DELAYS ENCOUNTERED BY TOLL OPERATORS 553 



tables should be used. These latter tables, constructed from the Poisson 

 formula, express a ser\ace relationship in terms of the percentage of calls 

 encountering NC rather than the average duration of NC. When trunks 

 are provided on a basis as liberal as that implied by the interlocal tables 

 the frequency of NC is deemed to be the more important service consider- 

 ation because the duration of NC is so short as to be of lesser consequence. 



Since the Pollaczek formula expresses the delay as a percentage of the 

 holding time per circuit attempt but the intertoU trunk engineer is accustomed 

 to dealing with holding times per message the delays indicated for each of 

 Tables T-1 to T-5 have been expressed in the latter terms, using a 1.5 ratio 

 of attempts per message. This is consistent with previous computations. 

 With Table T-4 and a five-minute message holding time, for example, we 

 have: 



5-minute HT per message -^ 1.5 = 3.33 minutes HT per attempt 

 3.33 minutes x .30 delay = 1.0 minute delay 

 This one minute delay shown in the heading of Table T-4 is, therefore, 

 actually the delay per attempt when the holdmg time per message is five 

 minutes. The delay per attempt is the important criterion because the 

 "speed of toll service" as quoted from service observations is generally the 

 speed of the first attempt and the two are, therefore, comparable.^ 



As the usage approaches 100 per cent, there may be an indeterminate 

 backed-up potential demand and the normal relationship between service 

 and loading no longer holds true. From other data assembled for this 

 purpose, it appears that about 96-97 per cent, represent the practical upper 

 limit of usage, beyond which trunk speeds can not be accurately predicted. 

 For practical reasons, therefore, group capacities have not been computed 

 for percentages of use higher than 97 even though, from a theoretical view- 

 point, the curves derived from the Pollaczek formula would permit extending 

 the usage virtually to 100 per cent. This would also apply to Tables T-1 

 and T-2 if they were extended above 75 trunks. 



Relation of Circuit Delays ix Busy Hour to Total Day 



Up to this point the trunk speed of service has been discussed in terms of 

 the busiest hour. However, the overall speed of service is generally quoted 

 in terms of the total day. Therefore, one additional step is necessary, 

 namely to determine the relationshii) of the trunk speed in the busy hour to 

 that of the total day. 



2 There is one exception to the statement that the "speed of toll service" is the speed 

 on the first attempt. That is the case of a l)uilt-ui) connection where an NC condition 

 is encountered at an intermediate office which persists so long that the first circuit is 

 released. When the connection is established it is at least the second attempt. The full 

 time interval during which the ticket is held awaiting completion is included in the speed 

 quoted on that call. Similar intervals were also included in the empirical data for this 

 study and the results arc, therefore, comparable in this case also. 



