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“Scheduling with Dynamic Voltage/Speed Adjustment Using Slack Reclamation

This paper explores energy-efficient scheduling in multi-processor real-time systems using slack reclamation and dynamic voltage/speed adjustment strategies. It covers task and energy models, power management, slack reclamation schemes, and various scheduling algorithms with examples.

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“Scheduling with Dynamic Voltage/Speed Adjustment Using Slack Reclamation

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  1. “Scheduling with Dynamic Voltage/Speed Adjustment Using Slack Reclamation In Multi-processor Real-Time Systems” Dakai Zhu, Rami Melhem, and Bruce Childers Computer Science Department University of Pittsburgh Presented by Jin W. Lee October, 2001

  2. Outline 1. Task Model and Problem Description 2. Energy Model and Power Management 3. Power aware scheduling for independent tasks 4. Power aware scheduling for dependent tasks 5. Conclusion

  3. Task Model and Problem Description - Ti = (ci, ai) ci is the task’s worst case execution time (WCET) based on full CPU speed ai is actual case execution time (ACET) - Problem: Scheduling Scheme for Multi-Processor Systems that Minimizes energy consumption for CPU while still meet Deadline

  4. Energy Model and Power Management • ProcessorPower Dissipation • Pd= Cef*Vdd2* f • - Cef is the switch capacitance • - f is processor frequency • Vdd is processor supply voltage • Processor Speed • f = k (Vdd –Vt )2/ Vdd • - k is a constant • - Vt is the threshold voltage • Energy per Task • E/task = Pd * t = Cef* Vdd2 • - t is the time to execute the task

  5. Basic Idea Deadline D Smax Cpu time units for task = X t Cpu time units for task = X

  6. Slack Reclamation Schemes • Task’s Dynamic Behavior • Actual Execution Time: 40% [9] • Slack • Unused time considered as slack and can be reused by the following tasks • at run-time • Reclaim Slack • Greedy Scheme • Shared Scheme

  7. Basic Scheduling Schemes T1=(10, 7), T2=(8,4), T3=(6,6), T4=(6,6), T5=(6,6) T1 T2 T3 T4 T5 Ready Queue T1 T4 T1 T2 P1 P1 T2 T3 T5 T3 T4 T5 P2 P2 0 20 Time 0 20 Time LTF priority assignment Optimal priority assignment T1 T4 P1 T2 T3 T5 P2 0 20 Time Actual execution with max cpu speed

  8. Example for Global Scheduling with Slack Reclamation for Independent Tasks T1=(5, 2), T2=(4,4), T3=(3,3), T4=(2,2), T5=(2,2), T6=(2,2) T1 T2 T3 T4 T5 T6 Ready Queue P1 T1 T4 T5 P1 T1 T3 T5 P2 T2 T3 T6 P2 T2 T4 T6 0 9 Time 0 9 Time Canonical Execution Actual Execution with NPM

  9. Global Scheduling with Greedy Slack Reclamation T1=(5, 2), T2=(4,4), T3=(3,3), T4=(2,2), T5=(2,2), T6=(2,2) T1 T1 P1 P1 T3 T2 T2 P2 P2 0 9 Time 0 9 Time 2 3 3 T1 T3 We know c1 for T1 and c3 for T3 c1+c3 is the time T3 must be finished If T3 can start time 2, we can expend execution time for T3 to time 7 like below graph. P1 T1 T6 T3 P2 T2 T4 T5 T1 T3 0 9 Time Miss Deadline !!

  10. Global Scheduling with Shared Slack Reclamation T1=(5, 2), T2=(4,4), T3=(3,3), T4=(2,2), T5=(2,2), T6=(2,2) T1 T1 P1 P1 T2 T2 P2 P2 0 2 4 5 9 Time 0 4 5 9 Time P1 T1 T5 T3 P2 T2 T6 T4 0 9 Time Meet Deadline !!

