1. 1 Delta Network The delta network is one example of a multistage interconnection network that can be used as a switch fabric The delta network is an example of a banyan network In banyan networks, there is a single path from each input port to each output port A delta network looks like the following...

2. 2 8 x 8 DELTA NETWORK 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7

3. 3 Self Routing Delta 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!)

4. 4 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 4 Example of Self Routing Cell destined for output port 4 (= 100 ) 2

5. 5 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 2 4

6. 6 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 2 4

7. 7 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 2 4

8. 8 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 2 4

9. 9 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 2 4

10. 10 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 Example of Self Routing Cell destined for output port 4 (= 100 ) 2 4

11. 11 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 Example of Self Routing Cell destined for output port 4 (= 100 ) 2 4

12. 12 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 4 Example of Self Routing Cell destined for output port 4 (= 100 ) 2

13. 13 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 4 Example of Self Routing Cell destined for output port 4 (= 100 ) 2

14. 14 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 Example of Self Routing Cell destined for output port 4 (= 100 ) 2 4

15. 15 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 4 Example of Self Routing Cell destined for output port 4 (= 100 ) 2

16. 16 Multiple Concurrent Paths 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 7 5

17. 17 Multiple Concurrent Paths 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 5 7

18. 18 Multiple Concurrent Paths 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 5 7

19. 19 Multiple Concurrent Paths 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 5 7

20. 20 Multiple Concurrent Paths 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 5 7

21. 21 Multiple Concurrent Paths 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 7 5

22. 22 Multiple Concurrent Paths 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 7 5 1

23. 23 Multiple Concurrent Paths 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 5 7 1

24. 24 Multiple Concurrent Paths 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 5 7 1

25. 25 Multiple Concurrent Paths 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 5 7 1

26. 26 Multiple Concurrent Paths 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 5 7 1

27. 27 Multiple Concurrent Paths 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 7 5 1

28. 28 Output Port Contention Up to now, all examples have worked wonderfully because each incoming cell was destined to a different output port What happens if more than one cell destined to same output port? Answer: output port contention Result: cell loss in a bufferless network Alternatives: buffering, deflection routing, recirculation, tandem banyans,...

29. 29 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 4 4 Output Port Contention

30. 30 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 4 4 Output Port Contention

31. 31 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 4 4 Output Port Contention

32. 32 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 4 4 Output Port Contention

33. 33 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 4 4 Output Port Contention

34. 34 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 Output Port Contention

35. 35 44 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 Output Port Contention

36. 36 Path Contention It is also possible for two incoming cells that are destined to different output ports to require the same internal link in the switch Called path contention or internal blocking 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

37. 37 Path Contention 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 2 3

38. 38 Path Contention 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 2 3

39. 39 Path Contention 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 2 3

40. 40 Path Contention 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7

41. 41 Path Contention 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 3

42. 42 Path Contention 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 3

43. 43 Path Contention 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 3

44. 44 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 8 x 8 DELTA NETWORK Cell on input port 0 destined for output port 2

45. 45 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 8 x 8 DELTA NETWORK Cell on input port 4 destined for output port 3

46. 46 INTERNAL BLOCKING 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7 Cell on input port 0 destined for output port 2 Cell on input port 4 destined for output port 3

47. 47 Performance Degradation 0 1 2 3 4 5 6 7 1 2 3 4 6 7 5 0 5 3 2 0 4 6

48. 48 Performance Degradation 0 1 2 3 4 5 6 7 1 2 3 4 6 7 5 0 6 5 4 0 2 3

49. 49 Performance Degradation 0 1 2 3 4 5 6 7 3 5 2 0 4 6 1 2 3 4 6 7 5 0

50. 50 Performance Degradation 6 4 5 2 0 3 1 2 3 4 6 7 5 00 1 2 3 4 5 6 7

51. 51 Performance Degradation 0 1 2 3 4 5 6 7 0 3 2 6 1 2 3 4 6 7 5 0

52. 52 Performance Degradation 0 1 2 3 4 5 6 7 0 3 2 6 1 2 3 4 6 7 5 0 5

53. 53 Performance Degradation 0 1 2 3 4 5 6 7 5 6 2 3 0 1 2 3 4 6 7 5 0

54. 54 Performance Degradation 0 1 2 3 4 5 6 7 0 3 2 5 6 1 2 3 4 6 7 5 0

55. 55 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

56. 56 Batcher-Banyan Batcher Sorter Banyan (Delta)

57. 57 Batcher-Banyan Example 0 1 2 3 4 5 6 7 1 2 3 4 6 7 5 0 5 3 2 0 4 6

58. 58 Batcher-Banyan Example 0 1 2 3 4 5 6 7 1 2 3 4 6 7 5 0 4 3 6 2 5 0

59. 59 Batcher-Banyan Example 0 1 2 3 4 5 6 7 1 2 3 4 6 7 5 0 0 5 2 6 3 4

60. 60 Batcher-Banyan Example 0 1 2 3 4 5 6 7 1 2 3 4 6 7 5 0 4 6 5 2 3 0

61. 61 Batcher-Banyan Example 0 1 2 3 4 5 6 7 1 2 3 4 6 7 5 0 0 3 2 5 4 6

62. 62 Batcher-Banyan Example 0 1 2 3 4 5 6 7 1 2 3 4 6 7 5 0 0 3 2 5 4 6

63. 63 Batcher-Banyan Example 0 1 2 3 4 5 6 7 1 2 3 4 6 7 5 0 6 5 4 3 2 0