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 ！