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:

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

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 S max, then in optimal solution, the speed of the task is S max 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

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 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(SC EDF ) · E(SC) for any feasible schedule SC, where SC EDF is to execute tasks by the above strategy. Temperature minimization Schedule Executing all of the tasks at a constant speed following the earliest-deadline-first (EDF) strategy

UTAS: Ideal Processors (cont.) The maximum temperature of schedule The maximum temperature 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 s i to s j is denoted by σ i,j When σ i,j is negligible Energy minimization Execute at two consecutive speeds of effective speed s T * so that the utilization is 100% is optimal Temperature minimization Execute at two consecutive speeds of effective speed s T * so that the utilization is 100% and frequently change speeds When σ i,j is non-negligible More complicated

UTAS: σ i,j is negligible t speed

UTAS: σ i,j is non-negligible t speedSpeed transition overhead When α = 1, β = 0.01, and σ i,j = 1 for any 0 < i  j ≤ H

Multiprocessor: Largest-Task First (LTF) 11 33 22 44 55 L1L1 L2L2 L3L3 M = 3 11 22 33 44 55 1.Sort tasks in a non- increasing order of c i /p i 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 Jian-Jia Chen, Heng-Ruey Hsu, and Tei-Wei Kuo, "Leakage-Aware Energy-Efficient Scheduling of Real-Time Tasks in Multiprocessor Systems", in RTAS Algorithm LTF is a 1.13-approximation algorithm for energy efficiency. Loads (c i /p i )

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 First paperSecond paper What aboutEnergy, UniprocessorTemperature, Uniprocessor and Multiprocessors FocusAn optimization problemSuboptimal scheduling scheme design Difference from [1] System levelTemperature [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 ！