On Switching Networks and Block Designs, II

On Switching Networks and Block Designs, II By F. R. K. CHUNG (Manuscript received December 28, 1979) An important objective in designing switching networks is to minimize the probability of calls being blocked. A number of methods have been developed in the past for designing efficient switching networks that satisfy various constraints on their parameters. In this paper we investigate a special class of subnetworks of a switching network, called channel graphs. It is known that, under the usual assumptions made for calculating blocking probabilities, the blocking probability of a switching network is small if blocking probabilities of its channel graphs are small. With the use of certain combinatorial structures, known as block designs, we construct a large class of nearly optimal channel graphs. I. INTRODUCTION T w o switching networks having the same number of crosspoints but with different linking patterns can, in general, have different blocking performance. One widely used method to estimate the blocking performance of a switching network is to calculate the (Lee) blocking probabilities1 of the channel graphs (also called the linear graphs), each of which is the union of all paths that can be used to connect an input terminal and an output terminal.* T w o channel graphs G, G2 of two balanced2 &-stage networks Ni, N2, respectively, having the same number of crosspoints but with different Unking patterns, often satisfy the following properties: (i) The number of distinct paths in Gi is equal to the number of distinct paths in G2.