THE INTERCONNECTION OF TELEPHONE SYSTEMS SSI 



The corresponding subgroup variation obtaining throughout the 

 Second Division of the tests was then determined and appears in the 

 Figs. 18 and 19 as an auxihary broken line at the bottom of the charts. 

 Strangely enough, in both tests, the subgroup variation maintains an 

 almost constant magnitude whatever the load. In fact, as mentioned 

 in a later paragraph this criterion of variation seems rather to depend 

 in practice upon the particular trunking arrangement being con- 

 sidered. Entering Fig. 20 with the observed average subgroup vari- 

 ation of .3542 for the 36 trunks in the State to Dearborn group, we 

 should expect the proportion of calls lost at a total load of 18.00 sub- 

 mitted to be about .000289. Likewise, we should find that this same 

 variation occurring in total loads of 20.5 and 24.0 gives us losses of 

 .00278 and .0239, respectively. The dotted curve on Fig. 18 is drawn 

 through these three points and represents the theoretical probability- 

 load curve for this arrangement of trunks when the index of variation 

 in loads from subgroup to subgroup is equal to the average observed. 

 This schedule falls slightly above the observed losses over a consider- 

 able portion of the important range of loads although at the lower 

 losses it seems quite likely to coincide fairly well with a curve drawn 

 by eye through the data represented by the irregular line. 



Similarly, in the case of the 52 trunks between State and Wabash, 

 we may construct a schedule of losses based on a subgroup load vari- 

 ation having a measure equal to the observed value, .8271. Such a 

 curve is shown dotted in Fig. 19 and as before indicates that upon 

 taking into approximate consideration the variation in loads being 

 submitted to the subgroups the resultant discrepancy between a curve 

 fitted to the observed losses and the "Full Gain" theoretical grades 

 of service is, in the main, slightly more than accounted for. In Figs. 

 20 and 21 the observed points fall one above and one below the 

 theoretical schedules. These deviations do not appear to be of any 

 significance except to illustrate the many chance elements which enter 

 into telephone traffic problems. 



A priori one might expect also that there would be some correlation 

 between the proportion of lost calls and the subgroup variation for 

 half hours in any given unit interval of total load. The number of 

 calls lost in these tests, however, is so small that plotting by half hours 

 the large natural fluctuation due to other causes seems to completely 

 mask any such small eft'ects which might be predicted. 



To further study the manner and amount of this subgroup variation 

 in carried loads, similar calculations were performed by half-hour units 

 on the First Division of the tests (busy hours only) wherein the restric- 

 tion of unit range of average was not present. The results shown by 