  11. Global Scheduling with Shared Slack Reclamation Algorithm Implementation • While (Ready-Q is not Empty) • { • Tk = Dequeue (Ready-Q); • If ( STNTid > STNT~id ) • STNTid STNT~id ; • EETk = STNTid + ck ; • STNTid = EETk; • Sid = Smax * ck / ( EETk - t ); • Execute(Tk, Sid); • }

  12. Algorithm : Example Step 1 T1=(5, 2), T2=(4,4), T3=(3,3), T4=(2,2), T5=(2,2), T6=(2,2) T1 T2 T3 T4 T5 T6 Ready Queue Time 0 Task 1(c1=5) dequeue id = 1 STNT1 = 0, STNT2 = 0 EET1 = 0 + 5 STNT1 = 5 Cpu Speed 5/(5-0)  100 % Task 2(c2=4) dequeue id = 2 STNT1 = 5, STNT2 = 0 EET2 = 0 + 4 STNT2 = 4 Cpu Speed 4/(4-0)  100 % T1 P1 T2 P2 0 9

  13. Algorithm : Example Step 2 T1=(5, 2), T2=(4,4), T3=(3,3), T4=(2,2), T5=(2,2), T6=(2,2) T4 T5 T6 Ready Queue Time 2 Task 3(c1=3) dequeue id = 1 STNT1 = 5, STNT2 = 4 Switch STNT for sharing Slack !! STNT1 = 4, STNT2 = 5 EET3 = 4 + 3 STNT1 = 7 Cpu Speed 3/(7-2)  60 % P1 T1 P2 T2 0 4 5 9 Time P1 T1 T3 P2 T2 0 9 Time

  14. Algorithm : Example Step 3 T1=(5, 2), T2=(4,4), T3=(3,3), T4=(2,2), T5=(2,2), T6=(2,2) T5 T6 Ready Queue Time 4 Task 4(c1=2) dequeue id = 2 STNT1 = 7, STNT2 = 5 EET4 = 5 + 2 STNT2 = 7 Cpu Speed 2/(7-4)  67 % P1 T1 T3 P2 T2 T4 0 9 Time

  15. Algorithm : Example Step 4 T1=(5, 2), T2=(4,4), T3=(3,3), T4=(2,2), T5=(2,2), T6=(2,2) Ready Queue Time 7 Task 5(c1=2) dequeue id = 1 STNT1 = 7, STNT2 = 7 EET5 = 2 + 7 STNT1 = 9 Cpu Speed 2/(9-7)  100 % Task 6(c2=2) dequeue id = 2 STNT1 = 9, STNT2 = 7 EET6 = 2 + 7 STNT2 = 9 Cpu Speed 2/(9-7)  100 % P1 T1 T5 T3 P2 T2 T6 T4 0 9 Time Meet Deadline !!

  16. Example for Global Scheduling with Slack Reclamation for Dependent Tasks (3,3) T4 (2,2) (4,4) T2 (6,6) T3 T6 (3,1) T1 (6,6) T5 Precedence Graph

  17. List Scheduling for Dependent Tasks List scheduling is a standard algorithm used to schedule task sets with precedence constraints T1=(3,1), T2=(2,2), T3=(4,4), T4=(3,3), T5=(6,6), T6=(6,6) Worst Case Ready Time Actual Case Ready Time 0 2 3 6 0 1 2 6 T1 T2 T3 T4 T5 T6 T1 T2 T5 T3 T4 T6 P1 T1 T4 T5 P1 T1 T5 T6 P2 T2 T3 T6 P2 T2 T3 T4 Miss Deadline !! 0 12 Time 0 12 Time Canonical Execution Actual Execution with NPM

  18. List Scheduling with Shared Slack Reclamation for Dependent Tasks T1=(3,1), T2=(2,2), T3=(4,4), T4=(3,3), T5=(6,6), T6=(6,6) Ready Time 0 1 2 6 T1 T2 T5 T3 T4 T6 P1 T1 T6 T5 P2 T2 T4 Miss Deadline !! T3 0 12 Time Actual Execution with NPM

