DELAYS ENCOUNTERED BY TOLL OPERATORS 557 



The figure .1864 deri\-ed above represents the average delay expressed as a 

 per cent, of the holding time per circuit use (attempt). The last step, 

 therefore, is to relate this figure to the message holding times contemplated 

 in Table T-5, as follows; 



Holding Time Per Ratio of Attempts 

 Message Per Message 



Holding Time Per 

 Attempt 



% of H. T. Delayed 



Average Delay 



5 min. 



8 min. 



11 min. 



1 50 = 3.33 X .1864 = .62 min. 



1.50 = 5.33 X .1864 = 1.00 min. 



1.50 = 7.33 X .1864 = 1.37 min. 



The results of similar calculations are summarized in Fig. 11. 



As pointed out previously, actual delays experienced will deviate from 

 those shown in Fig. 11 to the extent that the actual hourly distribution 

 varies from that which has been used. If a particular group has a higher 

 per cent busy hour the total day delays should be less than indicated. 

 Conversely, if the group has a lower per cent busy hour the delays should be 

 greater. However, the variations in distribution which are most likely to be 

 encountered in practice will not have any marked effect on the total day 

 delays except possibly for groups of about five trunks or less which are loaded 

 as heavily as indicated in Tables T-4 and T-5. 



Per Cent. NC Encountered 



The per cent, of calls delayed by NX as noted by the operators on the 

 tickets analyzed for this study was plotted for each level of usage in steps of 

 10% as shown in Fig. 12, using a 3 point moving average. Each of these 

 cur\'es w^as then redrawn in relation to the others and the combined results 

 are in Fig. 13. The results are very similar to those obtained in the Cleve- 

 land study of 1929-30, as shown in the same figure. 



It should be noted that there is a difference between the per cent, calls 

 encountering NC and the per cent. NC existing. In the present study no 

 data were obtained to indicate NC existing. However, the Cleveland study 

 included such data which showed that the NC existing follows the Erlang 

 "B" formula (Fig. 14) in this respect. The individual points in Fig. 14 

 were derived by selecting from the Erlang "B" table of overflows the point 

 at which the call-seconds carried (offered minus overflow) gave the desired 

 level of usage. 



The difference between NC existing and NC encountered may be due to 

 several factors, some of which are suggested below: 



1. Effect of alternate routes. 



