504 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1956 



Replacing 10.14 in columns 7 and 8 of Table XVII with 1.26 and 2.80, 

 respectively, gives new estimates characterizing the offer to the final 

 route. A" = 7.39 and V" — 18.26. We now proceed to insure that the 

 poorest service parcel obtains 0.03 service. This occurs on the Phila- 

 delphia and Harrisburg groups, which overflow to the final group ap- 

 proximately 0.224 of their original offered loads. The final group must 

 then, according to equation (34) be engineered for 



R2 = 0.03/0.224 = 0.134 service. 



This value lies above the highest R2 engineering chart (Fig. 49, R2 = 

 0.10), so an ER calculation is indicated. 



The Equivalent Random average is 28.6 erlangs, and S = 23.5 

 trunks. We determine the total trunks S -\- R which, with 28.6 erlangs 

 offered, will overflow 0.134(7.39) = 0.99 erlang. From Fig. 12.2, 35.6 

 trunks are required. Then the final route provision should be C = 35.6 — 

 23.5 = 12.1 trunks; and a total of 12 + 12.1 or 24.1 Scranton trunks 

 is indicated. 



Simplified Alternative Solution: In Section 8.2 a simplified approxi- 

 mate procedure was described using a modified probability P' for the 

 average overall service for all parcels of traffic, instead of P for the poor- 

 est service parcel. Suppose P' = 0.01 is chosen as being acceptable. 

 Then 



P' 01 



«' = T = am = oo^" 



Interpolating between the R2 = 0.05 and 0.10 curves (Figs. 48 and 49) 

 gives with A" = 7.39 and F" = 18.26, C = 13.4, the number of final 

 trunks required. Again the same result could have been obtained by 

 making the suitable ER computation. It may be noted that if P' had 

 been chosen as 0.015 (one-half of P), R2 would have become 0.134, 

 exactly the same value found in the poorest-service-parcel method. The 

 final trunk provision, of course, would have again l)een 12.1 trunks. 



Disscussion 



In the first solution above, 24.1 full access final trunks from Blooms- 

 burg to Scranton were refiuired. The service on the first routed traffic 

 was 0.03; however, the service enjoyed by the offered traffic as a whole 

 was markedly better than 0.03. The corresponding ER calculation 

 shows (.4 = 28.3, .S -\- C = 12.3 + 24.1) a total overflow of a" = 0.72 

 erlangs, or an overall service of 0.72/91.21 = 0.008. 



