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Indirect Networks or Dynamic Networks

Interconnection Networks. Indirect Networks or Dynamic Networks. Guihai Chen …with major presentation contribution from José Flich, UPV (and Cell BE EIB slides by Tom Ainsworth, USC). Questions in mind. Difference between Static/direct and Dynamic/indirect Networks

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Indirect Networks or Dynamic Networks

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  1. Interconnection Networks Indirect Networks orDynamic Networks Guihai Chen …with major presentation contribution from José Flich, UPV (and Cell BE EIB slides by Tom Ainsworth, USC)

  2. Questions in mind • Difference between Static/direct and Dynamic/indirect Networks • Why Multi-Stage Interconnection Networks • Large Switch and Small Switch • How to design non-blocking MINs

  3. Outline • Network Topology • Preliminaries and Evolution • Centralized Switched (Indirect) Networks • From non-blocking crossbar to blocking MINs • From blocking MINs to non-blocking MINs

  4. Network Topology Preliminaries and Evolution • One switch suffices to connect a small number of devices • Number of switch ports limited by VLSI technology, power consumption, packaging, and other such cost constraints • A fabric of interconnected switches (i.e., switch fabric or network fabric) is needed when the number of devices is much larger • The topology must make a path(s) available for every pair of devices—property of connectedness or full access (What paths?) • Topology defines the connection structure across all components • Bisection bandwidth: the minimum bandwidth of all links crossing a network split into two roughly equal halves • Full bisection bandwidth: • Network BWBisection = Injection (or Reception) BWBisection= N/2 • Bisection bandwidth mainly affects performance • Topology is constrained primarily by local chip/board pin-outs; secondarily, (if at all) by global bisection bandwidth

  5. Network Topology Preliminaries and Evolution • Several tens of topologies proposed, but less than a dozen used • 1970s and 1980s • Topologies were proposed to reduce hop count • 1990s • Pipelined transmission and switching techniques • Packet latency became decoupled from hop count • 2000s • Topology still important (especially OCNs, SANs, P2P Overlays, DCNs) when N is high • Topology impacts performance and has a major impact on cost

  6. 4 4 5 5 7 7 0 0 1 1 2 2 3 3 6 6 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 Network Topology Centralized Switched (Indirect) Networks • Crossbar network • Crosspoint switch complexity increases quadratically with the number of crossbar input/output ports, N, i.e., grows as O(N2) • Has the property of being non-blocking

  7. Network Topology From Crossbar to MINs

  8. 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 Network Topology Centralized Switched (Indirect) Networks • Multistage interconnection networks (MINs) • Crossbar split into several stages consisting of smaller crossbars • Complexity grows as O(N×log N), where N is # of end nodes • Inter-stage connections represented by a set of permutation functions Omega topology, perfect-shuffle exchange

  9. 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 Network Topology Appendix • Shuffle function • N= 0…N-1 • f(i)= 2i, when I <N/2 • f(i)=(2i+1), mod N when i ≥ N/2 • Often used as a connection pattern • unshuffle function, also often used unshuffle perfect-shuffle

  10. Network Topology Centralized Switched (Indirect) Networks 0000 0000 0001 0001 0010 0010 0011 0011 0100 0100 0101 0101 0110 0110 0111 0111 1000 1000 1001 1001 1010 1010 1011 1011 1100 1100 1101 1101 1110 1110 1111 1111 16 port, 4 stage Omega network

  11. Network Topology Centralized Switched (Indirect) Networks 0000 0000 0001 0001 0010 0010 0011 0011 0100 0100 0101 0101 0110 0110 0111 0111 1000 1000 1001 1001 1010 1010 1011 1011 1100 1100 1101 1101 1110 1110 1111 1111 16 port, 4 stage Baseline network

  12. Network Topology Centralized Switched (Indirect) Networks 0000 0000 0001 0001 0010 0010 0011 0011 0100 0100 0101 0101 0110 0110 0111 0111 1000 1000 1001 1001 1010 1010 1011 1011 1100 1100 1101 1101 1110 1110 1111 1111 16 port, 4 stage Butterfly network

  13. Network Topology-Correction to Butterfly Centralized Switched (Indirect) Networks 0000 0000 0001 0001 0010 0010 0011 0011 0100 0100 0101 0101 0110 0110 0111 0111 1000 1000 1001 1001 1010 1010 1011 1011 1100 1100 1101 1101 1110 1110 1111 1111 16 port, 4 stage Butterfly network

  14. Network Topology Centralized Switched (Indirect) Networks 0000 0000 0001 0001 0010 0010 0011 0011 0100 0100 0101 0101 0110 0110 0111 0111 1000 1000 1001 1001 1010 1010 1011 1011 1100 1100 1101 1101 1110 1110 1111 1111 16 port, 4 stage Cube network

