Transcript Investigating the Effect of Voltage

Investigating the Effect of VoltageSwitching on Low-Energy Task
Scheduling in Hard Real-Time
Systems
Paper review
Presented by
Chung-Fu Kao
What’s the Problem ?
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The relationship between voltage-switching
and energy consumption.
Switching times have a significant effect on the
energy consumed in hard real-time systems.
How to reduce the voltage switching time ?
2
Introduction
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Energy consumption is becoming an
important design parameter for portable and
embedded systems.
– Battery cost
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One approach to conserve energy is to employ
low-power design methodology.
Scheduling algorithm is proposed.
– To minimize the energy consumed by a periodic task
set
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Idea & Assumption
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The algorithm is based on “earliest-deadlinefirst (EDF)” algorithm.
The voltage of the CPU may be switched
between two or more values dynamically at
run-time through OS system call.
Voltage switching takes time and consumes
energy.
Find the minimum voltage of entire set of
tasks.
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Preliminaries
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A set of n periodic tasks
– Notation: R  {r1, r 2,...,rn}, each taskri  R
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Each task has the following parameters
– A release (or arrival) time ai,
– A deadline di,
– A length li (# of instruction cycle), and
– A period pi
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CPU can operate at one of two voltage: v1 or
v2, e.g. 1.3v or 2.5v
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Preliminaries (contd.)
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Each task ri may be executed at a voltage vi,
vi {v1, v2}
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The system uses up C units of energy
The relation between power consumption and
CPU voltage
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– Equation: Pi   Vdd2  Ci  f  Ei *
2
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So, power (energy) consumption Ei consumed
by task ri of length li is Ei  vi2  li
*
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Reference “Logic Synthesis for Low Power VLSI Designs”
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MILP Goal
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MILP: Mixed-Integer Linear Programming
Minimize a linear objective function on a set of integer
and/or real variables, while satisfying a set of linear
constraints
Task set R  {r1, r 2,...,rn}, each taskri  R
–
–
–
–
–
–
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A release time ai  Z 0
A deadline
di  Z 
A length
li  Z 
An operating voltage
vi {v1, v2}
A corresponding execution speed xi {x1, x2}
A cost to switch Ci
Goal:
min (i 1 (vi2li  Ci ))
n
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MILP Method
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Assume a linear relationship between the operating
voltage v and its execution speed x
vi  displaysty le
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The execution speed of task i, to be either s1 or s2
(CPU speed), and ai, bi are binary variables
xi  ai s1  bi s2 , 1  i  n
ai  bi  1, 1  i  n

xi
vi2 
xi2

2
 ai 
s12

2
 bi 
s22
2
Goal:
min (i 1 (vi2li  Ci ))
n
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The E-LEDF Algorithm
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E-LEDF: Extend-Low-energy Earliest Deadline First
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Experimental Results
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Assume that the two processor speeds to be 300 MIPS at 2.47V
and 400MIPS at 3.3V
Assume that the switching time is 0.4 units(milliseconds) and
switching power is 50 units(mW)
Task
ti
Release
ai
Deadline
di
Length li
(x 106)
Li / 300
(x 106)
Li / 400
(x 106)
t1
t2
t3
t4
3
9
0
18
7
21
5
25
800
750
1600
1000
2.66
2.5
5.33
3.33
2.0
1.875
4.0
2.5
Task Set
Configuration
24 tasks
ts=5, vs=200
ts=5, vs=10
ts=1, vs=200
ts=1, vs=10
39 tasks
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ts=5, vs=200
ts=5, vs=10
ts=1, vs=200
ts=1, vs=10
LEDF
199418.76
309338.65
E-LEDF
% increase
213376.26
212236.26
201771.65
200631.65
6.99
6.42
1.17
0.60
380317.625
378987.625
345221.25
342751.25
22.90
22.50
11.59
10.80
E-LEDF
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Conclusions
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Energy consumption is becoming an
increasingly important design issue.
The need for algorithms that attempt to
minimize energy usage both at the system
synthesis/design level, as well as the run-time/
operating system level are being increasingly
felt.
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