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A more economical solution: Banyan Networks

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• The Banyan Switch
  • A 2x2 Banyan switch has two inputs
    • numbered 0 and 1

    and two outputs

    • numbered 0 and 1

  • Banyan switch:

  • The Banyan switch has a switching control built into the switch itself:

    Every packet (messages) that comes into the Banyan switch has a header that contains a bit indicating what its destination is (either 0 or 1). The header is usually the first bit of the packet (message) If the switch reads the bit and it has value 0, it sends the packet to its upper output (which is marked with 0 in the figure) If the switch reads the bit and it has value 1, it sends the packet to its lower output (which is marked with 1 in the figure)

  • By connecting these simple Banyan switching elements in series and parallel, it is possible to route packets in more complicated ways depending on the desired routes to establish.

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• The Delta Network
  • The Delta Interconnection Network is a digit controlled multi-stage interconnection network made up with Banyan Switches

  • Here is an example of a 8x8 Delta Network

  • Each rectangle represents a 2x2 Banyan Switch

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• (Self) Routing method in Delta Network
  • A request from the source to the destination will be transmitted as follows:

    100aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa +++********************************** ^ |<------------------------------>| | Address value (data) | Routing information

  • The first bit is used to control the Banyan Switching fabric

  • After making routing decision, the Banyan Switching removes the routing (first) bit and the rest of the message is forwarded to the next stage.

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• (Self) Routing in Delta Network - Example 1
  • Suppose CPU 1 wants to send an address value to Memory Module 4

  • Step 1 of the transmission:

    Because the routing (first) bit is 1 , the entire message (except the routing bit) is forwarded onto the lower connection

  • Step 2 of the transmission:

    Because the routing (first) bit is 0 , the entire message (except the routing bit) is forwarded onto the upper connection

  • Step 3 of the transmission:

    Because the routing (first) bit is 0 , the entire message (except the routing bit) is forwarded onto the upper connection

  • The address value is then "delivered" (connected) to the memory module 4

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• (Self) Routing in Delta Network - Example 2
  • Suppose CPU 6 wants to send an address value to Memory Module 4

  • Step 1 of the transmission:

    Because the routing (first) bit is 1 , the entire message (except the routing bit) is forwarded onto the lower connection

  • Step 2 of the transmission:

    Because the routing (first) bit is 0 , the entire message (except the routing bit) is forwarded onto the upper connection

  • Step 3 of the transmission:

    Because the routing (first) bit is 0 , the entire message (except the routing bit) is forwarded onto the upper connection

  • The address value is then "delivered" (connected) to the memory module 4

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• Concurrent Routing in Delta Network - Example 1
  • Multiple requests can be routed simultaneously through the Delta Network

  • Example:
    • CPU 1 sends a memory request (address) to memory module 5, and
    • CPU 3 sends a memory request (address) to memory module 7

  • Step 1:

  • Step 2:

  • Step 3:

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• Concurrent Routing in Delta Network - Example 2

  • Example:
    • CPU 1 sends a memory request (address) to memory module 5, and
    • CPU 3 sends a memory request (address) to memory module 7
    • CPU 6 sends a memory request (address) to memory module 1

  • Step 1:

  • Step 2:

  • Step 3:

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• Output Port Contention

  • Just like in the Cross Bar switch, if multiple CPUs request to access the SAME memory module, only ONE request can be granted.

  • Example:
    • CPU 1 and CPU 6 both want to access Memory Module 4

  • Step 1:

  • Step 2:

  • Step 3:

  • Switch only forwards ONE of the conflicting requests:

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• Internal Blocking
  • It is obvious that multiple requests for the SAME memory module cannot be satified.

  • We saw that the Cross Bar switch was non-blocking:
    Multiple requests destined for different outputs can always be transmitted by a Cross Bar switch.

  • Unlike the Cross Bar switch, it is also possible for 2 requests destined for different memory modules to be in conflict in the Delta switch.

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  • Example:
    • CPU 0 sends request to memory module 2, and simultaneously
    • CPU 4 sends request to memory module 3

  • Step 1:

  • Step 2:

    This kind of conflict happens inside the switching fabric and it is called internal blocking requests

  • Again, the switch only forwards ONE of the conflicting requests: