Expected Capacity of (m2)-Networks

A concentrator is an interconnection network with n inputs and m outputs, n > m, wherein any specified subset of inputs of size less than or equal to some number, called the network's actual capacity, can always be simultaneously connected to some equal-sized but unspecifiable subset of outputs. Guaranteed throughput as described by actual capacity has heretofore been the principle measure for evaluating concentrator performance. In many applications, however, a more practical measure of a concentrator's capability is a probabilistic measure of its throughput in the following sense: given an input subset of size k, k ≤ m, what is the average number of inputs that can be connected to outputs? This measure will be called expected capacity. This paper considers the expected capacity of a special class of sparse crossbar concentrators called ( m 2 ) networks. It is seen that the expected capacity values for ( m 2 ) networks are usually quite close to k.