energy efficient real-time scheduling - mit - massachusetts
TRANSCRIPT
Energy Efficient Real-Time Scheduling
Amit Sinha and Anantha Chandrakasan
Massachusetts Institute of Technology
2
Outline
! Dynamic voltage and frequency scaling! Overview! Energy workload model
! Real-time algorithms! Performance metrics! Earliest Deadline First (EDF) algorithm
! Slacked Earliest Deadline First (SEDF) algorithm! Bounds on energy savings! Rate Monotonic extensions
3
Motivation for Energy Efficiency
! Electricity cost of servers, desktops and network equipment! Currently accounts for about 100
TWHr/year in the US
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1995
1996
1997
1998
2001
! Proliferation of portable devices! Battery technology lags behind! 50X µP power vs. 4X in battery
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Dynamic Voltage Scaling
ACTIVE IDLE
EFIXED = ½ C VDD2
Fixed Power Supply
ACTIVE
EVARIABLE = ½ C (VDD/2)2 = EFIXED / 4
Variable Power Supply
0.2 0.4 0.8 1.0
0.2
0.4
0.6
0.8
1.0
Normalized Workload
Nor
mal
ized
Ene
rgy
Fixed Supply
VariableSupply
00 0.6
! Variable frequency processors ! Transmeta�s Crusoe
! LongRun Technology
! AMD K6-2+! PowerNOW!
! Mobile Pentium III! SpeedStep
! StrongARM SA-1100! 59 MHz � 206 MHz
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Energy Workload Model
( )2
2
00
20 22
+++= r
VVrr
VVrfTCVrE tt
refs
[Gutnik97]
( )
+++=
2
00
0
22r
VVrr
VV
VVrIrI tt
refref
0 0.2 0.4 0.6 0.8 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Workload (r)
Nor
mal
ized
Ene
rgy
No Voltage Scaling
Ideal
E(r) = r3
E(r) = r2
Energy vs Workload
! Quadratic model fairly accurate! E-r graph convex
( ) 2rrE ≈
( ) 21 rrEsave −≈
6
Real-Time DVS Scheduling
! At time ti scheduler decides! Next task that will run on the processor, τi
! Optimum operating voltage and frequency
! Maximize energy savings and real-time efficiency metric
Variable VoltageProcessor
DC
/DC
C
onve
rter
Wor
kloa
dM
onit
or
Vfixed
V(r) w f(r)
r
λ1
λ2
λn
Task Queue
λ
Pro
cess
or U
tiliz
atio
n (
%)
Time (s)
Dialup Server
WorkstationFileserver
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Real-Time Metrics
Maximum lateness
Weighted completion time
Number of late tasks
Total completion time
Average response time
Cost FunctionMetric
( )∑=
−=N
iiir af
Nt
1
1
( ) ( )iic aft minmax −=
∑=
=N
iiiw fwt
1
( ) ( ) ≤
== ∑= other
dffmissfmissN iii
N
iilate 1
0
1
( )ii dfL −= maxmax
! Lmax appropriate metric for hard real-time algorithms
8
Earliest Deadline First
! EDF optimal in minimizing Lmax amongst all possible dynamic priority algorithms [Dertouzos]
c2
c1
a2 d2
a1
г2
г1
EDF schedule
d1
d3a3
г3 c3
г1 г2 г3 г2 г1
Time
Task
s
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DVS with Real-Time Deadlines
c2
c1
a2 d1,d2
a1
г2
г1
Earliest Deadline First
Greedy DVS
c2
c1/2
a2 d1,d2
a1
г2
г1r1=0.5
c1/2
! Need an intelligent scheduling algorithm
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Proposed Optimal Scheduling
ti-1 ti ti+1 di∆t
τi scheduled
ci
di
i
ii d
cS =
! The Slacked Earliest Deadline First (SEDF) algorithm! Optimum processing rate is approximated by
( ) ( ) ≤<−+
=otherwise
SUSSUSr iiii
iii ,110,1
,
( ) ( ){ }rErP save⋅maxOptimum rate, r
11
SEDF Analysis
( ) ( ) kdi
ki
d
rck
i ii
i
UUkd
rP −
=
−
= ∑ 1
! Probability that task τi completes before its deadline for a given slack, r, and utilization Ui
! Expected energy savings
( ) ( )( )21 rrPr −=ξ
! Optimal slack, ropt
( ) ( )( )rPrP
rr
rr ′
=−
⇒=∂
∂21
20ξ
! Optimal slack well approximated by linear solution
12
Why SEDF is Optimal
! Maximizes expectedenergy savings
Si increasing
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SEDF Scheduling Example
! SEDF is optimal in minimizing maximum lateness (Lmax) and processor energy
SEDF Schedule
Arrival time
Deadline
Computation
ProcessorUtilization, U
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SEDF Results
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Processor Utilization
Ener
gy R
atio
! Energy savings of 60% with 10% Lmax degradation (averaged over 3x106 experiments)
! SEDF approaches EDF as utilization increases
Energy Ratio
Maximum Lateness Ratio
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Bounds on Energy Savings
! Averaging is energy efficient because of convex E(r)
T 2T
Time
Wor
kloa
d
1.0
0.5
W1
W2
0.675
Ener
gy
1.0
0.5
W1 W2
0.5625
)()(22
221
22
21 rErErrrr ≥→
+≥+
! Best schedule tries to! Minimize workload variance! Maximize utilization! Use all possible slack
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Bounds on Energy Savings [cont ..]
! Maximum energy savings
2
≥
∑∑∑k
kk
kkk k
k crcrc
( ) ∑∑∑ ≥=k
kk
kkk
kk
k rcrcrErc
min
Time
Wor
kloa
d
1.0
0.5
ττττ2
ττττ1
( )k
kk
d
cr
maxmin
∑=
2minmax, 1 rEsave −=
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Periodic Scheduling
! Rate Monotonic Analysis (RMA) [Liu73]
−≤∑ 12
1N
i i
i NTc Guaranteed schedulability criteria
Smaller period tasks have higher priority
83.012265.0 21
2
2
1
1 =
−≤=+
Tc
Tc
Example
г1
г2
c1 = 2 T1 = 5
c2 = 1 T2 = 4
RM Schedule
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Slacked Rate Monotonic Analysis
! A set of periodic real-time tasks is guaranteed to be schedulable with maximum energy savings iffprocessing rate is set to rmin
−
=∑
121min
N
ii
i
N
Tc
rTi → PeriodN → Total TasksCi → Computation Time
! Slack processing rate, r, till utilization approaches RM bound
19
Conclusions
! Dynamic voltage and frequency scheduling can yield quadratic energy savings
! Slacked Earliest Deadline First (SEDF) algorithm is optimal in minimizing expected energy consumption under Lmax criteria
! Optimal slacking possible under Rate Monotonic scheduling for static periodic task sets