1. Lev Finkelstein ISCA/Thermal Workshop 6/2004
Overview
Motivation (Kevin)
Thermal issues (Kevin)
Power modeling (David)
Thermal management (David)
Optimal DTM (Lev)
Clustering (Antonio)
Power distribution (David)
What current chips do (Lev)
HotSpot (Kevin)
Lev Finkelstein ISCA/Thermal Workshop 6/2004

2. Optimal DTM strategies

3. Lev Finkelstein ISCA/Thermal Workshop 6/2004
Agenda
Motivation
DTM as an optimization problem
Thermal models
Theoretical analysis
Numerical approach
Example
Possible applications
Lev Finkelstein ISCA/Thermal Workshop 6/2004

4. Lev Finkelstein ISCA/Thermal Workshop 6/2004
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?
Lev Finkelstein ISCA/Thermal Workshop 6/2004

5. Lev Finkelstein ISCA/Thermal Workshop 6/2004
DVS scenario for 2 cores
Air
Heat Sink
Heat Pipe
Silicon
CPU1
CPU2
Unit
2D power
Map
freq
volt
freq
volt
DVS1
DVS2
Lev Finkelstein ISCA/Thermal Workshop 6/2004

6. Optimal behavior (cont’d)
We need a methodology for analysis of optimal behavior
Offline analysis of existing strategies
Guide for the design of new strategies
Lev Finkelstein ISCA/Thermal Workshop 6/2004

7. DTM as an optimization problem
What is the optimization criterion?
What is the set of possible strategies?
What are the constraints?
Lev Finkelstein ISCA/Thermal Workshop 6/2004

8. DTM optimization criterion
Goal: maximize the “performance”
To a first approximation, similar to frequency maximization
Lev Finkelstein ISCA/Thermal Workshop 6/2004

9. Lev Finkelstein ISCA/Thermal Workshop 6/2004
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
Frequency
Time
Instead
Lev Finkelstein ISCA/Thermal Workshop 6/2004

10. Lev Finkelstein ISCA/Thermal Workshop 6/2004
Constraints
Thermal constraints: do not exceed Tmax
Frequency constraints: do not exceed maximal frequency
Additional constraints: frequency should be consistent with the voltage
Lev Finkelstein ISCA/Thermal Workshop 6/2004

11. Lev Finkelstein ISCA/Thermal Workshop 6/2004
RC networks
Heat
Pipe
Silicon
Heat Sink
Lev Finkelstein ISCA/Thermal Workshop 6/2004

12. Lev Finkelstein ISCA/Thermal Workshop 6/2004
1D heat flow
Power in
Core
Heat Pipe
Heat Sink
Lev Finkelstein ISCA/Thermal Workshop 6/2004

13. Lev Finkelstein ISCA/Thermal Workshop 6/2004
3D heat flow
Lev Finkelstein ISCA/Thermal Workshop 6/2004

14. Lev Finkelstein ISCA/Thermal Workshop 6/2004
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
Lev Finkelstein ISCA/Thermal Workshop 6/2004

15. Theoretical analysis (cont’d)
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
Lev Finkelstein ISCA/Thermal Workshop 6/2004

16. Theoretical analysis (cont’d)
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
Lev Finkelstein ISCA/Thermal Workshop 6/2004

17. Lev Finkelstein ISCA/Thermal Workshop 6/2004
Numerical approach
The mathematical problem is solved by numerical methods
May handle rather complex thermal models
Used as an offline procedure
Lev Finkelstein ISCA/Thermal Workshop 6/2004

18. Numerical approach (cont’d)
Developed a methodology based on mathematical programming
Handles large RC networks
May handle time-dependent power profiles, leakage power, etc.
Lev Finkelstein ISCA/Thermal Workshop 6/2004

19. Lev Finkelstein ISCA/Thermal Workshop 6/2004
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
Lev Finkelstein ISCA/Thermal Workshop 6/2004

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
Lev Finkelstein ISCA/Thermal Workshop 6/2004

21. Optimal strategy behavior (cont’d)
A non-typical thermal behavior (decreases while power increases)
The reason – a non-uniform power map
Lev Finkelstein ISCA/Thermal Workshop 6/2004

22. Possible applications
Combining with power predictor
Optimization of activity migration
Just a nice fact – for a single-RC thermal model a PID controller that is tuned for performance behaves similarly to the optimal strategy
Lev Finkelstein ISCA/Thermal Workshop 6/2004