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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

Acknowledge Dr. Jian-Jia Chen from ETH providing PPT Slides for IEEE RTAS 2007

Outline of presentation
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:

Outline of presentation1
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

What is system level energy management
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.

Energy efficient speed assignments for a task set
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.

Dynamic reclaiming
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
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.


  • 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.

Motivations for power saving
Motivations for Power Saving Periodic Real-Time Tasks

  • 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
Heat versus Energy Periodic Real-Time Tasks

  • 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 Model Periodic Real-Time Tasks

  • 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 model1
Cooling Model Periodic Real-Time Tasks

  • The ambient temperature is scaled to 0 Modeled by Fourier’s Law

  • Initialization

Problem definitions

CHIP Periodic Real-Time Tasks





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
UTAS: Ideal Processors Periodic Real-Time Tasks

  • 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
UTAS: Ideal Processors (cont.) Periodic Real-Time Tasks

  • The maximum temperature of schedule

  • The maximumtemperature of any feasible schedule

  • The ratio between the above two

Utas ideal processors cont1
UTAS: Ideal Processors (cont.) Periodic Real-Time Tasks

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
UTAS: Non-Ideal Processors Periodic Real-Time Tasks

  • 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

Utas i j is negligible

speed Periodic Real-Time Tasks


UTAS: σi,j is negligible

Utas i j is non negligible
UTAS: σ Periodic Real-Time Tasksi,j is non-negligible


Speed transition overhead


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

Multiprocessor largest task first ltf
Multiprocessor: Largest-Task First (LTF) Periodic Real-Time Tasks

M = 3






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









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
SMTAS and MMTAS Periodic Real-Time Tasks

Applying Algorithm LTF for scheduling

  • (1.13e)-approximation for MMTAS

  • (2.371e)-approximation for SMTAS

Conclusions Periodic Real-Time Tasks

  • 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
Comparison of two papers Periodic Real-Time Tasks

[1] Dynamic and Aggressive Power-Aware Scheduling Techniques for Real-Time Systems

Selected critiques i
Selected Critiques I Periodic Real-Time Tasks

  • 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
Selected Critiques II Periodic Real-Time Tasks

  • Optimizing other QoS parameters for power aware real time system.

    Examples: Thermal, fault tolerance, through-output.

Any question
Any Question? Periodic Real-Time Tasks

Thank you!