THE INTERCONNECTION OF TELEPHONE SYSTEMS 547 



done this we should have been able, at P = .01, to carry a total load 



(reading the gain of 21.3 per cent at ^'^ ^' = 2.75 on Fig. 9) of 



X ~p y 



As = (1.213) (.554) (55) = 36.96. At the same time the load we could 

 have carried on 58 trunks with three subgroups is only A3 = (1.03) 

 X (.554) (58) = 33.10. Hence, we could reduce the total number of 

 trunks by three in the six-subgroup case and still carry more load than 

 if we were to use the three-subgroup arrangement and the original 

 number of trunks. This decided advantage in favor of the larger 

 number of subgroups is even more pronounced if the P = .001 com- 

 parison is made {As — 26.9 vs. ^e = 32.2). 



The secret of the large gains in certain cases is easily found. After 

 a short study of the curve charts it will readily be verified that, in 

 general, the modal or maximum gain point on any curve comes very 

 nearly at the midpoint of the range between x + y and g{x + y). 

 This midpoint is reached by always setting x = y or x = |(x + y), 

 that is, by making the individuals compose one-half of the access or 

 assignment. 



Comparisons of Theory and Practice 

 It is, of course, eminently desirable to know whether the formula 

 just described for the probability of loss of any simple arrangement is 

 consistent wdth the grades of service which it will actually render in 

 practice. This we could ascertain only after a prolonged and careful 

 study of typical graded groups already at work in the Bell System. 

 Accordingly, a set of tests lasting over a period of six months, in the 

 latter part of 1927, was made in Chicago by the Department of Opera- 

 tion and Engineering of the American Telephone and Telegraph 

 Company in cooperation with the Illinois Bell Telephone Company. 

 The tests were performed on district multiples, believed to be 

 representative, by connecting holding time recorders to the groups to 

 indicate the load being carried by each trunk. Then through the 

 use of overflow and peg count (number of calls) registers the proportion 

 of calls being delayed (or lost) was readily found for any particular 

 busy hour load. 



In the First Division of these tests two groups of interoffice trunks, 

 State to Dearborn and State to Wabash, were selected as typical cases 

 of the kinds of fluctuating busy hour loads to be found in ordinary 

 panel graded practice. No attempt was made here to regulate the 

 load being submitted in any busy hour or to any subgroup since what 

 was particularly desired was not what %vould happen if such and such 

 conditions obtained, but rather what does happen under the fluctuating 

 load conditions which actually occur in the busy hours from day to day. 



