Blocking Probability for a Multistage Clos Connecting Network

In this paper, we consider the application of the the rmodynamic concepts to the study of connect ing networks such as those found in telephone systems as illustrated in Fig. 1. Basically, the problem is to obtain all possible connections between N inputs and N outputs given by the permutat ion group by means of a physical structure. This could, for example, be an N • N matrix. For telephone applications in which the value of N can reach several thousands, this hardware assembly, requiring N 2 crosspoints, is obviously quite difficult to make. The technological solution, therefore, generally consists in breaking this large matrix into much smaller ones linked in such a way to enable the realization of all connections between inputs and outputs.