1 / 38

CC513 Computing Systems

CC513 Computing Systems. Interconnection Networks Ω Network. Omega Network. The omega network is another example of a banyan multistage interconnection network that can be used as a switch fabric

nen
Download Presentation

CC513 Computing Systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CC513 Computing Systems Interconnection Networks Ω Network

  2. Omega Network • The omega network is another example of a banyan multistage interconnection network that can be used as a switch fabric • The omega differs from the delta network in the pattern of interconnections between the stages • The omega MIN uses the “perfect shuffle”

  3. Perfect Shuffle • The interconnections between stages are defined by the logical “rotate left” of the bits used in the port ids • Example: 000 ---> 000 ---> 000 ---> 000 • Example: 001 ---> 010 ---> 100 ---> 001 • Example: 011 ---> 110 ---> 101 ---> 011 • Example: 111 ---> 111 ---> 111 ---> 111

  4. 8 x 8 OMEGA NETWORK 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7

  5. Self Routing • Omega network has self-routing property • The path for a cell to take to reach its destination can be determined directly from its routing tag (i.e., destination port id) • Stage k of the MIN looks at bit k of the tag • If bit k is 0, then send cell out upper port • If bit k is 1, then send cell out lower port • Works for every possible input port (really!)

  6. Example of Self RoutingCell destined for output port 4 (= 100 ) 2 0 0 1 1 4 2 2 3 3 4 4 5 5 6 6 7 7

  7. Example of Self RoutingCell destined for output port 4 (= 100 ) 2 0 0 1 1 2 2 4 3 3 4 4 5 5 6 6 7 7

  8. Example of Self RoutingCell destined for output port 4 (= 100 ) 2 0 0 1 1 2 2 3 4 3 4 4 5 5 6 6 7 7

  9. Example of Self RoutingCell destined for output port 4 (= 100 ) 2 0 0 1 1 2 2 3 3 4 4 5 5 6 4 6 7 7

  10. Example of Self RoutingCell destined for output port 4 (= 100 ) 2 0 0 1 1 2 2 3 3 4 4 5 5 6 4 6 7 7

  11. Example of Self RoutingCell destined for output port 4 (= 100 ) 2 0 0 1 1 2 2 3 3 4 4 4 5 5 6 6 7 7

  12. Example of Self RoutingCell destined for output port 4 (= 100 ) 2 0 0 1 1 2 2 3 3 4 4 4 5 5 6 6 7 7

  13. Path Contention • The omega network has the problems as the delta network with output port contention and path contention • Again, the result in a buffer less switch fabric is cell loss (one cell wins, one loses) • Path contention and output port contention can seriously degrade the achievable throughput of the switch

  14. Path Contention 0 0 1 1 4 2 2 3 3 5 4 4 5 5 6 6 7 7

  15. Path Contention 0 0 1 1 2 2 4 3 3 4 4 5 5 6 5 6 7 7

  16. Path Contention 0 0 1 1 2 2 3 4 3 4 4 5 5 6 6 7 5 7

  17. Path Contention 0 0 1 1 2 2 3 3 4 4 5 5 6 4 6 7 5 7

  18. Path Contention 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7

  19. Path Contention 0 0 1 1 2 2 3 3 4 4 5 5 6 5 6 7 7

  20. Path Contention 0 0 1 1 2 2 3 3 4 4 5 5 5 6 6 7 7

  21. Path Contention 0 0 1 1 2 2 3 3 4 4 5 5 5 6 6 7 7

  22. Performance Degradation 0 0 1 1 4 2 2 3 6 3 4 4 1 7 5 5 6 0 6 7 3 7

  23. Performance Degradation 0 0 1 1 1 2 2 4 3 7 3 4 4 0 5 5 6 6 6 7 3 7

  24. Performance Degradation 0 0 1 1 1 2 2 3 3 4 0 4 5 5 6 3 6 7 6 7

  25. Performance Degradation 0 0 1 1 1 2 2 3 7 3 4 0 4 5 5 6 3 6 7 6 7

  26. Performance Degradation 0 0 1 1 1 0 2 2 3 3 4 4 3 5 5 6 7 6 7 6 7

  27. Performance Degradation 0 0 1 1 2 2 3 3 4 4 3 5 5 6 6 7 7

  28. Performance Degradation 0 0 0 1 1 2 2 3 3 4 4 3 5 5 6 6 7 6 7

  29. Performance Degradation 0 0 0 1 1 2 2 3 3 3 4 4 5 5 6 6 7 6 7

  30. Performance Degradation 0 0 0 1 1 2 2 3 3 3 4 4 5 5 6 6 6 7 7

  31. A Solution: Batcher Sorter • One solution to the contention problem is to sort the cells into monotonically increasing order based on desired destination port • Done using a bitonic sorter called a Batcher • Places the M cells into gap-free increasing sequence on the first M input ports • Eliminates duplicate destinations

  32. Batcher-Banyan Example 0 0 0 1 1 1 2 2 3 3 4 3 4 6 4 7 5 5 6 6 7 7

  33. Batcher-Banyan Example 0 0 0 1 1 6 2 2 1 3 7 3 4 3 4 5 5 6 4 6 7 7

  34. Batcher-Banyan Example 0 0 0 1 1 6 2 2 1 3 7 3 4 3 4 5 5 6 6 7 4 7

  35. Batcher-Banyan Example 0 0 0 1 1 3 2 2 6 3 3 4 1 4 5 5 6 7 6 7 4 7

  36. Batcher-Banyan Example 0 0 0 1 1 3 2 2 3 6 3 4 1 4 5 5 6 4 6 7 7 7

  37. Batcher-Banyan Example 0 0 0 1 1 1 2 2 3 3 3 4 4 4 5 5 6 6 6 7 7 7

  38. Batcher-Banyan Example 0 0 0 1 1 1 2 2 3 3 3 4 4 4 5 5 6 6 6 7 7 7

More Related