Output Port Blocking 



The probability of a Butterfly switching module not blocking is 1/2. A 16 input Butterfly multistage network requires 4 levels. The overall nonblocking probability is thus (1/2)^{4} = 0.0625, or 6.25% 
The probability of a 12 port MetaRouter switching module requires 3 levels. The overall nonblocking probability is thus (5/6)^{3} = 0.578, or 57.8%. 
The nonblocking probability for a 532 port MetaRouter is 0.57 while the nonblocking probability for a 512 port Banyan or Butterfly Network is 0.0037. The probability that a packet will traverse a 532 port MetaRouter without collision is more than 2 orders of a magnitude larger than the probability that a packet will traverse a 512 port Banyan or Butterfly. The larger the nonblocking probability, the larger the effective isochronous bandwidth. 
Bottom line: The larger the fanout, the smaller, the number of levels, the greater the effective isochronous bandwidth. 


Output blocking also affects the
topology of the Internet. Currently the Internet is designed to maximize
the connectivity rather the endtoend bandwidth. The effective bandwidth
of the Internet goes down exponentially with the number of hops. 
The fiber network will physically remain a backbone, however a virtual fully connected network will be constructed out of wavelength division multiplexed channels and digital access crossconnects. 

