We study size-based schedulers, and focus on the impact of inaccurate job size information on response time and fairness. Our intent is to revisit previous results, which allude to performance degradation for even small errors on job size estimates, thus limiting the applicability of size-based schedulers. We show that scheduling performance is tightly connected to workload characteristics: in the absence of large skew in the job size distribution, even extremely imprecise estimates suffice to outperform size-oblivious disciplines. Instead, when job sizes are heavily skewed, known size-based disciplines suffer. In this context, we show -- for the first time -- the dichotomy of over-estimation versus under-estimation. The former is, in general, less problematic than the latter, as its effects are localized to individual jobs. Instead, under-estimation leads to severe problems that may affect a large number of jobs. We present an approach to mitigate these problems: our technique requires no complex modifications to original scheduling policies and performs very well. To support our claim, we proceed with a simulation-based evaluation that covers an unprecedented large parameter space, which takes into account a variety of synthetic and real workloads. As a consequence, we show that size-based scheduling is practical and outperforms alternatives in a wide array of use-cases, even in presence of inaccurate size information.

1. Revisiting Size-Based Scheduling
with Estimated Job Sizes
Matteo Dell’Amico (EURECOM, France),
Damiano Carra (Univ. Verona, Italy)
Mario Pastorelli, Pietro Michiardi (EURECOM, France)
MASCOTS 2014
These slides at http://bit.ly/schedsim
1

2. On Size-Based Scheduling

3. On Size-Based Scheduling An Example
Processor-Sharing vs. Size-Based
100
cluster
usage (%)
50
time
(s)
job 3
job 2
10 15 37.5 42.5 50
100
cluster
usage (%)
10 20 30 50
50
time
(s)
job 1
job 1 job 2 job 3 job 1
3

4. On Size-Based Scheduling An Example
Processor-Sharing vs. Size-Based
100
cluster
usage (%)
50
time
(s)
job 3
job 2
10 15 37.5 42.5 50
100
cluster
usage (%)
10 20 30 50
50
time
(s)
job 1
job 1 job 2 job 3 job 1
3

5. On Size-Based Scheduling Properties
Size-Based Scheduling: Some Properties
Shortest Remaining Processing Time (SRPT)
Minimizes mean sojourn time (MST) [Schrage, OPER RES ’68]
Sojourn time: interval between job submission and completion
4

6. On Size-Based Scheduling Properties
Size-Based Scheduling: Some Properties
Shortest Remaining Processing Time (SRPT)
Minimizes mean sojourn time (MST) [Schrage, OPER RES ’68]
Sojourn time: interval between job submission and completion
Fair Sojourn Protocol (FSP)
Jobs are scheduled in the order they would complete if doing
Processor Sharing (PS)
Efficiency: very close to SRPT
Fairness: each job completes not later than Processor Sharing
[Friedman & Henderson, SIGMETRICS ’03]
4

7. On Size-Based Scheduling Related Work
Where Are All the Size-Based Schedulers?
Job size is almost never known a priori
5

8. On Size-Based Scheduling Related Work
Where Are All the Size-Based Schedulers?
Job size is almost never known a priori
Related Work: Inexact Job Size Information
Simulation-based study: estimations need to be precise
[Lu et al., MASCOTS 2004]
Analytic study: bounded errors, over-estimation only
[Wierman & Nuyens, SIGMETRICS PER, 2008]
5

9. On Size-Based Scheduling Related Work
Where Are All the Size-Based Schedulers?
Job size is almost never known a priori
Related Work: Inexact Job Size Information
Simulation-based study: estimations need to be precise
[Lu et al., MASCOTS 2004]
Analytic study: bounded errors, over-estimation only
[Wierman & Nuyens, SIGMETRICS PER, 2008]
What Motivated Us
We developed HFSP, a size-based scheduler for Hadoop
We found it works very well even with very rough estimations
[Pastorelli et al., BIGDATA 2013]
5

10. Understanding Size-Based Scheduling With Errors

11. Understanding Size-Based Scheduling With Errors Simulation
Scheduling Simulation
Main Features
Simulates single-server, preemptive scheduling
Can create synthetic traces or replay real ones
Injects artificial size estimation errors
in this case, SRPT and FSP become SRPTE and FSPE
Efficient and easy to prototype new schedulers
10,000 jobs are simulated in half a second on an old laptop
FSP is ~50 lines of Python code
Free Software: Apache License 2.0
https://bitbucket.org/bigfootproject/schedsim
7

12. Understanding Size-Based Scheduling With Errors Simulation
Log-Normal Error Distribution
4.0
3.5
3.0
2.5
PDF
2.0
1.5
1.0
0.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0
x
0.0
sigma= 0.125
sigma= 0.25
sigma= 1
sigma= 4
Error: real size
estimated size
8

