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

This report presents a taxonomy of maximally elastic buffers in the context of system architecture and networking. It explores basic building blocks, composition methods, design parameters, performance metrics, optimal buffers, and more.

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

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  1. Taxonomy of maximally elastic buffers(based on CS-Report 04-26) Rudolf Mak November 5, 2004 Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  2. Motivation Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  3. Basic Building Blocks • One-place buffer • Split component • Merge component Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  4. One-place buffer Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  5. Split component Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  6. Merge component Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  7. Composition Methods • Serial composition • Wagging composition • Multi-wagging composition Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  8. Class S Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  9. Wagging Composition Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  10. Tree Buffers Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  11. Diamond Buffer Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  12. Class Wn Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  13. Multi-wagging Composition Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  14. Square Buffers Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  15. Class Mn Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  16. Lattice of Buffer Classes Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  17. Design Parameters • Capacity • I/o-distance Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  18. Design Space Area A2 con-tains all equi-distant buffers in class M Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  19. Performance Metrics • Average throughput (X) • Average occupancy (X) • Elasticity (X) Rudolf Mak r.h.mak@tue.nl 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 Rudolf Mak r.h.mak@tue.nl 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? Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  22. Bisection Lemma (before) U V Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  23. Bisection Lemma (after) U V Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  24. Production rules • Application of the bisection lemma using • each of the construction methods yields: Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  25. Contours Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  26. Design Space revisited Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  27. Contour Computation • Is based on production rules in (, )-space: Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  28. Wagging Contours Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  29. Multi-wagging Contours Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

  30. Limit Contours Rudolf Mak r.h.mak@tue.nl 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 Rudolf Mak r.h.mak@tue.nl TU/e Computer Science, System Architecture and Networking

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