Properties of Random Traffic in Nonblocking Telephone Connecting Networks

In the continuing effort to understand the nature of congestion in telephone connecting networks, it is important to have a thorough knowledge of the special case of no congestion, exemplified by traffic in a nonblocking network. Such knowledge is useful not merely as a guide to theoretical investigations, but also in answering questions that are of immediate practical import in the design of networks with small congestion. It is the purpose of this paper to describe some results concerning random traffic in nonblocking connecting networks; these results have important applications to traffic in networks that are not nonblocking. For although nonblocking networks are rare in present telephone practice, and are therefore of limited immediate interest to engineers, they form an important limiting case that is approached as the probability of blocking is reduced by the addition of links and switches to the network. Moreover, many parameters descriptive of the traffic can be calculated with ease for a nonblocking network, and only arduously or not at all for a network that, has a nonzero probability of blocking. Hence for low blocking, certain results pertaining to the nonblocking case can be used to approximate those in the blocking case. 509