“Scheduling with Dynamic Voltage/Speed Adjustment Using Slack Reclamation In Multi-processor...
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1 heduling with Dynamic Voltage/Speed Adjustme 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
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“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. Outline. - PowerPoint PPT Presentation
Transcript of “Scheduling with Dynamic Voltage/Speed Adjustment Using Slack Reclamation In Multi-processor...
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“Scheduling with Dynamic Voltage/Speed Adjustment Using Slack Reclamation
In Multi-processor Real-Time Systems”
Dakai Zhu, Rami Melhem, and Bruce ChildersComputer Science Department
University of Pittsburgh
Presented by Jin W. LeeOctober, 2001
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Outline
1. Task Model and Problem Description2. Energy Model and Power Management3. Power aware scheduling for independent tasks4. Power aware scheduling for dependent tasks5. Conclusion
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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
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Processor Power DissipationPd= Cef*Vdd
2* 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 TaskE/task = Pd * t = Cef* Vdd
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- t is the time to execute the task
Energy Model and Power Management
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Basic Idea
Deadline D
Cpu time units for task= X
Smax
Cpu time units for task= X
t
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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
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P1
P2
T1=(10, 7), T2=(8,4), T3=(6,6), T4=(6,6), T5=(6,6)
Ready Queue
T3
T4
T5
0 20 Time
P1
P2
T1 T2
T3 T4 T5
0 20 Time
T1
T2
T1 T2 T3 T4 T5
LTF priority assignment Optimal priority assignment
P1
P2
T1
T2 T3
T4
T5
0 20 Time
Actual execution with max cpu speed
Basic Scheduling Schemes
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P1
P2
T1=(5, 2), T2=(4,4), T3=(3,3), T4=(2,2), T5=(2,2), T6=(2,2)
Ready Queue
0 9 Time
P1
P2
0 9 Time
T1 T2 T3 T4 T5
Canonical Execution Actual Execution with NPM
T6
T1
T2 T3
T4 T5
T6 T2
T3
T4
T5T1
T6
Example for Global Scheduling with Slack Reclamationfor Independent Tasks
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P1
P2
0 9 Time
Global Scheduling with Greedy Slack Reclamation
T1
T2
P1
P2
0 9 Time
T1
T2
T3 T6
T4 T5
P1
P2
0 9 Time
T1
T2
T3
T1 T3
We know c1 for T1 and c3 for T3c1+c3 is the time T3 must be finishedIf T3 can start time 2, we can expend execution timefor T3 to time 7 like below graph.
T1 T3
Miss Deadline !!
2 3 3
T1=(5, 2), T2=(4,4), T3=(3,3), T4=(2,2), T5=(2,2), T6=(2,2)
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P1
P2
0 9 Time
Global Scheduling with Shared Slack Reclamation
T1
T2
P1
P2
0 9 Time
T1
T2
P1
P2
0 9 Time
T2
T3 T5
T6
T1
T4
Meet Deadline !!
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T1=(5, 2), T2=(4,4), T3=(3,3), T4=(2,2), T5=(2,2), T6=(2,2)
4 5 4 5
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1 While (Ready-Q is not Empty) 2 {3 Tk = Dequeue (Ready-Q);4 If ( STNTid > STNT~id )5 STNTid STNT~id ; 6 EETk = STNTid + ck ; 7 STNTid = EETk;8 Sid = Smax * ck / ( EETk - t );9 Execute(Tk, Sid);10 }
Global Scheduling with Shared Slack ReclamationAlgorithm Implementation
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T1=(5, 2), T2=(4,4), T3=(3,3), T4=(2,2), T5=(2,2), T6=(2,2)
Ready Queue T1 T2 T3 T4 T5 T6
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 %
P1
P2
0 9
T1
T2
Algorithm : Example Step 1
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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 %
T1=(5, 2), T2=(4,4), T3=(3,3), T4=(2,2), T5=(2,2), T6=(2,2)
Ready Queue T4 T5 T6
T1P1
P2
0 9 Time
T2
Algorithm : Example Step 2
T1P1
P2
0 9 Time
T2
T3
4 5
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Time 4 Task 4(c1=2) dequeue id = 2 STNT1 = 7, STNT2 = 5 EET4 = 5 + 2 STNT2 = 7 Cpu Speed 2/(7-4) 67 %
T1=(5, 2), T2=(4,4), T3=(3,3), T4=(2,2), T5=(2,2), T6=(2,2)
Ready Queue T5 T6
T1P1
P2
0 9 Time
T2
T3
T4
Algorithm : Example Step 3
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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 %
T1P1
P2
0 9 Time
T2
T3 T5
T6T4
Meet Deadline !!
