1. Energy-Aware Modeling and Scheduling of Real-Time Tasks for Dynamic Voltage Scaling Xiliang Zhong and Cheng-Zhong Xu Dept. of Electrical & Computer Engg. Wayne State University Detroit, Michigan http://www.cic.eng.wayne.edu

2. 2 Outline  Introduction and Related Work  A Filtering Model for DVS  Time-invariant Scaling  Time-variant Scaling  Statistical Deadline Guarantee  Evaluation  Conclusion

3. 3 Motivation  Mobile/Embedded devices power critical  Energy-Performance tradeoff Processor speed designed for peak performance Slowdown the processor when not fully utilized (DVS)  Challenges Maximize energy saving while providing deadline guarantee Real-time tasks could be periodic/aperiodic w/ highly variable execution time Aperiodic tasks have irregular release times, which calls for online decision making

4. 4 Related Work  Intensive studies for periodical tasks  Algorithms for aperiodic tasks Offline (Yao et al’95, Quan & Hu’01) Online: all timing information known only after job releases  Soft real-time: improve responsiveness (Aydin & Yang’04)  Occasionally uncontrollable deadline misses (Sinha & Chakrabarty’01)  Hard real-time w/complex admission control (Hong et al ’98)  Maximize energy saving w/ frequency scaling(Qadi et al ’03, DVSST)  On-line slack management for a general input (Lee & Shin ’04,OLDVS)  Objectives of this paper: Hard/statistical deadline guarantee for general input w/o assumptions of task periodicity Unified, online solutions for both WCET based scheduling and slack management

5. 5 Task Model  Independent tasks, preemptive w/ dynamic priorities  Job releases (requests) to system are characterized by a compound process in a discrete time domain: w i (t) is the size (WCET) of i t h jobs arrived during time [t-1,t) n(t) stands for number of jobs arrived, each w/deadline t d 0 1 w 1 (1) w 1 (2) w 2 (3) … 2 time Input arrivals

6. 6 System Model  Processor Model Support a continuous range of speed levels  Energy Model t: scheduling time slot, f(t): speed at time [t, t+1) l(t): load, #cycle allocated to all jobs during [t, t+1) P(l(t)): power as a function of load E(S): energy consumed according to a schedule S

7. 7 A Filtering Model of Speed Scaling  Allocation function denotes the # cycles allocated to one job w i (t) during [t, t+1)  Decomposition of allocation function g(), the impact of job sizes (WCETs) on scheduling h(), scaling function s(), the load ’ feedback to scheduling g h s Output load Job Arrivals Request Size

8. 8 A Filtering Model (cont.)  Each job should be finished in t d time g(w i (t))=w i (t)  Load Function l(t) is a sum of allocation to all jobs  Non-adaptive to load s(l(t)) = 1

9. 9 A Filtering Model (cont.)  The load function becomes a convolution of compounded input request process and scaling function,  Scaling function h(t): Portion of resource allocated at each scheduling epoch from the arrival time t s to finish time t s +t d  Design of scaling algorithm in a fitlerng system

10. 10 Time-Invariant Scheduling  The optimal policy is to find an allocation where  Treat h(t) as a time-invariant scaling function  The optimality is determined by the covariance matrix Ω of the input process w(t) in the order of deadline t d  The optimization has a unique, closed form solution

11. 11 Example Solutions with Different Input  Two multimedia traffic patterns (Krunz’00) Shifted Exponential Scene-length Distribution (ACFExp) Subgeometric scene- length distribution (ACFSubgeo)  Fractional Gaussian Noise (FGN) process with Hurst para. H=0.89  Simpsons MPEG Video Trace of 20,000 frames Auto-Correlations of Traffic

12. 12 Example Solution (t d =10)  Higher degree of input autocorrelation has a more convexed scaling function  The uniform distributed allocation is a generalization of several existing algorithms for Periodic tasks Sporadic tasks Aperiodic tasks

13. 13 Time-Variant Scaling  Energy consumption can be reduced if the scaling function h(t) is adaptive in response to change of input load  Make t d runnable queues. Jobs with deadline j are put to queue j Dispatcher Running queue 1 + … Running queue 2 Running queue t d Output load l(t) Input jobs l 1 (t) l 2 (t) l td (t)

