THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 473 



Table VI — High Usage Groups and Typical System 



Busy Hour Loads 



compare theory with the observed overflow from the final route, esti- 

 mates of the offered load A' and its ^-ariance V are required. In the 

 present case, the total load offered to the final route in each hour was 

 estimated as 



A' = Average of Offered Load 



Peg Count of Calls Offered 



to Pittsburgh Group 



(Peg Count of Offered Calls) 

 — (Peg Count of Overflow Calls) 



X Average Load Carried 



by Pittsburgh Group 



The variance V of the total load offered to the final route was estimated 

 for each hour as 



V' = Variance of Offered Load 



7 7 



= A' — 2 «i + 2 Vi 



i=l 



where «» and Vi are, respectively, the average and variance of the load 

 overflowing from the tth high usage group. (The expression. A' — 



7 



^ «i , is an estimate of the average — and, therefore of the variance 

 1=1 



— of the first-routed traffic offered directly to the final route. Thus the 

 total variance, V, is taken as the sum of the direct and overflow com- 

 ponents.) Using A', V and the actual number, C, of final route trunks in 

 service, the proportion of offered calls expected to overfloAv was calcu- 

 lated for the traffic and trunk conditions seen for 25 system busy hours 

 from February 17 to April 1, 1955 on the Pittsburgh route. The results 

 are displayed on Fig. 31, where certain traffic data on each hour are 

 given in the lower part of the figure. The hours are ordered — for con- 

 venience in plotting and viewing — by ascending proportions of calls 

 overflowing the group; observed results are shown by the double line 



