1. 6/22/20151 CLOS-NETWORK SWITCHES

2. H. Jonathan Chao 6/22/2015 Page 2 A Growable Switch Configuration i j

3. H. Jonathan Chao 6/22/2015 Page 3 Routing Constraint in Clos-Network Switch

4. H. Jonathan Chao 6/22/2015 Page 4 Routing In A Clos Network

5. H. Jonathan Chao 6/22/2015 Page 5 A TST Switch Representation After the Space- to-Time Transformation

6. H. Jonathan Chao 6/22/2015 Page 6 Matching of A i versus B j ( X =busy, blank=open)

7. H. Jonathan Chao 6/22/2015 Page 7 Parallel Assignments In a Cyclic Manner from Minislot to Minislot

8. H. Jonathan Chao 6/22/2015 Page 8 CRRD Switch with Virtual Output Queues (VOQs) In the Input Modules L I (i,r) L C (r,j)

9. H. Jonathan Chao 6/22/2015 Page 9 Terminology

10. H. Jonathan Chao 6/22/2015 Page 10 Schematic Configuration of a 40 X 40 Multistage ATLANTA Switch

11. H. Jonathan Chao 6/22/2015 Page 11 Three Main Principles in ATLANTA Switch

12. H. Jonathan Chao 6/22/2015 Page 12 Random Dispatching Scheme

13. H. Jonathan Chao 6/22/2015 Page 13 Random Dispatching Scheme (Cont’d) In Phase 2, a VOQ’s request from IM may lose contention in CM because of contention in the CM or backpressure from the corresponding output queue. If this request loses contention due to backpressure, IM will choose another VOQ as candidate at the next time slot. Otherwise, this VOQ will be chosen as candidate at the next time slot again.

14. H. Jonathan Chao 6/22/2015 Page 14 Example of A Multicast Connection In a 40x40 ATLANTA Switch with Multistage Fabric. The Minimum Multicast Tree for Cells of that Multicast Connection is Highlighted

15. H. Jonathan Chao 6/22/2015 Page 15 Random Dispatching Schemes ATLANTA Switch (need internal expansion) Washington University Gigabit Switch (cause the out-of-sequence)

16. H. Jonathan Chao 6/22/2015 Page 16 Example of Random Dispatching Scheme(n=m=k=2) VOQ(0,0,0) can send through CM(0) is The total link utilization of OP(0,0) is Throughput_Max:

17. H. Jonathan Chao 6/22/2015 Page 17 One question arises: Is it possible to achieve a high throughput by using a practical dispatching scheme, without allocating any buffers in the second stage to avoid the out-of-sequence problem and without expanding the internal bandwidth?

18. H. Jonathan Chao 6/22/2015 Page 18 Concurrent Round-Robin Dispatching (CRRD) Scheme The basic idea of CRRD is to use desynchronization effect.

19. H. Jonathan Chao 6/22/2015 Page 19

20. H. Jonathan Chao 6/22/2015 Page 20 Example of desynchronization effect of CRRD (n=m=k=2)

21. H. Jonathan Chao 6/22/2015 Page 21 Concurrent Master-Slave Round-Robin Dispatching (CMSD) Scheme CMSD uses hierarchy round-robin arbiters, it provides more features of scalability in terms of reduction of dispatching scheduling time and interconnection crosspoints, while preserving CRRD’s advantage. m n k 1 1 1

22. H. Jonathan Chao 6/22/2015 Page 22 Concurrent Master-Slave Round-Robin Dispatching (CMSD) Scheme (Cont’d) Note that, G(i,j) is denoted as a VOQ group that consists of n VOQs, each of which is denoted as VOQ(i,j,h).

23. H. Jonathan Chao 6/22/2015 Page 23

24. H. Jonathan Chao 6/22/2015 Page 24 Example of Desynchronization Effect of CMSD (n=m=k=2)

25. H. Jonathan Chao 6/22/2015 Page 25 Delay Performance of CRRD and RD Schemes (n=m=k=8) Bernoulli Traffic CRRD achieves100% throughput under uniform traffic, which is independent of number of iterations in the IM.

26. H. Jonathan Chao 6/22/2015 Page 26 Delay Performance of CMSD in Bursty Traffic Compared with CRRD (n=m=k=8) CMSD also achieves100% throughput under uniform traffic, which is independent of number of iterations in the IM.

27. H. Jonathan Chao 6/22/2015 Page 27 Relationship between Switch Throughput and Expansion Factor (n=k=8) RD needs the expansion ratio of more than 1.5 to achieve 100% throughput, which CRRD and CMSD do not need expansion by using simple round robin arbiters.

28. H. Jonathan Chao 6/22/2015 Page 28 Switch Throughput Under Non-Uniform Traffic (n=m=k=8) The throughput of CRRD and CMSD is higher than that of RD, when the traffic is slightly unbalanced.

29. H. Jonathan Chao 6/22/2015 Page 29 Analogy among scheduling schemes

30. H. Jonathan Chao 6/22/2015 Page 30 The Correspondence Between the Middle-Stage Route Scheduling In a Clos Network and the Edge-Coloring of the Regular Bipartite Multigraph

31. H. Jonathan Chao 6/22/2015 Page 31 Illustration of Time-Space Interleaving Principle

32. H. Jonathan Chao 6/22/2015 Page 32 Latin-Square Assignment

33. H. Jonathan Chao 6/22/2015 Page 33 Route Assignment By Latin Square for Uniform Traffic

34. H. Jonathan Chao 6/22/2015 Page 34 Route Scheduling In the Middle-Stage for Uniform Traffic

35. H. Jonathan Chao 6/22/2015 Page 35 Route Scheduling In Central Modules for the Second Example of Uniform Traffic

36. H. Jonathan Chao 6/22/2015 Page 36 Procedure of Capacity and Route Assignment

37. H. Jonathan Chao 6/22/2015 Page 37 Route Scheduling Example (Heterogeneous Traffic)