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 60201 USA

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

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

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

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.

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

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?

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.

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

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

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.

Scatter plot of example traces Y 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

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

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]

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

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

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

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.

Simulation Results: Slowdown (R=0.239)

Simulation Results: Slowdown (R=0.4022)

Simulation Results: Slowdown (R=0.5366)

Simulation Results: Slowdown (R=0.7322)

Simulation Results: Slowdown (R=0.9779)

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)

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

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)

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.

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”

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

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

For More Information Prescience Laboratory http://plab.cs.northwestern.edu 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.