with probability 75% and 10 Mc with probability 25% –Ideal constant speed is 200 MHz –Another speed schedule: run at 163 MHz for the first 30.675 ms, then 259 MHz for the next 19.325 ms –They are performance equivalent, but the latter’s expected energy consumption is 13.3% less.

8. Improving Dynamic Voltage Scaling Algorithms with PACE What is the Ideal Replacement for the Pre-Deadline Speed Schedule? Depends on the probability distribution of the task’s work W Define F to be the cumulative distribution function of W –F(w) is the probability that W  w; F c (w) is the probability that W > w Express speed schedule as a function of work completed, s(w) –Makes optimization problem easier –Straightforward to convert to a function of time Want to minimize expected pre-deadline energy consumption,  0 PDC F c (w) s(w) 2 dw, subject to  0 PDC 1/s(w) dw = D. Ideal speed schedule: s(w) = S 0 [F c (w)] -1/3, bounded between m and M. –Constant of proportionality S 0 chosen so the task meets its deadline We call this replacement approach PACE: Processor Acceleration for Conserving Energy

9. Improving Dynamic Voltage Scaling Algorithms with PACE Estimating Work Probability Distribution Obtain sample of recent tasks’ work requirements –Possibly weight more recent ones more heavily –Keep separate samples for different task types For example, tasks initiated by key presses in Microsoft Word or tasks initiated by releasing the left mouse button in Microsoft Excel Infer distribution from sample Task 2 4.2 Kc Task 1 5.1 Kc Task 4 5.3 Kc Task 3 6.3 Kc … Distribution estimation method Cycles Probability

10. Improving Dynamic Voltage Scaling Algorithms with PACE Sampling Methods Future –Use all tasks in the workload, even ones that haven’t occurred yet –Impractical, but can be simulated to show idealized effect All –Use all tasks seen so far, equally weighted Recent-k –Use the most recent k tasks seen, equally weighted LongShort-k –Use the most recent k tasks seen, weighting the most recent k/4 three times more Aged-a –Use all tasks seen so far –Weight the k th most recent by a k (a  1) … … …

11. Improving Dynamic Voltage Scaling Algorithms with PACE Distribution Estimation Methods Parametric –Assume a given form of distribution –Estimate parameters of that distribution –Examples Normal (mean and standard deviation) Gamma (shape and scale) Nonparametric –Do not assume any form for distribution –Let the data “speak for themselves” –Kernel density estimation Each sample point is represented by a small subdistribution We choose triangular subdistributions due to high efficiency and ease of implementation Cycles Probability Cycles Probability Cycles Probability

12. Improving Dynamic Voltage Scaling Algorithms with PACE Simulation Results (Simulated CPU: 100–500 MHz, maximum power consumption 3W)

13. Improving Dynamic Voltage Scaling Algorithms with PACE What Sampling Method Works Best? Future sometimes good but often quite bad –Shows value of recent information –Nice, considering method can’t be implemented Aged a bit better than LongShort, which is a bit better than Recent –Differences minor enough that implementation efficiency is most important

14. Improving Dynamic Voltage Scaling Algorithms with PACE Which Distribution Estimation Method Works Best? Statistical methods show low probability of either parametric model fitting the data –Nevertheless, for our limited purposes, parametric models work reasonably Gamma model never increases energy by more than 2.3% Normal model not as good

15. Improving Dynamic Voltage Scaling Algorithms with PACE Effect of PACE on Existing Algorithms Existing algorithms simulated –Past/Weiser-style: similar to Weiser et al –LongShort/Chan-style: practical version of one of Chan et al’s best –Flat/Chan-style: another of Chan et al’s best Always runs at constant speed –Past/Peg: Grunwald et al’s best Workloads simulated –Word: Letter key presses in Microsoft Word –Excel: Releases of left mouse button in Microsoft Excel –Groupwise: Releases of left mouse button in Groupwise –Low-Level: Key presses detected at low level –MPEG-One: Playing the “Red’s Nightmare” movie –MPEG-Many: Playing seven different movies sequentially

16. Improving Dynamic Voltage Scaling Algorithms with PACE Effect of PACE with Word Workload

17. Improving Dynamic Voltage Scaling Algorithms with PACE Effect of PACE with Excel Workload

18. Improving Dynamic Voltage Scaling Algorithms with PACE Effect of PACE with GroupWise Workload

19. Improving Dynamic Voltage Scaling Algorithms with PACE Effect of PACE with Low-Level Workload

20. Improving Dynamic Voltage Scaling Algorithms with PACE Effect of PACE with MPEG-One Workload

21. Improving Dynamic Voltage Scaling Algorithms with PACE Effect of PACE with MPEG-Many Workload

22. Improving Dynamic Voltage Scaling Algorithms with PACE Summary of Results: Effect of PACE on Existing Algorithms PACE always improves existing algorithms By definition, PACE never has any performance impact Also by definition, PACE does not alter post-deadline energy Gamma model reduces CPU energy consumption by 2.4–49.0% Kernel method reduces CPU energy consumption by 1.4–49.5% PACE reduces energy consumption by up to 49%, with an average of 21%, with no performance impact

23. Improving Dynamic Voltage Scaling Algorithms with PACE Overhead of Implementing PACE Computing PACE schedules takes time and energy Suggestion: match sampling and distribution estimation methods for maximum efficiency –Kernel method goes well with Recent-k, Gamma with Aged-a Simulations show overhead is low all-around –Aged-0.95/Gamma faster than Recent-28/Kernel

24. Improving Dynamic Voltage Scaling Algorithms with PACE Conclusions Dynamic voltage scaling can substantially reduce energy consumption at a cost of slower operation A common scenario where dynamic voltage scaling is useful is a task with a known deadline but unknown CPU requirements –User should not notice slower performance as long as deadline is met –Common in user-interface driven operation (which most operations are) as well as other times such as playing media Existing scheduling algorithms can be improved using PACE One can implement PACE practically and efficiently PACE reduces CPU energy consumption by up to 49%, with an average of 21%, with no impact on performance