1. VOLTAGE SCHEDULING HEURISTIC for REAL-TIME TASK GRAPHS D. Roychowdhury, I. Koren, C. M. Krishna University of Massachusetts, Amherst Y.-H. Lee Arizona State University

2. June 25, 2003 Motivation Energy Constrained Complex Real-Time Systems are becoming increasingly important Scheduling – an effective system management entity to exploit Schedule tasks such that energy expenditure is minimized while still meeting the deadline Exploit multiple voltage levels provided by processors to achieve our goal We focus on applications having tasks with precedence constraints (can be represented as task graphs)

3. June 25, 2003 CMOS system equations slow(v) is the factor by which processor is slower at voltage v than it is at the reference high voltage v h : Threshold voltage is v T energy_per_cycle(v) is the ratio of energy consumed per cycle at voltage v to that at v h :

4. June 25, 2003 System Assumptions Can run in discrete number of variable voltage levels Algorithms are provided for a 2-voltage level system followed by extensions for systems supporting multiple voltage levels A task can only continue if all preceding tasks on which it depends complete The energy cost during communication and idle state in processors is negligible Voltage switching costs are incorporated within the worst scale profiling of tasks

5. June 25, 2003 Required Inputs Task graph (directed acyclic graph) showing the precedence constraints between the tasks after their assignment Deadline by which the given task set must finish Worst case execution profile of individual tasks under different voltage levels Distribution of execution profile of each task

6. June 25, 2003 Key issues Static scheduling of the assigned Task Graph Run-time scheme for dynamic resource reclamation Extension to a Multi-Voltage System

7. June 25, 2003 Optimization Problem D - Deadline S i - speed up in time associated with task i t k - worst case time when all tasks in path P k run in low voltage Constraint equations: For path P k Objective function: Minimize :

8. June 25, 2003 Static Scheduling Start by keeping all tasks in low voltage Start speeding up tasks with highest weight gradually Weight of a task is number of critical paths of which that task is a member Critical path is a path that currently fails to meet its deadline under worst case execution profile. We speed up the task with highest weight until some other task has a higher weight For the tasks with equal weights break the tie by speeding up the task nearest to a leaf in graph We continue until all paths meet the deadline Assign start time and commit time for each task based on the above voltage scheduling

9. June 25, 2003 Example Graph 1 3 57 2 4 6 284 24 201618 Paths 1->5 2->4->5 2->4->6 2->4->7 3->7 1 21 2 1 3 3 DEADLINE=93 (60) (43) 2 4 6

10. June 25, 2003 Example Graph 1 2 4 5 6 284 24 2016 Paths 1->5 2->4->5 2->4->6 2->4->7 3->7 1 20 2 3 7 28 18 1 2 2 3 7

11. June 25, 2003 Gantt Chart (Static)

12. June 25, 2003 Run-Time Adjustments Each task has an assigned start time and commit time from static scheduling If a task can be issued before its statically assigned start time, we can slow down the task to save energy The slow down must still yield same commit time

13. June 25, 2003 Example Graph 1 2 3 4 57 6 22.88 2.5 26.1 26.8 11.8 14.86 11.2

14. June 25, 2003 Gantt Chart (dynamic)

15. June 25, 2003 Key issues Static scheduling Run-time dynamic resource reclamation Extension to a Multi-Voltage System

16. June 25, 2003 Using Multiple Voltage Levels Calculate start time and commit time for tasks using the static scheduling V unique - voltage at which we can finish task within specified interval without voltage switching 2 voltage levels are chosen within which V unique falls The switching point is chosen between the two levels such that task finishes exactly at commit time

17. June 25, 2003 Simulation Results We used systems which support the following voltage-frequency combinations We use sparse matrix calculation as an example application Voltage (V) Frequency (MHz) 11.751000 21.40800 31.20600 41.00466

18. June 25, 2003 Energy Saving after runtime adjustment Task execution time uniformly distributed in [A,100] of WCET

19. June 25, 2003 Energy Saving due to Dynamic Resource Reclamation

20. June 25, 2003 Energy saving over an Infinite Voltage Levels Algorithm (Zhu et al.) voltage switching allowed only during context switching

21. June 25, 2003 Energy saving when multiple (4) voltage levels used instead of 2

22. June 25, 2003 Conclusion Considerable energy can be saved by using our algorithm which takes into account the relationship among tasks in the set The algorithm is based on a practical assumption that processor supports two voltage levels We have extended the algorithm for cases which can use multiple voltage levels though the gain is not much more significant than two voltage level case

23. June 25, 2003 Thank You URL: http://www.ecs.umass.edu/ece/realtime