THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 495 



flowed from high usage groups. A comparison of Figs. 42 to 45, (which 

 indicate trunk provision for meeting a first routed traffic criterion Ri) 

 with Figs. 46 to 49 (which indicate trunk provision for meeting a com- 

 posite-load-offered-to-the-final-route criterion R2) gives a means for de- 

 ciding under what conditions in practice it is important to distinguish 

 between the two criteria. Fig. 50 shows the borders of areas, defined in 

 terms of A' and V, the characterizing parameters of the total load 

 offered to the final route, where a 2 and 5 per cent overprovision of final 

 trunks would occur using R2 for Ri as the loss measure for first routed 

 traffic. Thus in the alternate route examples displayed in Table XV, 

 where x = S, g = 2 to 10, A' = 4.0 and V varies from 5.80 to 5.45, 

 Fig. 50 shows that by failing to allow for the preferred position of the 2 

 erlang first routed parcel, we should at R = 0.02 engineered loss, provide 

 a little over 5 per cent more final trunks than necessary. (Actually 10.2 

 and 9.9 versus 9.6 and 9.4 trunks f or gr = 2 and 10; respectively.) 



The curves of Fig. 50 for final route loads larger than a few erlangs, 

 are almost straight lines. At an objective engineering base of i? = 0.03, 

 for example, the 2 and 5 per cent trunk overprovision areas through 

 using i?2 instead of Ri are outlined closely by: 



2 per cent overprovision occurs at Fy(A' — 1) = 1.4 

 5 per cent overprovision occurs at V'/(A' — 1) = 1.8. 



Thus in the range of loads covered by Fig. 50, one might conclude that 

 useful and determinable savings in final trunks can be achieved by use 

 of the specialized /?i-curves instead of the more general 7?2-curves, when 

 the ratio V'/(A' — 1) exceeds some figure in the 1.4 to 1.8 range, say 1.6. 

 (In the examples just cited the V'/{A' — 1) ratio is approximately 1.9.) 



8.4. Character of Traffic Carried on Non-Final Routes 



Telephone traffic which is carried by a non-final route will ordinarily 

 be subjected to a peak clipping process which will depress the variance 

 of the carried portion below that of the offered load. If this traffic ter- 

 minates at the distant end of the route, its character, while conceivably 

 affecting the toll and local switching trains in that office, will not require 

 further consideration for intertoll trunk engineering. If, however, some 

 or all of the route's load is to be carried on toll facilities to a more distant 

 point (the common situation), the character of such parcels of traffic will 

 l)e of interest in providing suitable subsequent paths. For this purpose 

 it will be desirable to have etimates of the mean and variance of these 

 carried parcels. 



When a random traffic of "a" erlangs is offered to a group of "c" paths 



