Surprising results on task assignment for high-variability workloads

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Surprising results on task assignment for
high-variability workloads
Mor Harchol-Balter, CMU, Computer Sci. Alan
Scheller-Wolf, CMU, Tepper Business Andrew
Young, Morgan Stanley
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Server farm model
Goal Minimize mean response time ET
FIFO
Assignment Policy
incoming jobs
FIFO
Poisson(l)
FIFO
Q What is a good Assignment Policy?
(high-variability jobs)
POLICY MATTERS!
Mor Harchol-Balter, CMU
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Good Answers
Protects against high variability
High throughput
Isolation for smalls
Mor Harchol-Balter, CMU
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Prior Work on SITA
All conclude SITA far superior for high
variability
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Should at least beat all commonly used policies
when variability is high enough.
In search of a proof of SITAs total dominance.
OK, so not optimal, but definite win for high
variability.
Years later
Months later
Cant prove anything because its not true!
Mor Harchol-Balter, CMU
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The TRUTH about SITA,under very high job size
variability
Alternative Title
Mor Harchol-Balter, CMU
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Q In this talk we will show ...
as C2?8

1. SITA diverges LWL diverges?
2. SITA converges LWL diverges ?
3. SITA diverges LWL converges?
4. SITA converges LWL converges?

A All of the above
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Q In this talk we will show ...
as C2?8
Mor Harchol-Balter, CMU
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Results (2 server system)
or
Mor Harchol-Balter, CMU
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Results (2 server system)
or
Mor Harchol-Balter, CMU
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Results (2 server system)
Mor Harchol-Balter, CMU
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Bimodal Results
pa QEX
(1-p)b (1-Q)EX
Mor Harchol-Balter, CMU
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Understanding LWL
Isnt LWL always bad for high C2?
It depends
But shorts stuck behind longs, so ET ?8
Need 2 longs for this to be a problem!
So we need Pr 2 longs ET 2 longs ?
Suffices to just look at EX3/2.
Mor Harchol-Balter, CMU
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Understanding LWL
Mor Harchol-Balter, CMU
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Bimodal Results
Lemma As C2 ? 8, but EX, Q const, a?
QEX, b ? 8, p ? 1
Mor Harchol-Balter, CMU
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Trimodal Results
Mor Harchol-Balter, CMU
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Results (2 server system)
Mor Harchol-Balter, CMU
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Mor Harchol-Balter, CMU
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Bounded Pareto (2 server system)
Extends to ngt2 servers when r lt n-1
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Bounded Pareto Results
Mor Harchol-Balter, CMU
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Summary
or
or
Mor Harchol-Balter, CMU
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Old Nursery Rhyme
There once was a girl, who had a little
curl right in the middle of her
forehead. When she was good, she was
very very good. But when she was bad,
she was horrid.
When SITA is good, it is very, very good But
when it is bad, it is horrid.
Mor Harchol-Balter, CMU
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Epilogue
Mor Harchol-Balter, CMU
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Where did SITA go wrong?
SITA designed to keep shorts from getting stuck
behind longs. Isnt that good?
But stringent segregation of shorts longs can
lead to underutilization of servers.
Also, for some distributions, cant subdivide to
avoid infinite variability.
Mor Harchol-Balter, CMU
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Must be a better way
Protects against high variability
High throughput
Isolation for smalls
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Must be a better way
WIN/WIN ! Shorts have isolation from longs
And server utilization is high WRONG! Thm
Whenever SITA diverges, CS diverges too.
Mor Harchol-Balter, CMU
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SITA Split jobs by size.
Thm Whenever SITA diverges, CS diverges too.

• PROOF There are 2 reasons why SITA diverges
  under given y
• Any way of slicing leads to
• (2) There is a way of slicing
• away variability, but it forces

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SITA Split jobs by size.
Thm Whenever SITA diverges, CS diverges too.

• PROOF There are 2 reasons why SITA diverges
  under given y
• Any way of slicing leads to
• (2) There is a way of slicing
• away variability, but it forces

• Small job sees L of age Le.
• Small server has been in overload for Le time
• Small sees Le work ? experiences Le delay.
• Delay of small ? 8 as C2 ? 8

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Conclusion
Maybe isolating short jobs is not the panacea for
high-variability workloads after all
Mor Harchol-Balter, CMU