I 



THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 501 



the number of trunks which should be installed on the Bloomsburg- 

 Harrisburg route, so that the last trunk will carry approximately 18 

 CCS (0.50 erlang). Following this determination, (a) the number of final 

 trunks from Bloomsburg to Scranton is desired so that the poorest 

 service given to any of the original parcels of traffic will be no more than 

 3 calls in 100 meeting NC. Also (6) the modified Bloomsburg-Scranton 

 trunk arrangement is to be determined when a high usage group is pro- 

 vided for the first routed traffic. 



Solution (a): First Routed Traffic Offered Directly to Final Group 



The offered loads in CCS to each distant point are shown in column 

 (2) of Table XVII; the corresponding erlang values are in column (3). 

 Consulting Figs. 12 and 13, the direct group overflow load parameters, 

 average and variance, are read and entered in columns (5) and (6) re- 

 spectively for the four groups overflowing to Harrisburg, and in columns 

 (7) and (8) for the four groups directly overflowing to Scranton. The 

 variance for the direct Bloomsburg-Harrisburg traffic equals its average ; 

 likewise for the direct Bloomsburg-Scranton traffic. They are so entered 

 in the table. The parameters of the total load on the Harrisburg group 

 are found by totalhng, giving A' = 11.19, and V = 19.90. 



The required size Ci of the Harrisburg group is now determined by 

 the Equivalent Random theory. Entering Fig. 25 with A' and V just 

 determined, the ER values of trunks and load found are Si = 13.55, 

 and Ai = 23.75. Ci is to be selected so that on a straight group of Si + 

 Ci trunks with offered load A, the last trunk will carry 0.50 erlang. 

 Reading from Fig. 40, the load carried by the 26th trunk approximates 

 this figure. Hence Ci = 26 — *Si = 12.45 trunks; or choose 12 trunks. 



The overflow load's mean and variance from the Harrisburg group 

 v/ith 12 trunks, is now read from Figs. 12 and 13, entering with load 

 Ai = 23.75 and Ci -\- Si = 25.55 trunks. The overflow values (a' = 

 2.50 and v' = 7.50) are entered in columns (7) and (8) of the table. 

 The total offered load to Scranton is now obtained by totalling columns 

 (7) and (8), giving A" = 16.27 and V" = 25.60. 



We desire now to know the number of trunks C2 for the Scranton 

 group which will provide NC 3 per cent of the time to the poorest service 

 parcel of traffic, i.e., the first routed Bloomsburg-Scranton parcel. The 

 Ri = 0.03 and R2 = 0.03 solutions are available, the former of course 

 being more closely applicable. A check reference to Fig. 50 shows a 

 difference of approximately 4 per cent in trunk provision would result 

 from the two methods. Entering Figs. 43 and 47 with A" = 16.27 and 



