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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

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ECE555 Topic Presentation Energy-efficient real-time scheduling Xing Fu 20 September 2008

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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-dependentactive power components of the entire system,

  • Variations in the system power dissipation during the executionof different tasks

  • On-chip / off-chip workload characteristics of individualtasks.


Task and Processor Model


Power Model


Derivation of Energy-Efficient Speed for a Single Task


Energy-Efficient Speed Assignments for a Task Set

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


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


CHIP

Proc.

Proc.

SMTAS

MMTAS

Problem Definitions

Generate a feasible schedule SC for a set of tasks T such that Ψ(SC) is minimized.

  • UTAS : uniprocessor temperature-aware scheduling problem

  • SMTAS : single-chip multiprocessor temperature-aware scheduling problem

  • MMTAS : multi-chip multiprocessor temperature-aware scheduling problem


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

    • Executingall of the tasks at a constant speed following the earliest-deadline-first (EDF) strategy


UTAS: Ideal Processors (cont.)

  • The maximum temperature of schedule

  • The maximumtemperature of any feasible schedule

  • The ratio between the above two


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.


UTAS: Non-Ideal Processors

  • The timing overhead in speed transition from si to sj

    is denoted by σi,j

  • When σi,j is negligible

    • Energy minimization

      Execute 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


speed

t

UTAS: σi,j is negligible


UTAS: σi,j is non-negligible

speed

Speed transition overhead

t

When α = 1, β = 0.01, and σi,j = 1 for any 0 < i j ≤ H


Multiprocessor: Largest-Task First (LTF)

M = 3

2

3

4

5

1

Loads (ci/pi)

  • Sort tasks in a non-increasing order of ci/pi

  • Assign tasks in a greedy manner to the processor with the smallest load

  • Execute tasks on a processor at the speed with 100% utilization

L1

1

L2

2

5

L3

3

4

Algorithm LTF is a 1.13-approximation algorithm

for energy efficiency.

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.


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 papers

[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!


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