ECE555 Topic Presentation Energy-efficient real-time scheduling Xing Fu 20 September 2008
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Transcript of ECE555 Topic Presentation Energy-efficient real-time scheduling Xing Fu 20 September 2008
ECE555 Topic Presentation
Energy-efficient real-time scheduling
Xing Fu
20 September 2008
Acknowledge Dr. Jian-Jia Chen from ETH providing PPT Slides for IEEE RTAS 2007
Outline of Presentation
System-level Energy Management for Periodic Real-Time Tasks
On the Minimization of the Instantaneous Temperature for Periodic Real-Time Tasks
Further reference:http://www.cs.pitt.edu/PARC/
http://www.cs.utsa.edu/~dzhu/parc-2005.htm
http://www.cs.pitt.edu/PARTS/publications.html
Outline of Presentation
Why those two papers? Paper 1: Systematic results. Other related
papers can be treated as special cases. Paper 2: A closely related field: temperature
efficient real time scheduling. What will be covered? 1. Main concepts 2. Key ideas 3. Introduction of underlying mathematics if
time allowed
System-level Energy Management for Periodic Real-Time Tasks
What is System-level Energy Management?
A generalized power model which includes the static, frequency-independent active and frequency-dependent active power components of the entire system,
Variations in the system power dissipation during the execution of different tasks
On-chip / off-chip workload characteristics of individual tasks.
Task and Processor Model
min max
Task Model:
1. A set of independent periodic real-time tasks
2. Preemptive Earliest-Deadline-First (EDF) policy.
Processor Assumptions:
1. DVS-enabled
2. frequency S between S and S .
3. Normalize the max CPU speed with respect to S
Power Model
, ,
,
,
Power consumption P:
( )
- static power, removed only by powering off.
- frequency-independent active power
- frequency-dependent active power.
-system states activ
s ind i dep i
s
ind i
dep i
P P P P
P
P
P
e (1) or inactive (0).
Derivation of Energy-Efficient Speed for a Single Task
'
Energy consumption Calculation:
( ) ( ( ) ) ( )
( ) ( )
The speed that minimizes E(S) can be found by
setting its derivative E (S) to zero.It is called
energy-effi
dep ind
dep dep ind ind
xE S P S P y
Sx x
P S P S y P P yS S
cient speed of , denoted by .Seff
Energy-Efficient Speed Assignments for a Task Set
1
1 1
min max
The problem is finding the {S } values so as to:
minimize ( )
1Subject to
1,
This problem in some cases converted to so called
ENERGY-LU problem.
i
n
i ii
xn nyi
bound ii ii
i
E S
uU u
S
S S S i n
Minimize Energy
Guarantee Real Time
ENERGY-LU
Case 1: If energy efficient speed of a particular task is great than Smax, then in optimal solution, the speed of the task is Smax
Case 2: If ,
speed of all tasks will be Case 3: If ,then In case 3, ENERGY-LU is formulated as
,1( ) 1.0
n
i low iiU S
, min, ,max{ }low i eff iS S S
,low iS
,1( ) 1.0
n
i low iiU S
1
( ) 1.0n
i iiU S
1 1
1 ,
max
1
minimize ( ) Subject to1,
1,
xn nyiin
i ii
i ii low i i
i
uu
SE S
S S i n
S S i n
Solving ENERGY-LU
First Reduce to ENERGY-L problem by relaxing the last constrain of ENERGY-LU and solve ENERGY-L problem first.
Case 1: the solution of ENERGY-L problem is also the solution of ENERGY-LU.
Case 2: the solution of ENERGY-L problem is NOT the solution of ENERGY-LU.
If case 2, iteratively adjust solutions of ENERGY-L to solve ENERGY-LU.
Experiment Results I
Dynamic Reclaiming
Why Dynamic Reclaiming?
In practice, many task instances (Jobs) complete without presenting their worst-case workload.
Dynamic Reclaiming is introduced to reclaim unused computation time to reduce the CPU speed while preserving feasibility.
Different scheduling scheme has its own Dynamic Reclaiming.
Dynamic Reclaiming Algorithm
When a job is to be dispatched, it will get the unused computation time from completed higher priority jobs.
Use those time, reduce further CPU speed to save more power.
A supported data structure - queue is needed to store related information.
Experiment Results II
Conclusions
Addressed the problem of minimizing overall energy consumption of a real-time system, considering a generalized power model.
Formulated the problem as a convex optimization problem and derived an iterative, polynomial time solution using Kuhn-Tucker optimality conditions.
Provided a dynamic reclaiming extension for settings where tasks complete early.
