On Rearrangeable Three-Stage Connecting Networks

Most communications systems contain a connecting network as a basic functional unit. A connecting network is an arrangement of switches and transmission links through which certain terminals can be connected together in many combinations. The calls in progress in a connecting network do not usually arise in a predetermined time sequence. Requests for connection (new calls) and terminations of connection (hangups) occur more or less at random. For this reason the performance of a connecting network when subjected to random traffic is used as a figure of merit. This performance is measured, for example, by the fraction of requested connections that cannot be completed, or the probability of blocking. The performance of a connecting network for a given level of offered traffic is determined largely by its configuration or structure. This structure may be described by stating what terminals have a switch placed between them, and can be connected together by closing the switch. The structure of a connecting network determines what combinations of terminals can be connected together simultaneously. If this structure is 1481