Energy-Aware Modeling and Scheduling of Real-Time

Tasks for Dynamic Voltage Scaling

Xiliang Zhong and Cheng-Zhong Xu

Dept. of Electrical & Computer Engg. Wayne State University

Detroit, Michiganhttp://www.cic.eng.wayne.edu

2

Outline

Introduction and Related Work A Filtering Model for DVS Time-invariant Scaling Time-variant Scaling Statistical Deadline Guarantee Evaluation Conclusion

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Motivation Mobile/Embedded devices power critical Energy-Performance tradeoff

Processor speed designed for peak performance Slowdown the processor when not fully utilized (DVS)

Challenges Maximize energy saving while providing deadline guarantee Real-time tasks could be periodic/aperiodic w/ highly

variable execution time Aperiodic tasks have irregular release times, which calls for

online decision making

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Related Work Intensive studies for periodical tasks Algorithms for aperiodic tasks

Offline (Yao et al’95, Quan & Hu’01) Online: all timing information known only after job releases

Soft real-time: improve responsiveness (Aydin & Yang’04) Occasionally uncontrollable deadline misses (Sinha & Chakrabarty’01) Hard real-time w/complex admission control (Hong et al ’98) Maximize energy saving w/ frequency scaling(Qadi et al ’03, DVSST) On-line slack management for a general input (Lee & Shin ’04,OLDVS)

Objectives of this paper: Hard/statistical deadline guarantee for general input w/o

assumptions of task periodicity Unified, online solutions for both WCET based scheduling and

slack management

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Task Model Independent tasks, preemptive w/ dynamic priorities Job releases (requests) to system are characterized

by a compound process in a discrete time domain: wi

(t) is the size (WCET) of ith jobs arrived during time [t-1,t)

n(t) stands for number of jobs arrived, each w/deadline td

0 1

w1(1) w1(2) w2(3) …

2 time

Input arrivals

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System Model

Processor Model Support a continuous range of speed levels

Energy Model t: scheduling time slot, f(t): speed at time [t, t+1) l(t): load, #cycle allocated to all jobs during [t, t+1) P(l(t)): power as a function of load E(S): energy consumed according to a schedule S

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A Filtering Model of Speed Scaling

Allocation function denotes the # cycles allocated to one job wi(t) during [t, t+1)

Decomposition of allocation function

g(), the impact of job sizes (WCETs) on scheduling h(), scaling function s(), the load’ feedback to scheduling

g h s Outputload

JobArrivals

Request Size

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A Filtering Model (cont.)

Each job should be finished in td time g(wi(t))=wi(t)

Load Function l(t) is a sum of allocation to all jobs

Non-adaptive to load s(l(t)) = 1

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A Filtering Model (cont.) The load function becomes a convolution of compounded

input request process and scaling function,

Scaling function h(t): Portion of resource allocated at each scheduling epoch from the arrival time ts to finish time ts+td

Design of scaling algorithm in a fitlerng system

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Time-Invariant Scheduling

The optimal policy is to find an allocation

where

Treat h(t) as a time-invariant scaling function

The optimality is determined by the covariance matrix Ω of the input process w(t) in the order of deadline td

The optimization has a unique, closed form solution

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Example Solutions with Different Input

Two multimedia traffic patterns (Krunz’00) Shifted Exponential

Scene-length Distribution (ACFExp)

Subgeometric scene-length distribution (ACFSubgeo)

Fractional Gaussian Noise (FGN) process with Hurst para. H=0.89

Simpsons MPEG Video Trace of 20,000 frames

Auto-Correlations of Traffic

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300

Lag

ACF

ACFSUBGEO

ACFEXPON

ACFMPEG

ACFFGN

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Example Solution (td=10)

Optimal Scaling Function

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 1 2 3 4 5 6 7 8 9

time

h(t)

ACFSUBGEO

ACFEXPON

ACFFGN

ACFMPEG

Uniform Distributed

Higher degree of input autocorrelation has a more convexed scaling function

The uniform distributed allocation is a generalization of several existing algorithms for Periodic tasks Sporadic tasks Aperiodic tasks

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Time-Variant Scaling Energy consumption can be reduced if the

scaling function h(t) is adaptive in response to change of input load

Make td runnable queues. Jobs with deadline j are put to queue j

Dis

patc

her Running

queue 1

+

…

Running queue 2

Running queue td

Outputload l(t)

Inputjobs

l1(t)

l2(t)

ltd(t)

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Time-Variant Scaling Minimize energy consumption is to

Resource cap of queue j at time t

subject to:

The optimization has a unique solution:

where qj(t) is the backlog of queue j at time t.

