Size-Based Scheduling Policies with Inaccurate Scheduling Information

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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

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Outline

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

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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
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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
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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

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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

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Motivation

• 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

• How does performance depend on
• quality of job size information?

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

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

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Simulation Setup Trace generator
Correlation (Pearsons R)
Distribution A
Distribution B
Trace Generator

• 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

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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

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Scatter plot of example traces
Y
Y
X
X
R0.78
R0.13
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Simulation Setup Performance metrics

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

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Simulation Setup Simulator

• Simulator
• Written in C
• Supports M/G/1 and G/G/n/m queuing model
• Simulator validation
• Littles law
• Repeat the simulations in the FSP paper
  Friedman, et al, Sigmetrics 03
• Compare with available theoretical results
  Bansal and Harchol-Balter, Sigmetrics 01

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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

Each simulation is repeated 20 times and we
present the average
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Outline

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

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Simulation Results Mean response time
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Simulation Results Slowdown (R0.0224)
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Simulation Results Slowdown (R0.239)
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Simulation Results Slowdown (R0.4022)
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Simulation Results Slowdown (R0.5366)
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Simulation Results Slowdown (R0.7322)
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Simulation Results Slowdown (R0.9779)
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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)

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Outline

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

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New Applications Web server scheduling (TR
NWU-CS-04-33)

• Is file size a good estimator of a jobs service
  time (processing time)? Not Really (R ? 0.14)

File Size
Service time (wall clock time)
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New Applications Web server scheduling

• Domain-based estimator much more accurate
  prediction of the service time at low overhead

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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 cant 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.
  

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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

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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

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For MoreInformation

• 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.