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Omega Network

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”. Perfect Shuffle.

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Omega Network

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  1. 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”

  2. 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

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

  4. 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!)

  5. 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

  6. 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

  7. 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

  8. 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

  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 4 5 5 6 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. Path Contention • The omega network has the problems as the delta network with output port contention and path contention • Again, the result in a bufferless 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  30. 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

  31. 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

  32. 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

  33. 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

  34. 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

  35. 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

  36. 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

  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

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