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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

- 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

- 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

- 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.

Minimize Energy

Guarantee Real Time

- 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

- 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.

- 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.

- 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.

On the Minimization of the Instantaneous Temperature for 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

- Energy
- Minimize the accumulative energy
- Prolong battery lifetime
- Reduce execution cost

- Heat
- Minimize the instantaneous temperature
- Prevent from overheating
- Reduce packing cost

- 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.

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

CHIP

Proc.

Proc.

SMTAS

MMTAS

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

- 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

- The maximum temperature of schedule
- The maximumtemperature of any feasible schedule
- The ratio between the above two

This is an e-approximation algorithm which means the maximum temperature of the suboptimal scheme is at most e times as any optimal scheme.

- 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

- Energy minimization
- When σi,j is non-negligible
- More complicated

speed

t

speed

Speed transition overhead

t

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

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.

Applying Algorithm LTF for scheduling

- (1.13e)-approximation for MMTAS
- (2.371e)-approximation for SMTAS

- 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

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

- 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.

- Optimizing other QoS parameters for power aware real time system.
Examples: Thermal, fault tolerance, through-output.

Thank you！