DELAYS ENCOUNTERED BY TOLL OPERATORS .S47 



The delay in securing a circuit varies directly with the holding time, 

 i.e., a call waiting for a circuit will be delayed twice as long if the group is 

 handling 10-minute calls as would be the case with 5-minute calls. This is 

 best illustrated by one call awaiting access to a single circuit group. The 

 new call may appear at any time during the progress of the existing call, 

 but the average delay for many such delayed calls will be one-half the hold- 

 ing time of the existing call. If the existing call uses the circuit for five 

 minutes, the new call will wait 5 ^ 2 = 2.5 minutes. If the existing call 

 uses the circuit for ten minutes, the new call will wait five minutes. It 

 should be noted that the average delay depends upon the average length of 

 time that the circuit is in use each time that it is used, in other words, the 

 holding time per circuit attempt. 



The Cleveland study did not go into this phase in detail, the statement 

 being made that the effect of holding time on speed of service "is slight." 

 This is so when considering the overall speed of ser\'ice, with which that 

 study was primarily concerned, because of the weight of operating and sub- 

 scriber time intervals. Reference to that study shows that the circuit 

 delay increased about in proportion to the holding time when a minimum oper- 

 ating and subscriber time inter\^al is subtracted from the overall speed, 

 as follows: 



Holding Time 

 5' 7.5' 10' 



Total Overall Speed 2.2 2.6 3.0 



Minimum Operating and Subscriber Time 



Interval 1-6 ^6 1L6 



' Average NC Delay-Trunk Speed 6 1.0 1.4 



COMBINATIOX OF MATHEMATICAL AND EMPIRICAL METHODS 



Because of the apparent close agreement between the Pollaczek delay 

 formula and two representative large samples of actual NC delay data taken 

 at different periods and under widely different conditions, 1930 and 1945, 

 the Pollaczek formula can be used for deriving expressions of the average 

 duration of NC with intertoU trunk operation without alternate routes. 

 The effect of alternate routes in reducing the duration of NC can be shown 

 with suthcient accuracy for practical needs from the empirical data. The 

 curves shown in Fig. 5 were constructed on this basis. For large groups 

 the formula has been extended in Fig. 6. 



It is advantageous to have available an acceptable mathematical formula 

 for expressing the relationship between the loads carried by the trunk groups 

 and the length of time that the average call will be delayed because of NC 

 conditions, i.e., the part played by trunk provision in the overall speed of 

 service. With such a formula results can be predicted for any given set of 



