
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. As an example, a packet has a (1/2) to the 4th power probability of
traversing a 16 port Butterfly network without a collision. Given a uniform
distribution of traffic such a network could maintain 1/16 of its theoretical
throughput before congestion.

