A virtually nonblocking self - routing permutation network which routes packets in O ( log 2 N ) time

Asymptotically nonblocking networks are O(log2 N) depth self-routing permutation devices in which blocking probability vanishes when N (the number of network inputs) increases. This behavior does not guarantee, also for very large N , that all information always and simultaneously reaches its destination (and consequently that a whole permutation passes through the device) which is a requirement of the PRAM machine. In this work the conditions for which an asymptotically nonblocking network becomes asymptotically permutation nonblocking are studied, finally a virtually nonblocking device is obtained by a retransmission procedure which guarantees that all permutations always pass through this permutation device.