Delta Network

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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...

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8 x 8 DELTA NETWORK
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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!)

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Example of Self RoutingCell destined for output
port 4 ( 100 )
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Example of Self RoutingCell destined for output
port 4 ( 100 )
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Example of Self RoutingCell destined for output
port 4 ( 100 )
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Example of Self RoutingCell destined for output
port 4 ( 100 )
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Example of Self RoutingCell destined for output
port 4 ( 100 )
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Example of Self RoutingCell destined for output
port 4 ( 100 )
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Example of Self RoutingCell destined for output
port 4 ( 100 )
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Example of Self RoutingCell destined for output
port 4 ( 100 )
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Example of Self RoutingCell destined for output
port 4 ( 100 )
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Example of Self RoutingCell destined for output
port 4 ( 100 )
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Example of Self RoutingCell destined for output
port 4 ( 100 )
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Example of Self RoutingCell destined for output
port 4 ( 100 )
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Multiple Concurrent Paths
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Multiple Concurrent Paths
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Multiple Concurrent Paths
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Multiple Concurrent Paths
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Multiple Concurrent Paths
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Multiple Concurrent Paths
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Multiple Concurrent Paths
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Multiple Concurrent Paths
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Multiple Concurrent Paths
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Multiple Concurrent Paths
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Multiple Concurrent Paths
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Multiple Concurrent Paths
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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, ...

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Output Port Contention
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Output Port Contention
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Output Port Contention
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Output Port Contention
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Output Port Contention
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Output Port Contention
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Output Port Contention
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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

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Path Contention
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Path Contention
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Path Contention
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Path Contention
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Path Contention
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Path Contention
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Path Contention
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8 x 8 DELTA NETWORK
Cell on input port 0 destined for output port 2
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8 x 8 DELTA NETWORK
Cell on input port 4 destined for output port 3
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INTERNAL BLOCKING
Cell on input port 0 destined for output port 2
Cell on input port 4 destined for output port 3
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Performance Degradation
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Performance Degradation
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Performance Degradation
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Performance Degradation
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Performance Degradation
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Performance Degradation
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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
Batcher Sorter
Banyan (Delta)
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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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