Overview

1
Overview

1. Motivation (Kevin)
2. Thermal issues (Kevin)
3. Power modeling (David)
4. Thermal management (David)
5. Optimal DTM (Lev)
6. Clustering (Antonio)
7. Power distribution (David)
8. What current chips do (Lev)
9. HotSpot (Kevin)

2
Optimal DTM strategies
3
Agenda

• Motivation
• DTM as an optimization problem
• Thermal models
• Theoretical analysis
• Numerical approach
• Example
• Possible applications

4
Optimal behavior

• There are various DTM techniques
• Can we say that a DTM method is good enough?
• Can we say that a DTM method may be tuned to
  perform well?
• Are there optimal strategies at all?

5
DVS scenario for 2 cores
Air
Heat Sink
Heat Pipe
Silicon
CPU1
CPU2
Unit
2D power Map
freq volt
freq volt
DVS1
DVS2
6
Optimal behavior (contd)

• We need a methodology for analysis of optimal
  behavior
• Offline analysis of existing strategies
• Guide for the design of new strategies

7
DTM as an optimization problem

• What is the optimization criterion?
• What is the set of possible strategies?
• What are the constraints?

8
DTM optimization criterion

• Goal maximize the performance
• To a first approximation, similar to frequency
  maximization

9
DVS strategies

• A strategy f(t) dictates how to change frequency
  and voltage
• An optimal strategy extracts more clock cycles
  than any other legal strategy

10
Constraints

• Thermal constraints do not exceed Tmax
• Frequency constraints do not exceed maximal
  frequency
• Additional constraints frequency should be
  consistent with the voltage

11
RC networks
12
1D heat flow
13
3D heat flow
14
Theoretical analysis

• Build a mathematical formulation of the problem
• Solve the optimization problem by one of the
  existing theoretical methods
• Feasible only for simple thermal models

15
Theoretical analysis (contd)

• Optimal strategy for a single-RC model1

1From Cohen et. al, On Estimating Optimal
Performance of CPU Dynamic Thermal Management."
Computer Architecture Letters, Volume 2, Oct.
2003
16
Theoretical analysis (contd)

• Optimal strategy consists of three stages
• Start from the maximal frequency
• Decrease exponentially until the temperature
  reaches Tmax
• Run with the natural frequency that keeps the
  temperature on Tmax

17
Numerical approach

• The mathematical problem is solved by numerical
  methods
• May handle rather complex thermal models
• Used as an offline procedure

18
Numerical approach (contd)

• Developed a methodology based on mathematical
  programming
• Handles large RC networks
• May handle time-dependent power profiles, leakage
  power, etc.

19
Example

• A 3D thermal model
• Power is assumed to be proportional to the cube
  of the frequency
• A constant power profile
• A non-uniform power distribution

20
Optimal strategy behavior

• Power starts at a high value and decreases
  exponentially until the maximal temperature is
  reached
• The maximal junction temperature is maintained,
  while the power approaches the steady state

Area of potential performance gain
21
Optimal strategy behavior (contd)

• A non-typical thermal behavior (decreases while
  power increases)
• The reason a non-uniform power map

22
Possible applications

• Combining with power predictor
• Optimization of activity migration
• Just a nice fact for a single-RC thermal model
  a PID controller (eg Skadron, HPCA 2002) that
  is tuned for performance behaves similarly to the
  optimal strategy