Committed resource for jobs in queue j at time t

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Determine cap of queue 5 at time 0: S5(0)

Illustration

Distribute the job as late as possible

load

The job is distributed to early slots as its size increases

L(t)=0

12 9 7

0 1 2 3 4 5 time slot

5

S5(0)=11

First determine current committed resource

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Example Solution for a Sporadic TaskInput J(WCET): J1(1) released at 0, 5, J2(2) at 1, 7, J3 (1) at 3, 9. Deadline of all jobs: 4. Ji,j: jth instance of task i1. Schduling using EDF w/o scaling

1

1

0 t

0.5

3 954 7

Normalized speed

J1,1 J2,1 J3,1J1,2 J2,2 J3,2

6 10

2. Schduling using the Time Variant Scaling

(a)

0.5

0.25 J1,1

5 t1 3 7 139 11

Normalized speed

(b)

0.690.50.25

J1,1

J2,1

5 t1 3 7 139 11

(c)

0.50.25

J1,1

J2,1

0.69

J3,1

5 t1 3 7 139 11

0.69

(d)

0.5

0.25 J1,1

J2,1J3,1 J1,2 J2,2 J3,2

0.75

5 t1 3 7 139 11

Using a square energy function: 35% more energy saving compared to EDF. 8% to DVSST

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Statistical Deadline Guarantee Worst case scenario schedulability test

Conservative pi: minimum interarrival

fmax

1

F(x)

v

worst case f

cumulative probability

Statistical guarantee Overload probability v=prob(l(t) > fmax)

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Statistical Deadline Guarantee (cont.) Load tail distribution

A general bound w/ load mean and variance

Tight bounds based on load distribution Exact output distribution if input distribution known Estimate output distribution using a histogram

fmaxf’max

1

F(x)v

cumulative probability

b1 b2 bmaxbr-1 bmin

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Evaluation Objectives

Effectiveness in energy savings Effectiveness of the deadline miss bound

Scheduling based on WCET No-DVS: run jobs with the maximum speed. Offline: Offline optimal algorithm of Yao:95 et a. DVSST: On-line algorithm for sporadic tasks Qadi:RTSS03 et al. TimeInvar: Time-invariant voltage scaling. TimeVar: Time-variant voltage scaling.

On-line slack management DVSST+CC (Cycle-conserving EDF): Worst case schedule using

DVSST with the reclaiming algorithm of Pillai and Shin (SOSP01). TimeVar+OLDVS: The time-variant voltage scaling and the

reclaiming algorithm of Lee and Shin:RTSS2004. TimeVar+TimeVar: A unified solution.

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Energy consumption with the Robotic Highway Safety Marker application; A scenario in which robot keeps moving

Energy Savings

00.10.20.30.40.50.60.70.8

1 2 4 6 8 10

Path length of robot move

En

erg

y c

on

sum

pti

on

TimeVar is energy-efficient, close to Offline (5%); 7-11% better than DVSST

DVSST OfflineTimeVariant

11%

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#tasks=30; Interarrival ~ exp(50 ms)WCET ~ n(100, 10)K

Workload variation characterized by actual execution time over worst case (BCET/WCET)

Energy Savings w/ Workload Variation

0

0.1

0.2

0.3

0.4

0.5

0.6

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

BCET/WCET ratio

En

erg

y C

on

sum

pti

on

DVSST+CC TimeVar+TimeVar Offline

TimeVariant adapts with workload variation effectively

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Computation Speed Configuration

Computation requirement based on a general bound is better than worst case with mean interarrivals > 60 ms Tight bounds reduce the computation speed in half as interarrivals > 40 ms

Mean Interarrival time (ms)

Req

uir

ed s

pee

d (

MH

z)

Target deadline guarantee: 99%

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Statistical Deadline Guarantee

No deadline misses under bound derived based on a general input: 100MHz

Statistics of TimeVar/TimeInvar under a tight bound: 40MHz Overload handling: reject new jobs or serve unfinished jobs in a

best-effort mode Target deadline guarantee 99%

SchedulingTimeInvariant TimeVariant

Reject Besteffort Reject Besteffort

Load mean (106) 21.6 21.7 21.6 21.74

Load var 166.7 168.9 141.3 142.8

Time mean 10.1 10.09 10.4 10.07

Time variance 8.7 8.4 8.4 8.8

Overload/Deadline misses

0.63% 0.63% 0.61% 0.61%

Deadline miss rate is effectively bounded

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Conclusion Voltage/Speed scaling for a general task model A Filtering Model for DVS Two online policies to minimize energy usage

Time-invariant : A generalization of several existing approaches

Time-variant : Optimal in the sense it is online w/o future task timing information. Also effective for on-line slack management

Statistical deadline guarantee based on computation speed configuration.

Future work System-wide energy savings, e.g., wireless communication

and its interaction with CPU

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Energy-Aware Modeling and Scheduling of Real-Time Tasks for

Dynamic Voltage Scaling

Thank you!