As an example, two paths through an 8 port Butterfly or Banyan network can be shown to block the other 6 paths. This results in an effective factor of three increase in the traffic. The best way to get around this problem is to add topological redundancy. Simulations are being used to study this further. Congestion is also determined by statistical blocking.
Packets have a certain probability of colliding at the same router output port.
This probability decreases with the router fanout and increases geometrically with each router traversed. The larger the router fanout and the fewer routers traversed, the larger the probability is that a packet will traverse the network without a collision, the smaller the congestion, and the larger the throughput of the network. Simulations are being used to study this further. Extended results to encompass arbitrary networks. Realized that the number of hops in a network reduced the throughput by compounding the output port blocking probability.