Uncertainty Based Scheduling:Uncertainty Based Scheduling:Energy-Efficient OrderingEnergy-Efficient Ordering

forforTasks with Variable Execution Tasks with Variable Execution

TimeTime

Flavius Gruian and Krzysztof Kuchcinski

Embedded Systems DesignLaboratory

Lund Institute of TechnologySweden

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Presentation OutlinePresentation Outline

• Problem Set-up• A Motivation• Uncertainty Based Scheduling• Experiments

– comparison to FullSearch– measurements on EVB80200 platform

• Summary & Conclusions

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Problem Set-up Problem Set-up

• tasks: period=deadline, variable execution

• off-line (static) ordering but• run-time speed selection

– speed for the kth task

– energy for a period(clock energy e(s)=Ks)

– average energy

s(1, ,k1) WCEii1

NAfref Xjj1

k1

E(X1, ,N ) X1K1s0 XiKii2

N s(1, , i1)

E(X ) E(x )xN

x1

(x1)(xN )dx1dxN

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A Motivational ExampleA Motivational Example

Task Set: 3 tasks, uniform distribution (BCE,WCE) = {1:(12,20),2:(10,30),3:(24,40)}A = 100, K=1, fref=1, =2

Execution Type

<1, 3, 2> 42.094 41.839 134%

<2, 3, 1> 37.482 36.978 119%

Ideal: always mean

31.443 (speed 0.68)

100%

Offline WCE 55.080 (speed 0.90)

175%

E[X]

E[X ]

E[X]%Ideal

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UBS in a NutshellUBS in a Nutshell

• Main ideas:– achieve a low speed ASAP by ordering tasks wisely– approximate by

• Priority:

• Observations:– prioritize short tasks– prioritize tasks with large variation in execution– prioritize power efficient tasks– algorithmic complexity O(N2) for ordering N tasks

E[X]

E[X ]

pubs(k) KkX k

s sk

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UBS vs. Full SearchUBS vs. Full Search

• 300 sets of each size(3,4,5,6 tasks)

• used the “real” E formula (4)

• under 2% difference

aa

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

2 3 4 5 6 7

% of No Scaling Avg. Energy

Task set size

UBSFull Search

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The Test Platform: EVB80200The Test Platform: EVB80200

•Intel i80200 (XScale)•MAX1855 voltage regulator•32MB SDRAM, 4MB Flash•RS232, JTAG, 7segLED

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UBS example on i80200: m6UBS example on i80200: m6

aa

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

Power (W)

Time (s)

UBS (21.11mJ)Reverse UBS (24.34mJ)

Random (22.78mJ)WCE-stretch (28.58mJ)

MAX (37.57mJ)

• 6 tasks2 LZ (K=770mW)2 QS (K=840mW)2 FOR (K=800mW)

•max speed time 49ms•variation 17ms•runtime rescheduling after every 5 x H

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More Experimental Results: More Experimental Results: m6m6

0

5

10

15

20

25

30

35

40

45

0% 25% 50% 75%

Deadline extension

Hyp

erp

eri

od

En

erg

y (

mJ)

Max WCE-S R-UBS Rand UBS

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Experimental Results: m15Experimental Results: m15

0

5

10

15

20

25

30

35

40

45

0% 25% 50% 75%

Deadline extension

Hyperp

eri

od E

nerg

y (

mJ)

Max WCE-S R-UBS Rand UBS

5x LZ5x QS5x FOR

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Summary & ConclusionsSummary & Conclusions

• use more information to derive better methods• UBS: runtime, non-intrusive ordering for tasks

with variable execution time• measurements on

– a real platform: EVB80200– realistic tasks: Lempel-Ziv codec & Quicksort

• execution order matters!• random reordering: OK• UBS strategy: BEST

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Thank You!Thank You!

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Measuring the core PowerMeasuring the core Power

aa

+-

9V470nF

470nF

diff

trimoffset

to Oscilloscope

LF351

Vcc

Vreg

3

2

Icc

U = Icc x 1

Vin = 10/11 Vreg

trim

9V

0.1

1k

1k

1k

5.1k

4.3k

51

4

7

10k

GND

CPU

-

+

-

+

-

+

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i80200 I/O Poweri80200 I/O Power

aaa

1. Assume system driving one PC-100 DIMM and a companion chip with 10pF/pin capacitance.

Bus Speed vs. Power (Moderat e BusUtilization)

0.00

0.10

0.20

0.30

0.40

0.50

0.60

3.00 3.10 3.20 3.30 3.40 3.50 3.60

Vccp (Volts)

Pin Power (Watts)

66MHz bus

100MHz bus

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i80200 Core Poweri80200 Core Power

aa

Cor e P ower ( on Dhry st one 2 .1: h ig h c ore a c t iv it y )

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6Vcc (Volts)

Core Power (Watts)

400MHz

600MHz

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UBO extension to EDFUBO extension to EDF

• Use preemption to extract regions• Push forward uncertain regions• Algorithm:

1. Start from the latest deadline2. Between two consecutive deadlines order

the regions according to the already given priorities

3. Preempt the task which does not fit entirely4. Proceed with the next consecutive deadlines

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An Example of UBO EDFAn Example of UBO EDF

m=3

mean=9Task 1

Task 2

WCE=10

WCE=6

T=16

D=15

D=16

Classic EDF10 6

Preemption for Reduced Energy

Reordering105 + 1

In the long run: 18% less energy than for the classic EDF!