Issue No. 07 - July (1983 vol. 32)
G.M. Masson , Department of Electrical Engineering and Computer Science, Johns Hopkins University
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.
prime decomposition, Actual capacity, binomial networks, concentrator, expected capacity, ( m 2 ) networks, prime component counts
S. Morris and G. Masson, "Expected Capacity of (m2)-Networks," in IEEE Transactions on Computers, vol. 32, no. , pp. 649-657, 1983.