Rudolf Mak [e-mail]

1
Taxonomy of maximally elastic buffers(based on
CS-Report 04-26)

• Rudolf Mak
• November 5, 2004

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Motivation
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Basic Building Blocks

• One-place buffer
• Split component
• Merge component

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One-place buffer
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Split component
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Merge component
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Composition Methods

• Serial composition
• Wagging composition
• Multi-wagging composition

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Class S
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Wagging Composition
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Tree Buffers
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Diamond Buffer
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Class Wn
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Multi-wagging Composition
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Square Buffers
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Class Mn
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Lattice of Buffer Classes
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Design Parameters

• Capacity
• I/o-distance

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Design Space
Area A2 con-tains all equi-distant buffers in
class M
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Performance Metrics

• Average throughput ?(X)
• Average occupancy ?(X)
• Elasticity ??(X)

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Optimal Buffers

• Elasticity bound
• A buffer is optimal when its elasticity attains
  its upper bound for every throughput

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Questions

• For a pair of design parameters we
• ask
• Does there exists an optimal buffer?
• Does there exist a simple optimal buffer, where
  simple means in class M?
• What is the simplest structure of an optimal
  buffer?

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Bisection Lemma (before)
U
V
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Bisection Lemma (after)
U
V
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Production rules

• Application of the bisection lemma using
• each of the construction methods yields

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Contours
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Design Space revisited
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Contour Computation

• Is based on production rules in (?, ?)-space

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Wagging Contours
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Multi-wagging Contours
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Limit Contours
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Conclusions

• Fine-grained, well-fitted taxonomy
• For almost all design parameters an optimal
  buffer is known.
• For almost all design parameters the optimal
  buffer has a simple structure
• The taxonomy is extendable
• With additional building blocks
• With additional construction methods