ucb kim g. larsen arne skou & peter koch anders brødløs henrik schiøler dynamic voltage...

UCb

Kim G. Larsen Arne Skou &

Peter Koch Anders Brødløs Henrik Schiøler

Dynamic Voltage Scalingusing

Optimal Infinite Schedulingwork in progress

POTENTIAL NEW CS

2AMETIST Aalborg Sep 2003 Kim G. Larsen

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Overview

Dynamic Voltage Scaling

Task Scheduling Principles using timed automata

Energy Optimal Task Scheduling using priced timed automata


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Energy vs. Batteries

Increased processor performance => Increasing power dissipation

Slow battery development

year

BatteryCapacity

required

expected


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Energy in Processor

Power consumption mainly by dynamic power

Supply voltage reduction => decreased frequency

1;V~f 1)-(ddclk

2ddL.

clk2ddLdynamic

VCE

fVCP

cycleprdynamic

energy

Vdd

delay

Vdd

We may miss deadlines

A non-experts understanding of CMOS


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Task Scheduling

FCFSFCFS

EDFEDF

Fixed PriorityFixed Priority

Time SliceTime Slice

CPU not always fully utilized !We may occationally/dynamically lower frequency/supply voltage !Save Energy

with/without preemption


UCb Task SchedulingScheduling utilization of CPU

T2 is running{ T4 , T1 , T3 } readyordered according to somegiven priority:(e.g. Fixed Priority, Earliest Deadline,)

T1T1

T2T2

TnTn

SchedulerScheduler

2 14 3

readydone

stoprun

P(i): period for Ti

C(i): execution time for Ti

D(i): deadline for Ti

P(i): period for Ti

C(i): execution time for Ti

D(i): deadline for Ti


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Modeling Task

T1T1

T2T2

TnTn

SchedulerScheduler

2 14 3

readydone

stoprun


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Modeling Sched.

T1T1

T2T2

TnTn

SchedulerScheduler

2 14 3

readydone

stoprun


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Modeling Queue

T1T1

T2T2

TnTn

SchedulerScheduler

2 14 3

readydone

stoprun


UCb Schedulability = Safety Property

A :(Task0.Error or Task1.Error or …)

:(Task0.Error or Task1.Error or …)

May be extended with preemption


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Energy Optimal Scheduling

T1T1

T2T2

TnTn

SchedulerScheduler

2 14 3

readydone

stoprun F:= ?? ; V:= ??

“Choose” Freq/Scaling

(Voltage/Cost)

Using PTA


UCb Energy Optimal Scheduling = Optimal Infinite Path

c1 c2

c3 cn

t1 t2

t3 tn

Value of path : val() = limn!1 cn/tn

Optimal Schedule *: val(*) = inf val()

Accumulated cost

Accumulated time:(Task0.Error or Task1.Error or …)


UCb Approximate Optimal Schedule

E[] (not (Task0.Error or Task1.Error or Task2.Error) and (cost>=M imply time >= N))=E[](N,M)

² (M,N) imply val()· M/N

C=M C=M C=M

T>=NT>=N

T<NT<N

T<NX XX

Optimal infinite schedulemodulo cost-horizon

C=M


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Preliminary Results

Computed Schedule without preemption


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Preliminary Results

Computed Schedule WITH preemption


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Event Periodic Distributed Burst

Job Constant Distributed Branch

RTOS (Scheduler) FCFS EDF (Pre-emptive, Non Pre-emptive) Fixed Priority

(Pre-emptive, Non Pre-emptive) RR (Time Slicing)

J o b 1J o b 2

J o b N

Eve nt 1Eve nt 2 Eve nt N

Pro c e sso r with RTO S(Sc he d uling & DVS)

. . .

. . .

