552 BELL SYSTEM TECHNICAL JOURNAL 



calls carried over the State to Dearborn group, with a suggested ex- 

 ponential fitting frequency curve superposed on it. From other 

 studies carried out on non-graded groups we are led to believe that as 

 far as the probability of loss is concerned it is almost independent of 

 the change in holding time from a constant to an exponential form, 

 the advantage, if any, favoring the varying case. Likewise the manner 

 of "holding" delayed calls is of negligible importance as long as losses 

 of .01 or .02 are not greatly exceeded. 



The first part of the third assumption regarding the incoming calls 

 being distributed according to the Poisson Law was not checked in 

 these particular tests but a wide study of results under similar con- 

 ditions readily leads us to believe that calls originating from a large 

 number of independent sources will exhibit this form of frequency 

 distribution. 



The third assumption also necessitates a study of the variations 

 among the loads submitted to the subgroups of a graded multiple. 

 This brings us to the Second Division of the tests made in Chicago. 

 At the same time the first division was in progress on the busy hours 

 of each day for the cases of 36 trunks in service on the State to Dear- 

 born group and 52 trunks on the State to Wabash group, all of the 

 hours of the day from 9 till 5 were observed by one-half hour periods 

 (to minimize the error due to trends) for the number of call-seconds on 

 each trunk, the number of calls carried over the group and the number 

 lost. Thus an extended range of load conditions was obtained for 

 study. For estimating the effects of subgroup load variations with a 

 given total submitted load, these short pieces of data were combined 

 so that the half hours having an average load in trunk hours per hour 

 within approximately one unit of range were thrown together. The 

 various analyses were then made on these narrow total load classifi- 

 cations to discover, if possible, whether the observed subgroup variation 

 when used in the theoretical formula would cause the latter's "Full 

 Gain' probability of loss to approach more closely the observed losses. 



First, the proportion of lost calls was determined for each of these 

 approximate unit intervals of load. The results are shown graphically 

 in Figs. 18 and 19 for State to Dearborn and State to Wabash, re- 

 spectively. On these same figures have been superposed the theoretical 

 curves for the losses to be gotten using "Full," "Half" and "No 

 Gain" efficiencies in the graded formula described above. These 

 theoretical computations have assumed that equal average loads are 

 submitted to each subgroup at all times. The observed data indicate 

 that the correct descriptive curves lie in both cases somewhere between 

 those for the "Half" and "Full Gain" efficiency theories. This 