13. Understanding Size-Based Scheduling With Errors Simulation
Weibull Job Size Distribution
2.0
1.5
PDF
1.0
0.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0
x
0.0
shape= 0.125
shape= 1
shape= 2
shape= 4
Interpolates between
heavy-tailed job size distributions (shape<1)
exponential distributions (shape=1)
bell-shaped distributions (shape>1) 9

14. Understanding Size-Based Scheduling With Errors Simulation
Other Parameters
Number of jobs (default: 10,000 per workload)
at least 30 repetitions per data point
System load (default: 0.9)
Ratio between requested and available resources
Job arrival time (default: exponential)
Bursts vs. regular
These parameters are not fundamental
more details in the paper
10

15. Understanding Size-Based Scheduling With Errors Simulation Results
Size-Based Scheduling With Errors
SRPTE FSPE
Problems for heavy-tailed job size distributions
Otherwise, size-based scheduling works very well
11

16. Understanding Size-Based Scheduling With Errors Simulation Results
Over-Estimations and Under-Estimations
t
Over-­‐es'ma'on
Under-­‐es'ma'on
t
t
t
Remaining
size
Remaining
size
Remaining
size
Remaining
size
J1
J2
J3
J2
J3
J^1
J4
J5
J6
J4
J5
J6
^
Over-estimating hurts a single job: limited damage
Under-estimating very large jobs can wreak havoc
12

17. Size-Based Scheduling For Approximate Sizes

18. Size-Based Scheduling For Approximate Sizes FSPE+PS
FSPE + PS
Idea
Without errors, real jobs always complete before virtual ones
When they don’t (they are late), there has been a mistake
The scheduler can realize this, and take corrective action
Realization
A scheduler such that late jobs don’t block the system
Just do processor sharing between them instead of scheduling
the “most late” one
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19. Size-Based Scheduling For Approximate Sizes FSPE+PS
FSPE + PS: Results
FSPE FSPE + PS
Performance becomes very close to optimal
Outperformed by PS only for extreme skew and errors
Replaying real-world traces gives analogous results
15

20. Size-Based Scheduling For Approximate Sizes Comparison With SRPT
Schedulers vs. SRPT
10
8
6
4
0.125 0.25 0.5 1 2 4
shape
2
MST / MST(SRPT)
SRPTE
FSPE
FSPE+PS
PS
LAS
FIFO
Sigma: 0.5
16

21. Size-Based Scheduling For Approximate Sizes Real Workloads
Hadoop @ Facebook
10
8
6
4
0.125 0.25 0.5 1 2 4
sigma
2
MST / MST(SRPT)
SRPTE
FSPE
FSPE+PS
PS
LAS
10
8
6
4
0.125 0.25 0.5 1 2 4
sigma
2
MST / MST(SRPT)
SRPTE
FSPE
FSPE+PS
PS
LAS
Synthetic workload (shape=0.25) Facebook Hadoop Cluster
17

22. Size-Based Scheduling For Approximate Sizes Real Workloads
Web Cache
100
10
0.125 0.25 0.5 1 2 4
sigma
1
MST / MST(SRPT)
SRPTE
FSPE
FSPE+PS
PS
LAS
10000
1000
100
10
0.125 0.25 0.5 1 2 4
sigma
1
MST / MST(SRPT)
SRPTE
FSPE
FSPE+PS
PS
LAS
FIFO
Synthetic workload (shape=0.177) IRCache Web Cache
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23. Take-Home Messages

24. Take-Home Messages
Take-Home Messages
For System Designers
Do not be afraid of size-based scheduling
it can work great even with very rough estimations
Further Research
Schedulers like FSPE+PS, designed for estimated sizes, work
very well
Can we design a scheduler that always outperforms PS?
Can we get better analytical understanding of the phenomena
we observed?
These slides (plus bonus content) available at
http://bit.ly/schedsim
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25. Bonus Content

26. Bonus Content Fairness
Fairness: Slowdown
1.0
0.8
0.6
ECDF
0.4
0.2
100 101 102
slowdown
0.0
SRPTE
FSPE
FSPE+PS
PS
LAS
FIFO
1.00
0.98
0.96
ECDF
0.94
0.92
100 101 102
slowdown
0.90
Shape: 0.25, sigma: 0.5
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27. Bonus Content Fairness
Fairness: Conditional Slowdown
107
106
105
slowdown
104
103
102
101
104 103 102 101 100 101 102
job size
100
SRPTE
FSPE
FSPE+PS
PS
LAS
FIFO
Shape: 0.25, sigma: 0.5
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