  19. Fixed-Order List Scheduling with Shared Slack Reclamation for Dependent Tasks T1=(3,1), T2=(2,2), T3=(4,4), T4=(3,3), T5=(6,6), T6=(6,6) Ready Time 0 1 2 6 T1 T2 T5 T3 T4 T6 Global Queue 0 2 1 6 T1 T2 T3 T4 T5 T6 Global Queue

  20. List Scheduling with Shared Slack Reclamation Algorithm Implementation • If (Head(Global-Q) is ready) • { • Tk = Dequeue (Global-Q); • If ( STNTid > STNT~id ) • STNTid STNT~id ; • EETk = max{ RTck, STNTid, t } + ck ; • STNTid = EETk; • Sid = Smax * ck / ( EETk - t ); • If((Head(Global-Q) is ready) AND (P~id is idle)) • Signal(P~id); • Execute(Tk, Sid); • } else wait();

  21. Algorithm : Example Step 1 T1=(3,1), T2=(2,2), T3=(4,4), T4=(3,3), T5=(6,6), T6=(6,6) Ready Time 0 2 1 6 Global Queue T1 T2 T3 T4 T5 T6 Time 0 Task 1(c1=3) dequeue id = 1 STNT1 = 0, STNT2 = 0 EET1 = max{0, 0, 0} + 3 STNT1 = 3 Cpu Speed 3/(3-0)  100 % Task 2(c2=2) dequeue id = 2 STNT1 = 3, STNT2 = 0 EET2 = max{0, 0, 0} + 2 STNT2 = 2 Cpu Speed 2/(2-0)  100 % P1 T1 P2 T2 0 2 3 12 Time

  22. Algorithm : Example Step 2 T1=(3,1), T2=(2,2), T3=(4,4), T4=(3,3), T5=(6,6), T6=(6,6) Ready Time 2 1 6 Global Queue T3 T4 T5 T6 Time 1 Head(Global-Q) is not ready so id = 1 is wait(); P1 T1 P2 T2 0 6 12 Time

  23. Algorithm : Example Step 2 T1=(3,1), T2=(2,2), T3=(4,4), T4=(3,3), T5=(6,6), T6=(6,6) Ready Time 2 1 6 Global Queue T3 T4 T5 T6 Time 2 Head(Global-Q) is ready Task 3(c1=4) dequeue id = 1 STNT1 = 3, STNT2 = 2 Switch STNT for sharing Slack !! STNT1 = 2, STNT2 = 3 EET3 = max{2, 2, 2} + 4 STNT1 = 6 Cpu Speed 4/(6-2)  100 % P1 T1 T3 P2 T2 0 2 3 6 12 Time

  24. Algorithm : Example Step 3 T1=(3,1), T2=(2,2), T3=(4,4), T4=(3,3), T5=(6,6), T6=(6,6) Ready Time 1 6 Global Queue T4 T5 T6 Time 2 Task 4(c1=3) dequeue id = 2 STNT1 = 6, STNT2 = 3 EET4 = max{2, 3, 2} + 3 STNT2 = 6 Cpu Speed 3/(6-2)  75 % P1 T1 T3 P2 T2 T4 0 2 3 6 12 Time

  25. Algorithm : Example Step 4 T1=(3,1), T2=(2,2), T3=(4,4), T4=(3,3), T5=(6,6), T6=(6,6) Ready Time 1 6 Global Queue T5 T6 Time 6 Task 5(c1=6) dequeue id = 1 STNT1 = 6, STNT2 = 6 EET5 = max{1, 6, 6} + 6 STNT1 = 12 Cpu Speed 6/(12-6)  100 % Task 6(c1=6) dequeue id = 2 STNT1 = 12, STNT2 = 6 EET6 = max{6, 6, 6} + 6 STNT2 = 12 Cpu Speed 6/(12-6)  100 % P1 T1 T3 T5 P2 T2 T6 T4 0 12 Time Meet Deadline !!

  26. Conclusion • Good Performance Result. • Up to 60% power saving in simulation. • - Problem for LSSR • Need to reorder ready queue before start scheduling. •  Enhanced List Scheduling with Shared Slack Reclamation • This technique does not need reordering queue

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