Time

Event 1

Event 2

CISS Project w Analog Devices


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DVS Simulation Tool

Execution Profile

RTOS

System Model

Simulation Evaluation/Presentation

DVS

Event Setup J ob Structure

ProcessorModel

DVSMethod

Scheduler

“Application Program”

MATLAB-based Tool developed in theADI/CISS project


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Future Work

Extension to EDF Extension to preemption

Evaluation how close DVS strategies (simulation) are wrt optimal strategy (synthesized).

Evaluation of performance of fixed DVS strategy on sporadic/non-deterministic/irregular task-models (worst/best perform.)


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Dynamic Voltage Scaling


UCb The Plate Juggling Problem thanks to Oded

Problem: avoid having the plates falling down


UCb The Plate Juggling Problem using Timed Automata

A Plate

The Joggler


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Optimal Infinite Schedulingwith respect to what ??


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64

72

Linearly Priced Timed Automata=

Timed Automata withCosts (rates and impulses)

1

5


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6/34/5

7/12/4

Linearly Multi-Priced Timed Automata=

Timed Automata withCosts (rates and impulses)

andRewards (rates and impulses)

1

5/1

1


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Optimal Infinite Scheduling

:(Plate1.Bang or Plate2.Bang or …)

c1 c2

c3 cn

r1 r2

r3 rn

Value of path : val() = limn!1 cn/rn



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Optimal Infinite Scheduling

:(Plate1.Bang or Plate2.Bang or …)

c1 c2

c3 cn

r1 r2

r3 rn

Value of path : val() = limn!1 cn/rn


CLAIM: If EITHER Cost or Reward is purely impulse-driven then * is computable [next AMETIST]

CLAIM: If EITHER Cost or Reward is purely impulse-driven then * is computable [next AMETIST]


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Discrete Case

Simplified Juggling Problem

whack1 whack2

2 1


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Discrete Case


whack1 whack2

2 1

x

y

1 2 3 4

1

2

3


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x

y

1 2 3 4

1

2

3

Discrete Case

Infinite Schedule: = ((2);whack1;epsilon(1); whack2;(3);whack2;whack1)*

whack1 whack2

2 1



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Discrete Case

val()= (2+1+1+2)/(2+1+3) = 1

whack1 whack2

2 1

Simplified Juggling ProblemInfinite Schedule: = ((2);whack1;epsilon(1); whack2;(3);whack2;whack1)*

x

y

1 2 3 4

1

2

3

2

3

12

2

11


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Discrete Case

whack1 whack2

2 1


Optimal Infinite Schedule (discrete case): Identify reachable cycle C* with smallest mean cost, i.e. cost(C*)/lgt(C*) is minimal.

Optimal Infinite Schedule (discrete case): Identify reachable cycle C* with smallest mean cost, i.e. cost(C*)/lgt(C*) is minimal.


x

y

1 2 3 4

1

2

3

2

3

12

2

11

val()= (2+1+1+2)/(2+1+3) = 1


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Appr Optimal Schedules using UPPAAL

whack1 whack2

2 1


optimal ??

cost: impulsereward: time


x

y

1 2 3 4

1

2

3

2

3

12

2

11

val()= (2+1+1+2)/(2+1+3) = 1


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Appr Optimal Schedules

int[0,N] cost;clock time;


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E[] (not (Plate1.Bang or Plate2.Bang) and (cost>=N-1 imply time >= M))=E[](N,M)


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² (N,M) imply val()· N/M


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(N,M) 9²[] (N,M)

(3,3) YES

(3,4) NO

(7,8) YES

(7,9) NO

(10,12) YES

(10,13) NO


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(N,M) 9²[] (N,M)

(3,3) YES

(3,4) NO

(7,8) YES

(7,9) NO

(10,12) YES

(10,13) NO

x

y

1 2 3 4

1

2

3

1012


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Conclusion & Future Work

CLAIM: and val() computable for LMPTA’s with cost or reward being impulse-driven

On-the-fly Computation

Interesting subclass: Impulse cost (reward) / time

ucb kim g. larsen arne skou & peter koch anders brødløs henrik schiøler dynamic voltage...

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