On the Minimization of the Instantaneous
Temperature for Periodic Real-Time Tasks
Motivations for Power Saving
Rapid Increasing of Power Consumption The power consumption of processors increases
dramatically. Slow Increasing of the Battery Capacity
The battery capacity increases about 5% per year Embedded Systems vs. Servers
The reduction of power is also needed to cut the power bill off
Heat versus Energy
Energy Minimize the accumulative energy Prolong battery lifetime Reduce execution cost
Heat Minimize the instantaneous temperature Prevent from overheating Reduce packing cost
Cooling Model Cooling is a complex phenomenon [Sergent and
Krum 1998]. For tractability, a simple first-order approximation is
needed. key assumptions:
1. Heat is lost via conduction
2. Ambient temperature of the environment is constant.
This is likely a reasonable first-order approximation in some, but certainly not all, settings.
Cooling Model
The ambient temperature is scaled to 0 Modeled by Fourier’s Law
Initialization
( ) : temperature at time t
'( ) ( ( )) ( )
heating cooling
t
t P s t t
0)(
0)0(
t
Problem Definitions
Generate a feasible schedule SC for a set of tasks T such that Ψ(SC) is minimized. UTAS : uniprocessor temperature-aware schedulin
g problem SMTAS : single-chip multiprocessor temperature-a
ware scheduling problem MMTAS : multi-chip multiprocessor temperature-a
ware scheduling problem
CHIP
Proc.
SMTAS
Proc.
MMTAS
UTAS: Ideal Processors Energy minimization
Executing at a constant speed in the earliest-deadline-first order is optimal in energy consumption minimization by Aydin et al. in RTSS 2001, where
E(SCEDF) · E(SC) for any feasible schedule SC, where SCEDF is to execute tasks by the above strategy.
Temperature minimization Schedule Executing all of the tasks at a constant speed following t
he earliest-deadline-first (EDF) strategy
},max{ min*
T i
iT
ip
cSs
*Ts
UTAS: Ideal Processors (cont.)
The maximum temperature of schedule
The maximum temperature of any feasible schedule
The ratio between the above two
dttsPeTSCt
t
tt 2
1
21 ))(())(( )(
)(
))((*
TEDF
sPTSC
eTSC
TSCEDF
))((
))((
UTAS: Ideal Processors (cont.)
This is an e-approximation algorithm which means the maximum temperature of the suboptimal scheme is at most e times as any optimal scheme.
eTSC
TSCEDF
))((
))((
UTAS: Non-Ideal Processors The timing overhead in speed transition from s i to sj
is denoted by σi,j
When σi,j is negligible
Energy minimizationExecute at two consecutive speeds of effective speed sT
*
so that the utilization is 100% is optimal Temperature minimization
Execute at two consecutive speeds of effective speed sT* so
that the utilization is 100% and frequently change speeds
When σi,j is non-negligible
More complicated
UTAS: σi,j is negligible
t
speed
UTAS: σi,j is non-negligible
t
speed Speed transition overhead
When α = 1, β = 0.01, and σi,j = 1 for any 0 < i j ≤ H
Multiprocessor: Largest-Task First (LTF)
132 4 5
L1
L2
L3
M = 3
1
2
3 4
5
1. Sort tasks in a non-increasing order of ci/pi
2. Assign tasks in a greedy manner to the processor with the smallest load
3. Execute tasks on a processor at the speed with 100% utilization
Jian-Jia Chen, Heng-Ruey Hsu, Kai-Hsiang Chuang, Chia-Lin Yang, Ai-Chun Pang, and Tei-Wei Kuo, "Multiprocessor Energy-Efficient Scheduling with Task Migration Considerations", in ECRTS 2004.
Jian-Jia Chen, Heng-Ruey Hsu, and Tei-Wei Kuo, "Leakage-Aware Energy-Efficient Scheduling of Real-Time Tasks in Multiprocessor Systems", in RTAS 2006.
Algorithm LTF is a 1.13-approximation algorithmfor energy efficiency.
Loads (ci/pi)
SMTAS and MMTAS
Applying Algorithm LTF for scheduling (1.13e)-approximation for MMTAS (2.371e)-approximation for SMTAS
Conclusions
Analysis for the maximum instantaneous temperature for energy-efficient scheduling algorithms in uniprocessor and multiprocessor systems e-approximation for uniprocessor scheduling on ideal
processors (1.13e)-approximation when multi processors are on a chip (2.371e)-approximation when each processor is on an
individual chip designs for non-ideal processors
Comparison of two papersFirst paper Second paper
What about Energy, Uniprocessor Temperature, Uniprocessor and Multiprocessors
Focus An optimization problem Suboptimal scheduling scheme design
Difference from [1]
System level Temperature
[1] Dynamic and Aggressive Power-Aware Scheduling Techniques for Real-Time Systems
Selected Critiques I
Maybe apply latest results from optimization community to derive Optimal solution.
Example, Linear Matrix Inequality. More accurate model of CPU cooling maybe
investigated. Then new scheduling algorithms or feedback control system can be designed accordingly.
Selected Critiques II
Optimizing other QoS parameters for power aware real time system.
Examples: Thermal, fault tolerance, through-output.
Any Question?
Thank you !