THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 491 



These four Ri levels would appear to cover the most used engineering 

 range. For example, if the traffic offered to the final route (including the 

 first routed traffic) has parameters A' = 12 and V ^ 20, reading on 

 Fig. 43 indicates that to give P = 0.03 "lost calls cleared" service to 

 the first routed traffic, C = 19 final route trunks should be provided. 

 (For random traffic (F' = A' = 12), 17.8 trunks would be required.) 



Other charts, of course, might be constructed from which Ri could be 

 read for specific values of A', V and C. They would become voluminous, 

 however, if a wide range of all three variables were required. 



8.2 Provision of Trunks Individual to First Routed Traffic to Equalize 

 Service 



If the difference between the service Ri given the first routed parcel of 

 traffic and the service given all of the other parcels, is material, it may be 

 desirable to take measures to diminish these inequities. This may readily 

 be accomplished by setting aside a number of the otherwise full access 

 final route trunks, for exclusive and first choice use of the first routed 

 traffic. High usage groups are now provided for all parcels of traffic. The 

 alternate route then services their combined overflow. The overall grade 

 of service given the ith. parcel of offered traffic in a single stage alter- 

 nate route system will then be approximately 



'* 

 Pi = Ei,Xi{ai)R2 = EiXiia.)^, (34) 



Thus the service will tend to be uniform among the offered parcels when 

 all send substantially identical proportions of their offered loads to the 

 alternate route. And the natural provision of "individual" trunks for the 

 exclusive use of the first routed traffic would be such that the same pro- 

 portion should overflow as occurs in the associated high \isage groups. 



This procedure cannot be followed literally since high usage group 

 size is fixed b}^ economic considerations rather than any predetermined 

 overflow value. The resultant overflow proportions will commonly vary 

 over a considerable range. In this circumstance it would appear reason- 

 able to estimate the objective overflow proportion to be used in estab- 

 lishing the individual group for the first routed traffic, as some weighted 

 average h of the overflow proportions of the several high usage groups. 

 Thus with weights g and overflow proportions h, 



h = ^'^' + ^'^' + • ' • (35) 



^1 + ^2+ • • • 



* Although not exact, this equation can probably be accepted for most engi- 

 neering purposes where high usage trunks are provided for each parcel of traffic. 



