Influence of heavytailed distributions on load balancing

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Analysis of Task Assignment with Cycle Stealing
Alan Scheller-Wolf GSIA, Carnegie Mellon
University
With Mor Harchol-Balter, Takayuki Osogami,
Cuihong Li, Mark Squillante.
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Two Task Assignment Models
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Some Task Assignment Policies for our Models

• ROUND-ROBIN
• - utilization
• - response time
• SHORTEST-QUEUE
• M/G/k W77, EVW80
• utilization
• - response time
• DEDICATED
• H02, HCM99, SH00
• - utilization
• response time

Non-preemptive service
S
Central Queue model
Immediate Dispatch model
L
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Motivation for Cycle Stealing
Separating shorts from longs is not enough (or
is too much)
short jobs go here
long jobs go here
Allow shorts to steal idle cycles of longs
improve utilization improve response times
increase stability region
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Goal of Paper Analysis of Cycle Stealing
Shorts only.
Shorts only
Longs. Short if no long.
Longs. Short if idle.
Immediate-Dispatch Cycle Stealing
Central-Queue Cycle Stealing
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Goal of Paper Analysis of Cycle Stealing
Beneficiary only.
Donors. Beneficiary if idle.
3 cases EBenef lt EDonor
EBenef EDonor EBenef gt
EDonor
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2D-infinite chain
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Our Idea

• Track beneficiary jobs exactly.
• Track effect of donor jobs
• via busy period transitions.

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Why is this problem harder?

• Non-preemptive service discipline
• Classes less separable
• Interactions more intricate
• 1D Chain more complex

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Our Solution 1D-chain
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Results of analysis
Beneficiary only.
Donors. Beneficiary if idle.

• What is the gain to the beneficiaries?
• What is the pain to the donors?

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Results of analysis
Stability condition on beneficiary load
Central-Queue cycle stealing
rBeneficiary
Immed-Dispatch cycle stealing
Dedicated
rDonor
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Results of analysis
Mean response time for beneficiaries
Dedicated Immed-Disp. Cycle Stealing Central-Queue
Cycle Stealing
Unbounded gain to beneficiaries!
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Results of analysis
Mean response time for donors
Dedicated Immed-Disp. Cycle Stealing Central-Queue
Cycle Stealing
Small finite pain to donors!
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Conclusion
What is gain to beneficiaries?

• PROBLEM Cycle stealing
• ANALYSIS
• RESULTS
• Gain to beneficiaries unbounded
• Pain to donors small, finite
• Cycle stealing with central queue beats
• cycle stealing with immediate-dispatch.

What is pain to donors?
1D-infinite chain
2D-infinite chain
INTRACTABLE
TRACTABLE
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Why is analysis so hard?
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Our Idea
2D-infinite chain
1D-infinite chain
INTRACTABLE
TRACTABLE
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Idea behind solution