Fabric Blocking

Banyan and Butterfly networks are blocking - some paths block other paths from their desired destinations.  This results in a multipler on the bandwidth consumed - in the diagram, 2 paths block 6 other paths

Galois network based on modules with a fanout of 12 has 6 independent paths between any input to any output and thus a factor of 6 less fabric blocking than a Banyan or Butterfly Network which only have one path between any input and output.

A 16-port Butterfly network with a 60% load factor has a 25% collision rate, while an 18-port Galois has only a 5% collision rate.

The collision rate of an 18-port Galois network with 60% load factor can be reduced to less than 2% by adding an extra layer of switching nodes.

The key to reducing the fabric blocking collision rate is increasing the path redundancy. A Butterfly network has only one path between any input to any output, while the number of paths through a Galois network can be increased by adding layers.