25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 1 Rudolf Mak November 5, 2004 Taxonomy of maximally elastic.

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Presentation transcript:

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 1 Rudolf Mak November 5, 2004 Taxonomy of maximally elastic buffers (based on CS-Report 04-26)

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 2 Motivation

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 3 B asic Building Blocks One-place buffer Split component Merge component

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 4 One-place buffer

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 5 Split component

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 6 Merge component

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 7 Composition Methods Serial composition Wagging composition Multi-wagging composition

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 8 Class S

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 9 Wagging Composition

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 10 Tree Buffers

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 11 Diamond Buffer

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 12 Class W n

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 13 Multi-wagging Composition

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 14 Square Buffers

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 15 Class M n

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 16 Lattice of Buffer Classes

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 17 Design Parameters Capacity I/o-distance

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 18 Design Space Area A2 con- tains all equi- distant buffers in class M

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 19 Performance Metrics Average throughput  (X) Average occupancy  (X) Elasticity   (X)

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 20 Optimal Buffers Elasticity bound: A buffer is optimal when its elasticity attains its upper bound for every throughput

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 21 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?

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 22 Bisection Lemma (before) UV

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 23 Bisection Lemma (after) UV

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 24 Production rules Application of the bisection lemma using each of the construction methods yields:

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 25 Contours

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 26 Design Space revisited

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 27 Contour Computation Is based on production rules in ( ,  )-space:

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 28 Wagging Contours

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 29 Multi-wagging Contours

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 30 Limit Contours

25-Jun-15 Rudolf Mak TU/e Computer Science, System Architecture and Networking 31 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