Analysis of SRPT Scheduling: Investigating Unfairness

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Analysis of SRPT SchedulingInvestigating
Unfairness

• Nikhil Bansal
• (Joint work with Mor Harchol-Balter)

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Motivation Problem

• Aim
• Good Scheduling Policy
• Low Response times
• Fair

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Time Sharing (PS)

• Server shared equally between all the jobs
• Low response times
• Fair
• Does not require knowledge of sizes
• Can we do better ?

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Shortest Remaining Proc. Time
Optimal for minimizing mean response times.
Objections

• Knowledge of sizes
• Improvements significant ?
• Starvation of large jobs

Biggest fear
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Questions
Bigs worse

• Smalls better

• How do means compare
• Elephant-mice property and implications

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M/G/1 Queue Framework

• Poisson Arrival Process with rate
• Job sizes (S) iid general distribution F

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Queueing Formulas for PS

• ET(x) Expected Response time for job of size
  x
• 
  
• 
  

Kleinrock 71
Identical for all!
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M/G/1 SRPT
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SRPT
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Waiting Time (EW(x))
Residence Time (ER(x))

• Load up to x
• Variance up to x
• Gains priority after it begins execution

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All-Can-Win under srpt put c

• Thm Every job prefers SRPT, when load lt ½, for
  all job size distributions.

Proof Know that
If
Key Observation
Holds for all x, if load lt 0.5
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What if load gt 0.5 ? problem
Still holds if
Irrespective of
The Heavy-Tailed Property (Elephant -Mice) 1
of the big jobs make up at least 50 of the load.
For a distribution with the HT property, gt99 of
jobs better under SRPT
In fact, significantly better, Under SRPT,
Bounded by 4
Arbitrarily high
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The very largest jobs

• If load lt 0.5, all jobs favor SRPT.
• At any load, gt 99 jobs favor SRPT, if HT
  property.
• Moreover significant improvements.

What about the remaining 1 largest jobs?
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1. Bounding the damage theorem
Fill in
2.
As
Implication Mean slowdown of largest 1 under
SRPT Same as PS
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Insert plots here 1 for BP 1.1 with load 0.9
showing how all Do better 2 for exp with load
0.9 showing how some do bad.
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Other Scheduling Policies

• Non-preemptive
• First Come First Serve (FCFS)
• Random
• Last Come First Serve (LCFS)
• Shortest Job First (SJF)

Very bad mean Performance, for HT workloads

• Preemptive
• Foreground Background (FB)
• Preemptive LCFS

Trivially worse
Same as PS
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Overload
Add some lines for why good we do work on this
in paper
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Actual Implementation
Add a plot or couple of lines
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Conclusions

• Significant mean performance improvements.
• Big jobs prefer SRPT under low-moderate loads.
• Big jobs prefer SRPT even under high loads for
  heavy-tailed distributions.

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Scratch
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Under h-t distributions
Job Percentile SRPT PS
90 1.28 10
99 1.62 10
99.9 2.08 10
99.99 2.69 10
100 9.54 10

• Load 0.9
• Heavy-tailed distribution with alpha1.1

Very largest job
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Under light-tailed distributions
Job Percentile SRPT PS
90 3.17 10
95 4.93 10
99 11.14 10
99.9 16.01 10
Load0.9 Exponential distribution