  15. Network Topology Centralized Switched (Indirect) Networks • Multistage interconnection networks (MINs) • MINs interconnect N input/output ports using k x k switches • logkNswitch stages, each with N/k switches • N/k(logkN) total number of switches • Example: Compute the switch and link costsof interconnecting 4096 nodes using a crossbar relative to a MIN, assuming that switch cost grows quadratically with the number of input/output ports (k). Consider the following values of k: • MIN with 2 x 2 switches • MIN with 4 x 4 switches • MIN with 16 x 16 switches

  16. Network Topology Centralized Switched (Indirect) Networks • Example: compute the relative switch and link costs, N = 4096 cost(crossbar)switches = 40962 cost(crossbar)links = 8192 relative_cost(2 × 2)switches = 40962 / (22 × 4096/2 × log2 4096) = 170 relative_cost(2 × 2)links = 8192 / (4096 × (log2 4096 + 1)) = 2/13 = 0.1538 relative_cost(4 × 4)switches = 40962 / (42 × 4096/4 × log4 4096) = 170 relative_cost(4 × 4)links = 8192 / (4096 × (log4 4096 + 1)) = 2/7 = 0.2857 relative_cost(16 × 16)switches = 40962 / (162 × 4096/16 × log16 4096) = 85 relative_cost(16 × 16)links = 8192 / (4096 × (log16 4096 + 1)) = 2/4 = 0.5

  17. Network Topology Centralized Switched (Indirect) Networks • Relative switch and link costs for various values of k and N (crossbar relative to a MIN) Relative switch cost Relative link cost

  18. Network Topology From blocking to non-blocking again

  19. 4 5 7 0 1 2 3 6 0 0 0 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 Network Topology Centralized Switched (Indirect) Networks • Reduction in MIN switch cost comes at the price of performance • Network has the property of being blocking • Contention is more likely to occur on network links • Paths from different sources to different destinations share one or more links X non-blocking topology blocking topology

  20. Network Topology Centralized Switched (Indirect) Networks • How to reduce blocking in MINs? Provide alternative paths! • Use larger switches (can equate to using more switches) • Clos network: minimally three stages (non-blocking) • A larger switch in the middle of two other switch stages provides enough alternative paths to avoid all conflicts • Use more switches • Add logkN - 1 stages, mirroring the original topology • Rearrangeably non-blocking • Allows for non-conflicting paths • Doubles network hop count (distance),d • Centralized control can rearrange established paths • Benes topology: 2(log2N) - 1 stages (rearrangeably non-blocking) • Recursively applies the three-stage Clos network concept to the middle-stage set of switches to reduce all switches to 2 x 2

  21. Network Topology Centralized Switched (Indirect) Networks 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 port Crossbar network

  22. Network Topology Centralized Switched (Indirect) Networks 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 port, 3-stage Clos network

  23. Network Topology Centralized Switched (Indirect) Networks 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 port, 5-stage Clos network

  24. Network Topology Centralized Switched (Indirect) Networks 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 port, 7 stage Clos network = Benes topology

  25. Network Topology Centralized Switched (Indirect) Networks 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 Alternative paths from 0 to 1. 16 port, 7 stage Clos network = Benes topology

  26. Network Topology Centralized Switched (Indirect) Networks 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 Alternative paths from 4 to 0. 16 port, 7 stage Clos network = Benes topology

  27. Network Topology Centralized Switched (Indirect) Networks 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 Contention free, paths 0 to 1 and 4 to 1. 16 port, 7 stage Clos network = Benes topology

  28. Network Bisection 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Network Topology • Bidirectional MINs • Increase modularity • Reduce hop count, d • Fat tree network • Nodes at tree leaves • Switches at tree vertices • Total link bandwidth is constant across all tree levels, with full bisection bandwidth • Equivalent to folded Benes topology • Preferred topology in many SANs Centralized Switched (Indirect) Networks Folded Clos = Folded Benes = Fat tree network

  29. Network Topology Myrinet-2000 Clos Network for 128 Hosts • Backplane of the M3-E128 Switch • M3-SW16-8F fiber line card (8 ports) http://myri.com

  30. Network Topology Myrinet-2000 Clos Network for 128 Hosts • “Network in a Box” • 16 fiber line cards connected to the M3-E128 Switch backplane http://myri.com

  31. Network Topology Myrinet-2000 Clos Network Extended to 512 Hosts http://myri.com

  32. Assignment 2-2 Chose one of the following exercises: • Calculate how many permutations nxn Omega network could support. • Prove that folded Clos network, folded Bens network, and Fat tree network are isomorphic to each other. Parallel Processing, Low-Diameter Architectures

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