1. Size-Based Scheduling Policies with Inaccurate Scheduling Information
Dong Lu*, Huanyuan Sheng+, Peter A. Dinda*
*Prescience Lab, Dept. of Computer Science
+Dept. of Industrial Engineering & Management Science
Northwestern University
Evanston, IL USA

2. Outline Review of size-based scheduling Motivation Simulation Setup
Simulation Results
New applications
Motivation: How does size-based scheduling performance depend on accurate job sizes

3. Non-size-based scheduling
FCFS, PS, etc.
FCFS: First Come First Serve
Intuitive
Easiest to implement
PS: Processor Sharing
Fair: all jobs accept equal resources
Also easy to implement
Problem: Unaware of job size information, which results in big mean response time

4. Review of size-based scheduling
SRPT, FSP, etc.
Utilize the job size (processing time, service time) information for scheduling
Optimal in mean response time
Fair?
Easy to implement?
We use Job Size to refer to the Processing Time (Service Time) of the job

5. Shortest Remaining Processing Time (SRPT)
Always serve the job with minimum remaining processing time first, Preemptive scheduling
Yields minimum mean response time [Schrage, Operations Research, 1968]
Performance gains of SRPT over PS do not usually come at the expense of large jobs, in other words, it is Fair for heavy-tail job size distribution [Bansal and Harchol-Balter, Sigmetrics ‘01]
Easy to implement?
With accurate a priori job size information, YES
Otherwise, NO
SRPT scheduler reassign the job’s priority when a new jobs come in. Always choose the one with the minimum remaining processing time.

6. Fair Sojourn Protocol (FSP)
Combined SRPT with PS, preemptive scheduling
Mean response time is close to that of SRPT; and more fair than PS [Friedman, et al, Sigmetrics ‘03]
Easy to implement?
With accurate a priori job size information, YES
Otherwise, NO
Talk more about FSP: SRPT + the longer a job stay in the queue, the higher priority it will get

7. Motivation How does performance depend on
Size-based scheduling requires accurate knowledge of job sizes
In practice, a priori job size information is not always
available
All the previous work assumes perfect knowledge of job sizes a priori
Question: How does the actual performance of size-based scheduling policies depend on the correlation between size estimates and actual sizes?
Higher level: How does performance depend on quality of job size information?
How does performance depend on
quality of job size information?

8. Correlation We study the performance of Size-based
schedulers as a function of the correlation
coefficient (Pearson’s R) between actual job sizes and estimated job sizes.

9. Outline Review of size-based scheduling Motivation Simulation Setup
Simulation Results
New applications

10. Simulation Setup: Trace generator
Correlation (Pearson’s R)
Distribution A
Distribution B
Trace Generator
Goal: Given some parametric distribution and a target correction coefficient R, we generate pairs of random numbers where each number of the pair is chosen from its required distribution and where the two numbers of the pair are correlated to degree R
X Y
100
300
Correlated random pairs of X and Y
X has distribution A
Y has distribution B
X and Y are correlated to R

11. Simulation Setup: Trace generator
Algorithm: “Normal-To-Anything”
First developed by Cario and Nelson, on INFORMS Journal on Computing 10, 1 (1998).
We simplified the algorithm and first introduced it into the simulation studies of computer systems
Details in our paper; details on the proof in Cario’s paper.

12. Scatter plot of example tracesY Y
What is the X and Y axis? Job size and estimated job sizes. In log-log scale
Related it back to slide 10.
R equals 1 means that Y is prepositional to X, therefore with bigger R, the scatter plot is closer to a straight line. X X
R=0.13
R=0.78

13. Simulation Setup: Performance metrics
Mean response time: Sojourn time, Turn-around time
Slowdown: the ratio of response time to its size. Fairness metric

14. Simulation Setup: Simulator
Written in C++
Supports M/G/1 and G/G/n/m queuing model
Simulator validation
Little’s law
Repeat the simulations in the FSP paper [Friedman, et al, Sigmetrics ‘03]
Compare with available theoretical results [Bansal and Harchol-Balter, Sigmetrics ‘01]

15. Simulation Setup: Scheduling Policies
PS: Processor sharing
Size-based scheduling policies
SRPT: Ideal SRPT scheduler
SRPT-E: SRPT scheduler using estimated job size
FSP: Ideal Fair Sojourn Protocol
FSP-E: FSP scheduler using estimated job size
Tie this back to figure about trace generator – that way you have fewer words:
(X,Y) pairs, SRPT uses X, SPRT-E uses Y
Each simulation is repeated 20 times and we present the average

16. Outline Review of size-based scheduling Motivation Simulation Setup
Simulation Results
New applications

17. Simulation Results: Mean response time
What is the X and Y axis? And each curve?
Y is in log scale, which implies exponential relation. A small improve in R will have much bigger impact on response time
What is the takeaway point? SRPT and FSP outperforms PS given an effective job size estimator

18. Simulation Results: Slowdown (R=0.0224)
Tell the audience how to read the figure: X, Y axis; each curve
Y is in log scale.
Tell the audience what is good performance in the figure.
The performance of ideal SRPT and FSP are very close and not distinguishable in most of the figures.

19. Simulation Results: Slowdown (R=0.239)

20. Simulation Results: Slowdown (R=0.4022)

21. Simulation Results: Slowdown (R=0.5366)

22. Simulation Results: Slowdown (R=0.7322)

23. Simulation Results: Slowdown (R=0.9779)

24. Simulation Results: Conclusions
Performance heavily depends on correlation
SRPT-E and FSP-E can outperform PS given an effective job size estimator
Crossover point of performance metrics is a function of correlation
Also of job size distributions (See TR NWU-CS-04-33)

25. Outline Review of size-based scheduling Motivation Simulation Setup
Simulation Results
New applications
New application enabled by effective estimators

26. New Applications: Web server scheduling (TR NWU-CS-04-33)
Is file size a good estimator of a job’s service time (processing time)? Not Really (R  0.14)
File Size
What is X and Y axis?
It is in log-log scale
Service time (wall clock time)

27. New Applications: Web server scheduling
Domain-based estimator: much more accurate prediction of the service time at low overhead
What is X and Y?
Use Class-less Inter-domain Routing (CIDR) to divide the Internet into smaller domains. More bits used, smaller the domain.
Use history and requester’s IP to estimate its service time.

28. New Applications: P2P server side scheduling (LCR ’04)
“Server side” of current file sharing P2P applications superficially similar to web server
Both send back files upon requests.
However, P2P application can’t even know the file size accurately a priori
Partial downloads
Our ongoing work shows that SRPT-E performs well using our time-series based job size estimators.
What is server side?
Each P2P node is both a client and a server. We referred to the function of providing service to other nodes as “server side”

29. New Applications: Network backup system scheduling
Incremental backup copies only the files that have been created or modified since a previous backup
With Incremental backup, the actual job sizes is difficult to know until the backup finishes
We believe that SRPT-E or FSP-E can be applied with time series based job size predictors
Drop this slide if you run out of time

30. Summary
Performance of size-based scheduling policies depends on correlation between size estimates and actual sizes
Fairness, mean response time, etc.
Estimator must preserve ordering of job sizes for high performance
Performance degrades as correlation degrades
Effective new estimators for Web and P2P

31. For More Information Prescience Laboratory
For more details on the applications, please also see our short paper “Applications of SRPT Scheduling with Inaccurate Scheduling Information” in digital proceedings of MASCOTS ‘04 and a poster this evening.