Algorithm : Example Step 4
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Example for Global Scheduling with Slack Reclamationfor Dependent Tasks
T2
T1
T3
T4
T6
T5
(2,2)
(3,1)
(3,3)
(4,4)(6,6)
(6,6)
Precedence Graph
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P1
P2
T1=(3,1), T2=(2,2), T3=(4,4), T4=(3,3), T5=(6,6), T6=(6,6)
Worst Case Ready Time
0 12 Time
P1
P2
0 12 Time
T1 T2 T3 T4
T5
Canonical Execution Actual Execution with NPM
T6
T1
T2 T3
T4
T5
T6
T1
T2
T5
T3 T4
T6
Actual Case Ready Time
T1 T2 T3 T4 T6T5
List Scheduling for Dependent Tasks
0 2 3 6 0 1 2 6
Miss Deadline !!
List scheduling is a standard algorithm used to schedule task sets with precedence constraints
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P1
P2
0 12 TimeActual Execution with NPM
T1
T2
T5
T3 T4
T6
Ready Time
T1 T2 T3 T4 T6T5
0 1 2 6
Miss Deadline !!
T1=(3,1), T2=(2,2), T3=(4,4), T4=(3,3), T5=(6,6), T6=(6,6)
List Scheduling with Shared Slack Reclamationfor Dependent Tasks
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Ready Time
T1 T2 T3 T4 T6T5
0 1 2 6
T1=(3,1), T2=(2,2), T3=(4,4), T4=(3,3), T5=(6,6), T6=(6,6)
Fixed-Order List Scheduling with Shared Slack Reclamation for Dependent Tasks
Global Queue
T1 T2 T3 T4 T6T5
0 2 1 6
Global Queue
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1 If (Head(Global-Q) is ready) 2 {3 Tk = Dequeue (Global-Q);4 If ( STNTid > STNT~id )5 STNTid STNT~id ; 6 EETk = max{ RTc
k, STNTid, t } + ck ; 7 STNTid = EETk;8 Sid = Smax * ck / ( EETk - t );9 If((Head(Global-Q) is ready) AND (P~id is idle))10 Signal(P~id);11 Execute(Tk, Sid);12 } else wait();
List Scheduling with Shared Slack ReclamationAlgorithm Implementation
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Global Queue
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 %
Algorithm : Example Step 1T1=(3,1), T2=(2,2), T3=(4,4), T4=(3,3), T5=(6,6), T6=(6,6)
Ready Time
T1 T2 T3 T4 T6T5
0 2 1 6
P1
P2
0 12 Time
T1
T2
2 3
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Global Queue
Time 1 Head(Global-Q) is not ready so id = 1 is wait();
Algorithm : Example Step 2T1=(3,1), T2=(2,2), T3=(4,4), T4=(3,3), T5=(6,6), T6=(6,6)
Ready Time
T3 T4 T6T5
2 1 6
P1
P2
0 12 Time
T1
T2
6
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Global Queue
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 %
Algorithm : Example Step 2T1=(3,1), T2=(2,2), T3=(4,4), T4=(3,3), T5=(6,6), T6=(6,6)
Ready Time
T3 T4 T6T5
2 1 6
P1
P2
0 12 Time
T1
T2
T3
2 3 6
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Global Queue
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 %
Algorithm : Example Step 3T1=(3,1), T2=(2,2), T3=(4,4), T4=(3,3), T5=(6,6), T6=(6,6)
Ready Time
T4 T6T5
1 6
P1
P2
0 12 Time
T1
T2 T4
2 3 6
T3
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Global Queue
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 %
Algorithm : Example Step 4T1=(3,1), T2=(2,2), T3=(4,4), T4=(3,3), T5=(6,6), T6=(6,6)
Ready Time
T6T5
1 6
P1
P2
0 12 Time
T1
T2
T3
T4
T5
T6
Meet Deadline !!
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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
