THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 503 



I Y" = 25.60, we obtain the trunk requirements: 



! Rx Method 23.8 trunks 



i?2 Method 24.8 trunks 



Thus the more precise method of sokition here yields a reduction of 1 .0 

 in 25 trunks, a saving of 4 per cent, as had been predicted. 



The above calculation is on a Lost Calls Cleared basis. Since the over- 

 flow direct traffic calls will return to this group to obtain service, to as- 

 sure their receiving no more than 3 per cent 'NC, the provision of the 

 final route would theoretically need to be slightly more liberal. An esti- 

 mate of the allowance required here may be made by adding the ex- 

 pected erlangs loss A for the direct traffic (most of the final route over- 

 flow calls which come from high usage routes will be carried by their 

 respective groups on the next retrial) to both the A" and Y" values 

 previously obtained, and recalculating the trunks required from that 

 point onward. (In fact this could have been included in the initial com- 

 putation.) Thus: 



A = 0.03 X 10.14 = 0.30 erlang 

 A'" = 16.27 + 0.30 = 16.57 erlangs 

 V" = 25.60 + 0.30 = 25.90 erlangs 



Again consulting Figs. 43 and 47 gives the corresponding final trunk 

 values 



Ri Method 24.1 trunks 



R2 Method 25.1 trunks 



Of the above four figures for the number of trunks in the Scranton 

 route, the i?i-Method with retrials, i.e., 24.1 trunks, would appear to 

 give the best estimate of the required trunks to give 0.03 service to the 

 poorest service parcel. 



Solution (h) : With High Usage Group Provided for First Routed Traffic 



Following the procedure outlined in Section 8.2, we obtain an average 

 of the proportions overflowing to the final route for all offered load par- 

 cels. The individual parcel overflow proportion estimates are shown in 

 the last column of Table XVII; their unweighted average is 0.112. With 

 a first routed offer to Scranton of 10.14 erlangs, a provision of 12 high 

 usage trunks will result in an overflow of a = 1.26 erlangs, or a propor- 

 tion, of 0.125 which is the value most closely attainable to the objective 

 0.112. With 12 trunks the overflow variance is found to be 2.80. 



