Quantifying the Properties of SRPT Scheduling

1
Quantifying the Properties of SRPT
Scheduling

• Mingwei Gong and Carey Williamson
• Department of Computer Science
• University of Calgary

2
Outline

• Introduction
• Background
• Web Server Scheduling Policies
• Related Work
• Research Methodology
• Simulation Results
• Defining/Refining Unfairness
• Quantifying Unfairness
• Summary, Conclusions, and Future Work

3
Introduction

• Web large-scale, client-server system
• WWW World Wide Wait!
• User-perceived Web response time is composed of
  several components
• Transmission delay, propagation delay in network
• Queueing delays at busy routers
• Delays caused by TCP protocol effects
  (e.g., handshaking, slow start, packet loss,
  retxmits)
• Queueing delays at the Web server itself, which
  may be servicing 100s or 1000s of concurrent
  requests
• Our focus in this work Web request scheduling

4
Example Scheduling Policies

• FCFS First Come First Serve
• typical policy for single shared resource
  (unfair)
• e.g., drive-thru restaurant Sens playoff tickets
• PS Processor Sharing
• time-sharing a resource amongst M jobs
• each job gets 1/M of the resources (equal,
  fair)
• e.g., CPU VM multi-tasking Apache Web server
• SRPT Shortest Remaining Processing Time
• pre-emptive version of Shortest Job First (SJF)
• give resources to job that will complete quickest
• e.g., ??? (express lanes in grocery
  store)(almost)

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Related Work

• Theoretical work
• SRPT is provably optimal in terms of mean
  response time and mean slowdown (classical
  results)
• Practical work
• CMU prototype implementation in Apache Web
  server. The results are consistent with
  theoretical work.
• Concern unfairness problem (starvation)
• large jobs may be penalized (but not always
  true!)

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Related Work (Contd)

• Harchol-Balter et al. show theoretical results
• For the largest jobs, the slowdown asymptotically
  converges to the same value for any preemptive
  work-conserving scheduling policies (i.e., for
  these jobs, SRPT, or even LRPT, is no worse than
  PS)
• For sufficiently large jobs, the slowdown under
  SRPT is only marginally worse than under PS, by
  at most a factor of 1 e, for small e gt 0.

M.Harchol-Balter, K.Sigman, and A.Wierman
2002, Asymptotic
Convergence of Scheduling Policies w.r.t.
Slowdown, Proceedings of IFIP Performance 2002,
Rome, Italy, September 2002
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Related Work (Contd)

• Wierman and Harchol-Balter 2003

SJF
LAS
FSP
Always Unfair
Always Fair
Sometimes Unfair
PS
FCFS
PLCFS
LRPT
SRPT
A. Wierman and M.Harchol-Balter 2003,
(Best Paper) Classifying
Scheduling Policies w.r.t. Unfairness in an
M/GI/1, Proceedings of ACM SIGMETRICS, San
Diego, CA, June 2003
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A Pictorial View
8
PS
Slowdown
SRPT
1
0
8
Job Size
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Research Questions

• Do these properties hold in practice for
  empirical Web server workloads? (e.g., general
  arrival processes, service time distributions)
• What does sufficiently large mean?
• Is the crossover effect observable?
• If so, for what range of job sizes?
• Does it depend on the arrival process and the
  service time distribution? If so, how?
• Is PS (the gold standard) really fair?
• Can we do better? If so, how?

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Overview of Research Methodology

• Trace-driven simulation of simple Web server
• Empirical Web server workload trace (1M
  requests from WorldCup98) for main expts
• Synthetic Web server workloads for the
  sensitivity study experiments
• Probe-based sampling methodology
• Estimate job response time distributions for
  different job size, load level, scheduling policy
• Graphical comparisons of results
• Statistical tests of results (t-test, F-test)

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Simulation Assumptions

• User requests are for static Web content
• Server knows response size in advance
• Network bandwidth is the bottleneck
• All clients are in the same LAN environment
• Ignores variations in network bandwidth and
  propagation delay
• Fluid flow approximation service time response
  size
• Ignores packetization issues
• Ignores TCP protocol effects
• Ignores network effects
• (These are consistent with SRPT literature)

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Performance Metrics

• Number of jobs in the system
• Number of bytes in the system
• Normalized slowdown
• The slowdown of a job is its observed response
  time divided by the ideal response time if it
  were the only job in the system
• Ranges between 1 and ?
• Lower is better

