The interconnection of telephone systems — Graded multiples

The general problem of subscriber interconnection is stated here, while some of the economic and service factors in the selection of trunking systems are briefly considered. The characteristic manner in which telephone calls fall upon ordinary straight trunk groups is presented from both common sense and theoretical standpoints. One of the widely used trunk rearrangements by which an improved capacity may be achieved under certain conditions is known as graded multiple. A theoretical analysis of this scheme is given, from which are constructed curves for common probabilities of loss. Illustrative examples are included to make clear their use. A detailed comparison between theory and observation is made with considerable attention paid to critically examining the validity of the assumptions underlying the theory. It is concluded that the present graded multiple engineering tables are based upon a proper modification of the theoretical formula.