Omega Network

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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

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Perfect Shuffle

• The interconnections between stages are defined
  by the logical rotate left of the bits used in
  the port ids
• Example 000 ---gt 000 ---gt 000 ---gt 000
• Example 001 ---gt 010 ---gt 100 ---gt 001
• Example 011 ---gt 110 ---gt 101 ---gt 011
• Example 111 ---gt 111 ---gt 111 ---gt 111

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8 x 8 OMEGA NETWORK
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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!)

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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

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Path Contention
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Path Contention
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Performance Degradation
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Performance Degradation
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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

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Batcher-Banyan Example
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Batcher-Banyan Example
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Batcher-Banyan Example
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Batcher-Banyan Example
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Batcher-Banyan Example
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Batcher-Banyan Example
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Batcher-Banyan Example
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