THE INTERCONNECTION OF TELEPHONE SYSTEMS 541 



3. The distribution of the load submitted to each subgroup follows 

 the Poisson Law and each subgroup carries the same average load as 

 every other subgroup. 



4. At no time shall a call be occupying a common trunk if an idle 

 trunk exists in the group of individual trunks assigned to the subgroup 

 of calling sources or switches from which the call under consideration 

 originated. In other words, it is assumed that calls which seized idle 

 common trunks because, at the time they originated, idle individual 

 trunks were not available, shall be immediately transferred (by some 

 fictitious redistributing apparatus) back to their individual trunks as 

 soon as these become idle. This assumption will be referred to below 

 as the assumption of "no-holes-in-the-multiple." 



Whether these are admissible assumptions must be decided by a 

 comparison of what actually results in practice with the formula which 

 they give rise to. Their concordance will be discussed in a following 

 section. 



In order to put this graded formula in a usable form for engineering 

 study curves or tables are needed showing how much load any given 

 arrangement of trunks will be able to carry at any specified grade of 

 service. Such charts have been constructed for the two more com- 

 monly used probabilities of loss, P = .01 and P = .001, compre- 

 hending all possible arrangements of trunks in simple symmetrical 

 graded multiples having an access or assignment of 10, 20, 30 and 40 

 terminals and subgroups from two to seven in number. These are 

 designated as Figs. 8 to 15, 8 to 11 corresponding to P = .01, and 12 

 to 15 to P = .001; the four at each probability cover the ranges of 

 access or assignment, 10, 20, 30 and 40, respectively. These dis- 

 tinguishing parameters are noted in the upper right-hand corner of 

 each chart. In order to simplify the necessary descriptive terms the 

 number of trunks in each individual subgroup is called ".r," the 

 number of common trunks is called "3'," and the number of sub- 

 groups, "g." Thus the access equals x + y, and the total number of 

 trunks equals gx -\- y. 



For the sake of compactness and brevity both the abscissa and 

 ordinate scales of these charts are plotted in terms of ratios ; the former 

 gives gx -f 3' or total trunks in terms of the access, x -\- y, and the 

 latter the per cent gain in efficiency (per cent increase in average load 

 per trunk) over the efficiency of a simple straight multiple oi x -}- y 

 trunks. A single one of the seven semi-circular curves on each figure 

 then yields the load information for any number of trunks having a 

 particular number of subgroups, a designated access, and a specified 

 grade of service. The dotted curve on each figure is included to show 



