Algebraic And Topological Properties of Connecting Networks

Any largo communication system contains a connecting network, an arrangement of switches and transmission links through which certain terminals can be connected together in many combinations, usually by many different possible routes through the network. Examples of connecting networks can be found in telephone central offices, toll centers, and military communications systems. The connections in progress in a connecting network usually do not arise in a predetermined temporal sequence; instead, requests for connection (new calls) and terminations of connection (hangups) occur more or less "at random." For this reason it is customary to use the performance of a connecting network when subjected to random traffic as a figure of merit. One precise measure of this performance is the fraction of requested connections that cannot be completed in a given time interval, or the ·probability of blocking. In a telephone connecting network this probability measures to some extent the grade of service given to the customers. The performance of a connecting network for a given traffic level is determined largely by its configuration or structure. This configuration may be described by stating what terminals or transmission links have a switch placed between them and can be connected together by closing the switch. The configuration of a connecting network determines what groups of terminals can be connected together simultaneously. Any one set of permissible connections maj r be called a state of the network.