14. 14 Time-Variant Scaling  Minimize energy consumption is to Resource cap of queue j at time t subject to:  The optimization has a unique solution: where q j (t) is the backlog of queue j at time t. Committed resource for jobs in queue j at time t

15. 15  Determine cap of queue 5 at time 0: S 5 (0) Illustration  Distribute the job as late as possible load  The job is distributed to early slots as its size increases L(t) =0 12 9 7 0 1 2 3 4 5 time slot 5 S 5 (0) =11  First determine current committed resource

16. 16 Example Solution for a Sporadic Task Input J(WCET): J 1 (1) released at 0, 5, J 2 (2) at 1, 7, J 3 (1) at 3, 9. Deadline of all jobs: 4. J i,j : jth instance of task i 1. Schduling using EDF w/o scaling 2. Schduling using the Time Variant Scaling Using a square energy function: 35% more energy saving compared to EDF. 8% to DVSST

17. 17 Statistical Deadline Guarantee  Worst case scenario schedulability test Conservative p i : minimum interarrival f max 1 F(x)F(x) v worst case f cumulative probability  Statistical guarantee Overload probability v=prob(l(t) > f max )

18. 18 Statistical Deadline Guarantee (cont.)  Load tail distribution A general bound w/ load mean and variance Tight bounds based on load distribution  Exact output distribution if input distribution known  Estimate output distribution using a histogram f max f’ max 1 F(x)F(x) v cumulative probability b 1 b 2 b max b r-1 b min

19. 19 Evaluation  Objectives Effectiveness in energy savings Effectiveness of the deadline miss bound  Scheduling based on WCET No-DVS: run jobs with the maximum speed. Offline: Offline optimal algorithm of Yao:95 et a. DVSST: On-line algorithm for sporadic tasks Qadi:RTSS03 et al. TimeInvar: Time-invariant voltage scaling. TimeVar: Time-variant voltage scaling.  On-line slack management DVSST+CC (Cycle-conserving EDF): Worst case schedule using DVSST with the reclaiming algorithm of Pillai and Shin (SOSP01). TimeVar+OLDVS: The time-variant voltage scaling and the reclaiming algorithm of Lee and Shin:RTSS2004. TimeVar+TimeVar: A unified solution.

20. 20  Energy consumption with the Robotic Highway Safety Marker application; A scenario in which robot keeps moving Energy Savings  TimeVar is energy-efficient, close to Offline (5%); 7-11% better than DVSST DVSSTOfflineTimeVariant 11%

21. 21  #tasks=30; Interarrival ~ exp(50 ms) WCET ~ n(100, 10)K  Workload variation characterized by actual execution time over worst case (BCET/WCET) Energy Savings w/ Workload Variation TimeVariant adapts with workload variation effectively

22. 22 Computation Speed Configuration  Computation requirement based on a general bound is better than worst case with mean interarrivals > 60 ms  Tight bounds reduce the computation speed in half as interarrivals > 40 ms Mean Interarrival time (ms) Required speed (MHz)  Target deadline guarantee: 99%

23. 23 Statistical Deadline Guarantee  No deadline misses under bound derived based on a general input: 100MHz  Statistics of TimeVar/TimeInvar under a tight bound: 40MHz  Overload handling: reject new jobs or serve unfinished jobs in a best-effort mode  Target deadline guarantee 99% Scheduling TimeInvariantTimeVariant RejectBesteffortRejectBesteffort Load mean (10 6 )21.621.721.621.74 Load var166.7168.9141.3142.8 Time mean10.110.0910.410.07 Time variance8.78.4 8.8 Overload/Deadline misses 0.63% 0.61% Deadline miss rate is effectively bounded

24. 24 Conclusion  Voltage/Speed scaling for a general task model  A Filtering Model for DVS  Two online policies to minimize energy usage Time-invariant : A generalization of several existing approaches Time-variant : Optimal in the sense it is online w/o future task timing information. Also effective for on-line slack management  Statistical deadline guarantee based on computation speed configuration.  Future work System-wide energy savings, e.g., wireless communication and its interaction with CPU

25. 25 Energy-Aware Modeling and Scheduling of Real-Time Tasks for Dynamic Voltage Scaling Thank you!