1. Dynamic Power Management for Streaming Data
Nathaniel Pettis, Le Cai, and Yung-Hsiang Lu
ISLPED’04, August 9-11, 2004
指導教授: Chia-Lin Yang
Reporter: Po-Liang Wu

2. Outline Introduction Problem Description Mathematical Solution
Experiments
Conclusion

3. Introduction
Currently, many devices have several power consumption states, such as idle, sleep, turned off.
Dynamic power management (DPM) changes a component’s power states to save power.
However, change power states may introduce extra overheads both on performance and energy

4. Introduction
This paper inserts a buffer between producer and consumer to achieve longer idle period and reduce power consumption.
Producer
Buffer
Consumer
Disk
Decoder
RAM

5. Outline Introduction Problem Description Mathematical Solution
Experiments
Conclusion

6. Problem Description constant
Producer Wake up
Producer Sleep
Producer Wake up
Producer Sleep
constant
variable
α: the rate of storing data into the buffer
β: the rate of removing data from the buffer
Q: Maximum data can be stored in the buffer
λ: awakening delay
w: awakening point

7. Problem Description
In reality, consuming rate β may vary, so this paper models β as a random variable.
f(β): the density function of β
Let γ be the expected value of β,
We assume that α > γ; otherwise, the buffer will eventually underflow.

8. Energy Penalty for Underflow
Awakening point w size:
Large: the buffer consumes more power
Small: the buffer will underflow easily
This paper qualifies underflow by assigning an energy penalty when underflow occurs.
The underflow occurs only if the consumed data exceeds awakening data w, that is λβ > w.

9. Energy Penalty for Underflow
Let ρ be the energy penalty for each MB of underflowed data.
Let p(w) be the penalty energy:
x: data consuming rate
f(x): consuming rate probability
amount of data overflow

10. Outline Introduction Problem Description Mathematical Solution
Experiments
Conclusion

11. Mathematical Solution
α: producing rate
γ: average consuming rate
w: awakening point
(w- λγ)+(α-γ)t1
w- λγ
average amount of data
Q = (w- λγ)+(α-γ)t1
Average data during t1: [(w- λγ) + (w- λγ+(α-γ)t1)] / 2

12. Mathematical Solution
System energy consumption in one period = producer energy + buffer energy + underflow penalty
Producer energy: pp*t1+k, k is a constant
Buffer energy:
Underflow penalty:
Power consumption: energy consumption/(t1+t2)

13. Mathematical Solution
Let S be the amount of data is produced in a period, S = α*t1
The expected length of one period t1+t2 = S/γ
Power consumption:
We have two variables, S and w, to minimize average power in one period.
We take partial derivatives with respect to S and w to derive optimal value S*, w* and Q*.

14. Mathematical Solution
When pb is large, we should decrease w*.
When ρ increases, w* should increase to avoid underflowing.
When γ is large, w* should increase to keep more data.
α: producing rate
γ: average consuming rate
w: awakening point
ρ: energy penalty per MB

15. Outline Introduction Problem Description Mathematical Solution
Experiments
Conclusion

16. Experiments Configurations
Application
MPEG-1 video codec
Consuming rate (β)
1.5 Mbps +- 50% with uniform distribution
Producing rate (α)
1.824 MB/s
Awakening delay (λ)
0.238 s
Energy penalty (ρ)
10 J/MB
Producer power consumption (pp)
0.221 W
Buffer power consumption (pb)
0.012 W/MB
Optimal awakening point (w*)
44.6 kB
Optimal buffer size (Q*)
2.06 MB

17. Experiment Results – Buffer vs. Unbuffered
The power saving is 74.5% if we can turn off each byte of buffer.
The power saving is 73.6% if we use 256KB as the unit of buffer.
For MPEG-2 video, the power saving is 34%
State-changing overhead
Energy Reduction

18. Experiment Results – Buffer Size and Awakening Point
When the awakening point is less the w*, power savings can be achieved by increasing the buffer size. w*

19. Outline Introduction Problem Description Mathematical Solution
Experiments
Conclusion

20. Conclusion
This paper presents a method to calculate optimal buffer size and awakening point for streaming data to reduce power consumption.
The results shows over 74% power reduction for MPEG-1 video and 34% for MPEG-2 video.

21. Q & A
Is it reasonable to assume that each unit of buffer can be turned? Can the overhead of turning on/off the buffer be neglected?
If we have the knowledge of working load, can we adaptively change the buffer size or change the device power mode appropriately?

22. Thank You !

23. Examples – DPM
Run
Idle
Sleep
10us
90us
160ms
P=400mW
P=50mW
P=0.16mW