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Analysis of SRPT Scheduling: Investigating Unfairness

A study on designing a "good" scheduling policy for servers, focusing on low response times and fair time sharing among jobs. The study explores the Shortest Remaining Proc. Time strategy and its implications, including addressing objections and considering the Elephant-Mice property.

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Analysis of SRPT Scheduling: Investigating Unfairness

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  1. Analysis of SRPT Scheduling:Investigating Unfairness Nikhil Bansal (Joint work with Mor Harchol-Balter)

  2. Client1 Client2 Client3 Server Motivation Problem • Aim: • “Good” Scheduling Policy • Low Response times • Fair

  3. Time Sharing (PS) Server shared equally between all the jobs: • Low response times • Fair • Does not require knowledge of sizes Can we do better ?

  4. Shortest Remaining Proc. Time Optimal for minimizing mean response times. Objections: • Knowledge of sizes • Improvements significant ? • Starvation of large jobs Biggest fear

  5. Questions • Smalls better Bigs worse • How do means compare • Elephant-mice property and implications

  6. Arrivals queue Server Load( ) = (arrival rate).E[S] M/G/1 Queue Framework • Poisson Arrival Process with rate • Job sizes (S) iid general distribution F

  7. Queueing Formulas for PS E[T(x)]: Expected Response time for job of size x [Kleinrock 71] Identical for all!

  8. M/G/1 SRPT x ò l + - 2 2 ( t f ( t ) dt x ( 1 F ( x ))) x dt ò = + 0 E [ T ( x )] SRPT - r ( 1 ( t )) - r 2 2 ( 1 ( x )) 0 Waiting Time (E[W(x)]) Residence Time (E[R(x)]) • Load up to x • Variance up to x • Gains priority after it begins execution

  9. All-Can-Win under srpt put c Thm: Every job prefers SRPT, when load <= ½, for all job size distributions. Proof: Know that If Key Observation Holds for all x, if load <= 0.5

  10. What if load > 0.5 ? problem Still holds if Irrespective of The Heavy-Tailed Property: (Elephant -Mice) 1%of the big jobs make up at least50%of the load. For a distribution with the HT property, >99% of jobs better under SRPT In fact, significantly better, Under SRPT, Bounded by 4 Arbitrarily high

  11. The very largest jobs • If load <= 0.5, all jobs favor SRPT. • At any load, > 99% jobs favor SRPT, if HT property. Moreover significantimprovements. What about the remaining 1% largest jobs?

  12. 1. Bounding the damage theorem Fill in… 2. As Implication: Mean slowdown of largest 1% under SRPT: Same as PS

  13. 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.

  14. 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

  15. Overload Add some lines for why good + we do work on this in paper

  16. Actual Implementation Add a plot or couple of lines

  17. 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.

  18. Scratch

  19. Under h-t distributions Load = 0.9 Heavy-tailed distribution with alpha=1.1 Very largest job

  20. Under light-tailed distributions Load=0.9 Exponential distribution

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