ECE555 Topic Presentation Energy-efficient real-time scheduling Xing Fu 20 September 2008

1. ECE555 Topic Presentation Energy-efficient real-time scheduling Xing Fu 20 September 2008 Acknowledge Dr. Jian-Jia Chen from ETH providing PPT Slides for IEEE RTAS 2007

2. Outline of Presentation • System-level Energy Management for Periodic Real-Time Tasks • On the Minimization of the Instantaneous Temperature for Periodic Real-Time Tasks Further reference: http://www.cs.pitt.edu/PARC/ http://www.cs.utsa.edu/~dzhu/parc-2005.htm http://www.cs.pitt.edu/PARTS/publications.html

3. Outline of Presentation • Why those two papers? Paper 1: Systematic results. Other related papers can be treated as special cases. Paper 2: A closely related field: temperature efficient real time scheduling. • What will be covered? 1. Main concepts 2. Key ideas 3. Introduction of underlying mathematics if time allowed

4. System-level Energy Management for Periodic Real-Time Tasks

5. What is System-level Energy Management? • A generalized power model which includes the static,frequency-independent active and frequency-dependentactive power components of the entire system, • Variations in the system power dissipation during the executionof different tasks • On-chip / off-chip workload characteristics of individualtasks.

6. Task and Processor Model

7. Power Model

8. Derivation of Energy-Efficient Speed for a Single Task

9. Energy-Efficient Speed Assignments for a Task Set Minimize Energy Guarantee Real Time

10. ENERGY-LU • Case 1: If energy efficient speed of a particular task is great than Smax, then in optimal solution, the speed of the task is Smax • Case 2: If , speed of all tasks will be • Case 3: If ,then • In case 3, ENERGY-LU is formulated as

11. Solving ENERGY-LU • First Reduce to ENERGY-L problem by relaxing the last constrain of ENERGY-LU and solve ENERGY-L problem first. • Case 1: the solution of ENERGY-L problem is also the solution of ENERGY-LU. • Case 2: the solution of ENERGY-L problem is NOT the solution of ENERGY-LU. • If case 2, iteratively adjust solutions of ENERGY-L to solve ENERGY-LU.

12. Experiment Results I

13. Dynamic Reclaiming • Why Dynamic Reclaiming? In practice, many task instances (Jobs) complete without presenting their worst-case workload. • Dynamic Reclaiming is introduced to reclaim unused computation time to reduce the CPU speed while preserving feasibility. • Different scheduling scheme has its own Dynamic Reclaiming.

14. Dynamic Reclaiming Algorithm • When a job is to be dispatched, it will get the unused computation time from completed higher priority jobs. • Use those time, reduce further CPU speed to save more power. • A supported data structure - queue is needed to store related information.

15. Experiment Results II

16. Conclusions • Addressed the problem of minimizing overall energy consumption of a real-time system, considering a generalized power model. • Formulated the problem as a convex optimization problem and derived an iterative, polynomial time solution using Kuhn-Tucker optimality conditions. • Provided a dynamic reclaiming extension for settings where tasks complete early.

17. On the Minimization of the Instantaneous Temperature for Periodic Real-Time Tasks

18. Motivations for Power Saving • Rapid Increasing of Power Consumption • The power consumption of processors increases dramatically. • Slow Increasing of the Battery Capacity • The battery capacity increases about 5% per year • Embedded Systems vs. Servers The reduction of power is also needed to cut the power bill off

19. Heat versus Energy • Energy • Minimize the accumulative energy • Prolong battery lifetime • Reduce execution cost • Heat • Minimize the instantaneous temperature • Prevent from overheating • Reduce packing cost

20. Cooling Model • Cooling is a complex phenomenon [Sergent and Krum 1998]. • For tractability, a simple first-order approximation is needed. • key assumptions: 1. Heat is lost via conduction 2. Ambient temperature of the environment is constant. • This is likely a reasonable first-order approximation in some, but certainly not all, settings.

21. Cooling Model • The ambient temperature is scaled to 0 Modeled by Fourier’s Law • Initialization

22. CHIP Proc. Proc. SMTAS MMTAS Problem Definitions Generate a feasible schedule SC for a set of tasks T such that Ψ(SC) is minimized. • UTAS : uniprocessor temperature-aware scheduling problem • SMTAS : single-chip multiprocessor temperature-aware scheduling problem • MMTAS : multi-chip multiprocessor temperature-aware scheduling problem

23. UTAS: Ideal Processors • Energy minimization • Executing at a constant speed in the earliest-deadline-first order is optimal in energy consumption minimization by Aydin et al. in RTSS 2001, where • E(SCEDF) · E(SC) for any feasible schedule SC, where SCEDF is to execute tasks by the above strategy. • Temperature minimization Schedule • Executingall of the tasks at a constant speed following the earliest-deadline-first (EDF) strategy

24. UTAS: Ideal Processors (cont.) • The maximum temperature of schedule • The maximumtemperature of any feasible schedule • The ratio between the above two

25. UTAS: Ideal Processors (cont.) This is an e-approximation algorithm which means the maximum temperature of the suboptimal scheme is at most e times as any optimal scheme.

26. UTAS: Non-Ideal Processors • The timing overhead in speed transition from si to sj is denoted by σi,j • When σi,j is negligible • Energy minimization Execute at two consecutive speeds of effective speed sT*so that the utilization is 100% is optimal • Temperature minimization Execute at two consecutive speeds of effective speed sT*so that the utilization is 100% and frequently change speeds • When σi,j is non-negligible • More complicated

27. speed t   UTAS: σi,j is negligible 

28. UTAS: σi,j is non-negligible speed Speed transition overhead t   When α = 1, β = 0.01, and σi,j = 1 for any 0 < i j ≤ H

29. Multiprocessor: Largest-Task First (LTF) M = 3 2 3 4 5 1 Loads (ci/pi) • Sort tasks in a non-increasing order of ci/pi • Assign tasks in a greedy manner to the processor with the smallest load • Execute tasks on a processor at the speed with 100% utilization L1 1 L2 2 5 L3 3 4 Algorithm LTF is a 1.13-approximation algorithm for energy efficiency. Jian-Jia Chen, Heng-Ruey Hsu, Kai-Hsiang Chuang, Chia-Lin Yang, Ai-Chun Pang, and Tei-Wei Kuo, "Multiprocessor Energy-Efficient Scheduling with Task Migration Considerations", in ECRTS 2004. Jian-Jia Chen, Heng-Ruey Hsu, and Tei-Wei Kuo, "Leakage-Aware Energy-Efficient Scheduling of Real-Time Tasks in Multiprocessor Systems", in RTAS 2006.

30. SMTAS and MMTAS Applying Algorithm LTF for scheduling • (1.13e)-approximation for MMTAS • (2.371e)-approximation for SMTAS

31. Conclusions • Analysis for the maximum instantaneous temperature for energy-efficient scheduling algorithms in uniprocessor and multiprocessor systems • e-approximation for uniprocessor scheduling on ideal processors • (1.13e)-approximation when multi processors are on a chip • (2.371e)-approximation when each processor is on an individual chip • designs for non-ideal processors

32. Comparison of two papers [1] Dynamic and Aggressive Power-Aware Scheduling Techniques for Real-Time Systems

33. Selected Critiques I • Maybe apply latest results from optimization community to derive Optimal solution. Example, Linear Matrix Inequality. • More accurate model of CPU cooling maybe investigated. Then new scheduling algorithms or feedback control system can be designed accordingly.

34. Selected Critiques II • Optimizing other QoS parameters for power aware real time system. Examples: Thermal, fault tolerance, through-output.

35. Any Question? Thank you！