Small Telescopes, Big Science Arne Henden Director, AAVSO [email protected].
UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling...
-
date post
15-Jan-2016 -
Category
Documents
-
view
213 -
download
0
Transcript of UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling...
![Page 1: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/1.jpg)
UCb
Kim G. Larsen Arne Skou &
Peter Koch Anders Brødløs Henrik Schiøler
Dynamic Voltage Scalingusing
Optimal Infinite Schedulingwork in progress
POTENTIAL NEW CS
![Page 2: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/2.jpg)
2AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Overview
Dynamic Voltage Scaling
Task Scheduling Principles using timed automata
Energy Optimal Task Scheduling using priced timed automata
![Page 3: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/3.jpg)
3AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Energy vs. Batteries
Increased processor performance => Increasing power dissipation
Slow battery development
year
BatteryCapacity
required
expected
![Page 4: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/4.jpg)
4AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
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
![Page 5: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/5.jpg)
5AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
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
![Page 6: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/6.jpg)
6AMETIST Aalborg Sep 2003 Kim G. Larsen
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
![Page 7: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/7.jpg)
7AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Modeling Task
T1T1
T2T2
TnTn
SchedulerScheduler
2 14 3
readydone
stoprun
![Page 8: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/8.jpg)
8AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Modeling Sched.
T1T1
T2T2
TnTn
SchedulerScheduler
2 14 3
readydone
stoprun
![Page 9: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/9.jpg)
9AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Modeling Queue
T1T1
T2T2
TnTn
SchedulerScheduler
2 14 3
readydone
stoprun
![Page 10: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/10.jpg)
10AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb Schedulability = Safety Property
A :(Task0.Error or Task1.Error or …)
:(Task0.Error or Task1.Error or …)
May be extended with preemption
![Page 11: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/11.jpg)
11AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Energy Optimal Scheduling
T1T1
T2T2
TnTn
SchedulerScheduler
2 14 3
readydone
stoprun F:= ?? ; V:= ??
“Choose” Freq/Scaling
(Voltage/Cost)
Using PTA
![Page 12: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/12.jpg)
12AMETIST Aalborg Sep 2003 Kim G. Larsen
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 …)
![Page 13: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/13.jpg)
13AMETIST Aalborg Sep 2003 Kim G. Larsen
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
![Page 14: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/14.jpg)
14AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Preliminary Results
Computed Schedule without preemption
![Page 15: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/15.jpg)
15AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Preliminary Results
Computed Schedule WITH preemption
![Page 16: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/16.jpg)
16AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
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
![Page 17: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/17.jpg)
17AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
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
![Page 18: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/18.jpg)
18AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
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.)
![Page 19: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/19.jpg)
19AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
![Page 20: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/20.jpg)
20AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Dynamic Voltage Scaling
![Page 21: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/21.jpg)
21AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb The Plate Juggling Problem thanks to Oded
Problem: avoid having the plates falling down
![Page 22: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/22.jpg)
22AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb The Plate Juggling Problem thanks to Oded
Problem: avoid having the plates falling down
![Page 23: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/23.jpg)
23AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb The Plate Juggling Problem using Timed Automata
A Plate
The Joggler
![Page 24: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/24.jpg)
24AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Optimal Infinite Schedulingwith respect to what ??
![Page 25: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/25.jpg)
25AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Optimal Infinite Schedulingwith respect to what ??
64
72
Linearly Priced Timed Automata=
Timed Automata withCosts (rates and impulses)
1
5
![Page 26: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/26.jpg)
26AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Optimal Infinite Schedulingwith respect to what ??
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
![Page 27: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/27.jpg)
27AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
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
Optimal Schedule *: val(*) = inf val()
![Page 28: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/28.jpg)
28AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
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
Optimal Schedule *: val(*) = inf val()
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]
![Page 29: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/29.jpg)
29AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Discrete Case
Simplified Juggling Problem
whack1 whack2
2 1
![Page 30: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/30.jpg)
30AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Discrete Case
Simplified Juggling Problem
whack1 whack2
2 1
x
y
1 2 3 4
1
2
3
![Page 31: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/31.jpg)
31AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
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
Simplified Juggling Problem
![Page 32: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/32.jpg)
32AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
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
![Page 33: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/33.jpg)
33AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Discrete Case
whack1 whack2
2 1
Simplified Juggling Problem
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.
Infinite Schedule: = ((2);whack1;epsilon(1); whack2;(3);whack2;whack1)*
x
y
1 2 3 4
1
2
3
2
3
12
2
11
val()= (2+1+1+2)/(2+1+3) = 1
![Page 34: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/34.jpg)
34AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Appr Optimal Schedules using UPPAAL
whack1 whack2
2 1
Simplified Juggling Problem
optimal ??
cost: impulsereward: time
Infinite Schedule: = ((2);whack1;epsilon(1); whack2;(3);whack2;whack1)*
x
y
1 2 3 4
1
2
3
2
3
12
2
11
val()= (2+1+1+2)/(2+1+3) = 1
![Page 35: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/35.jpg)
35AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Appr Optimal Schedules
int[0,N] cost;clock time;
![Page 36: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/36.jpg)
36AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Appr Optimal Schedules
int[0,N] cost;clock time;
E[] (not (Plate1.Bang or Plate2.Bang) and (cost>=N-1 imply time >= M))=E[](N,M)
![Page 37: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/37.jpg)
37AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Appr Optimal Schedules
int[0,N] cost;clock time;
E[] (not (Plate1.Bang or Plate2.Bang) and (cost>=N-1 imply time >= M))=E[](N,M)
² (N,M) imply val()· N/M
![Page 38: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/38.jpg)
38AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Appr Optimal Schedules
int[0,N] cost;clock time;
E[] (not (Plate1.Bang or Plate2.Bang) and (cost>=N-1 imply time >= M))=E[](N,M)
(N,M) 9²[] (N,M)
(3,3) YES
(3,4) NO
(7,8) YES
(7,9) NO
(10,12) YES
(10,13) NO
![Page 39: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/39.jpg)
39AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
Appr Optimal Schedules
int[0,N] cost;clock time;
(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
![Page 40: UCb Kim G. Larsen Arne Skou & Peter Koch Anders Brødløs Henrik Schiøler Dynamic Voltage Scaling using Optimal Infinite Scheduling work in progress POTENTIAL.](https://reader030.fdocuments.us/reader030/viewer/2022013101/56649d805503460f94a64d97/html5/thumbnails/40.jpg)
40AMETIST Aalborg Sep 2003 Kim G. Larsen
UCb
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