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Empirical Web Server Workload
1998 WorldCup Internet Traffic Archive http//ita.ee.lbl.gov/ 1998 WorldCup Internet Traffic Archive http//ita.ee.lbl.gov/
Item Value
Trace Duration 861 sec
Total Requests 1,000,000
Unique Documents 5,549
Total Transferred Bytes 3.3 GB
Smallest Transfer Size (bytes) 4
Largest Transfer Size (bytes) 2,891,887
Median Transfer Size (bytes) 889
Mean Transfer Size (bytes) 3,498
Standard Deviation (bytes) 18,815
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Preliminaries An Example
TIMESTAMP SIZE
0.000000 3038
0.000315 949
0.001048 2240
0.004766 2051
0.005642 366
0.005872 201
0.006380 298
0.006742 1272
0.007271 597
0.008008 283
Jobs in System
Bytes in System
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Observations

• The byte backlog is the same for each
  scheduling policy
• The busy periods are the same for each policy.

• The distribution of the number of jobs in the
  system is different

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General Observations (Empirical trace)
Load 50
Load 80
Load 95
Marginal Distribution (Num Jobs in System) for PS
and SRPT differences are more pronounced at
higher loads
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Objectives (Restated)

• Compare PS policy with SRPT policy
• Confirm theoretical results in previous work
  (Harchol-Balter et al.)
• For the largest jobs
• For sufficiently large jobs
• Quantify unfairness properties

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Probe-Based Sampling Algorithm

• The algorithm is based on PASTA (Poisson Arrival
  See Time Average) Principle.

Slowdown (1 sample)
Repeat N times
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Probe-based Sampling Algorithm

• For scheduling policy S (PS, SRPT, FCFS, LRPT,
  ) do
• For load level U (0.50, 0.80, 0.95) do
• For probe job size J (1B, 1KB, 10KB,
  1MB...) do
• For trial I (1,2,3 N) do
• Insert probe job at randomly chosen
  point
• Simulate Web server scheduling policy
• Compute and record slowdown value
  observed
• end of I
• Plot marginal distribution of slowdown
  results
• end of J
• end of U
• end of S

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Example Results for 3 KB Probe Job
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Example Results for 100 KB Probe Job
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Example Results for 10 MB Probe Job
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Statistical Summary of Results
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Two Aspects of Unfairness

• Endogenous unfairness (SRPT)
• Caused by an intrinsic property of a job, such as
  its size. This aspect of unfairness is invariant
• Exogenous unfairness (PS)
• Caused by external conditions, such as the number
  of other jobs in the system, their sizes, and
  their arrival times.
• Analogy showing up at a restaurant without a
  reservation, wanting a table for k people

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Observations for PS
Exogenous unfairness dominant
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Observations for SRPT
Endogenous unfairness dominant
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Asymptotic Convergence?
Yes!
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3M

• Illustrating the crossover effect (load95)

3.5M
4M
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Crossover Effect?
Yes!
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Summary and Conclusions

• Trace-driven simulation of Web server scheduling
  strategies, using a probe-based sampling
  methodology (probe jobs) to estimate response
  time (slowdown) distributions
• Confirms asymptotic convergence of the slowdown
  metric for the largest jobs
• Confirms the existence of the cross-over effect
  for some job sizes under SRPT
• Provides new insights into SRPT and PS
• Two types of unfairness endogenous vs. exogenous
• PS is not really a gold standard for fairness!

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Ongoing Work

• Synthetic Web workloads
• Sensitivity to arrival process (self-similar
  traffic)
• Sensitivity to heavy-tailed job size
  distributions
• Evaluate novel scheduling policies that may
  improve upon PS (e.g., FSP, k-SRPT, )

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Sensitivity to Arrival Process

• A bursty arrival process (e.g., self-similar
  traffic, with Hurst parameter H gt 0.5) makes
  things worse for both PS and SRPT policies
• A bursty arrival process has greater impact on
  the performance of PS than on SRPT
• PS exhibits higher exogenous unfairness than SRPT
  for all Hurst parameters and system loads tested

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Sensitivity to Job Size Distribution

• SRPT loves heavy-tailed distributions
  the heavier the tail the better!
• For all Pareto parameter values and all system
  loads considered, SRPT provides better
  performance than PS with respect to mean slowdown
  and standard deviation of slowdown
• At high system load (U 0.95), SRPT has more
  pronounced endogenous unfairness than PS

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Thank You!Questions?
For more information
M. Gong and C. Williamson, Quantifying the
Properties of SRPT Scheduling, to appear,
Proceedings of IEEE MASCOTS, Orlando, FL,
October 2003
Email gongm,carey_at_cpsc.ucalgary.ca