The Bell System Technical Journal 



October, 1931 



The Interconnection of Telephone Systems — 

 Graded Multiples 



By R. I. WILKINSON 



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 con- 

 structed 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. 



Introduction 



WITH the completion of the third commercial telephone instru- 

 ment some fifty odd years ago was born the problem of inter- 

 connection. And as the system has grown so has the demand for a 

 universal service. The present complexity of our communication 



Fig. 1 — Direct interconnection of subscribers. 



network makes it difficult to appreciate that in those early days it was 

 a comparatively simple thing to provide a direct line from each sub- 

 scriber to every other subscriber, as shown in the schematic intercon- 

 nection of the six telephone stations in Fig. 1. In such schemes there 



531 



