THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 431 



carried and " % NC existing." C. J. Truitt of the A.T. & T. Co. studied 

 i a number of operator-dialed T-engineered groups at Newark, New Jersey, 

 in 1954 with a traffic usage recorder (TUR) and group-busy timers, and 

 found the relationship of equation (1) still good. (This analysis has not 

 been published.) 



A study by Dr. L. Kosten has provided an estimate of the probability 

 that when an NC condition has been found, it will also appear at a time 

 T later." When this modification is made, the expected load-versus-NC 

 relationship is shown by Curve E on Fig. 5. (The re-trial time here was 

 taken as the operators' nominal 30 seconds; with 150-second circuit-use 

 time the return is 0.2 holding time.) The observed NC's are seen to lie 

 slightly above the E-curve. This could be explained either on the basis 

 that Kosten's analysis is a lower limit, or that the operators did not 

 strictly observe the 30-second return schedule, or, more probably, a 

 combination of both. 



3. CUSTOMERS DIALING ON GROUPS WITH CONSIDERABLE DELAY 



It is not to be expected that customers could generally be persuaded to 

 wait a designated constant or minimum re-trial time on their calls which 

 meet the NC condition. Little actual experience has been accumulated 

 on customers dialing long distance calls on high-delay circuits. However, 

 it is plausible that they would follow the re-trial time distributions of 

 customers making local calls, who encounter paths-busy or line-busy 

 signals (between which they apparently do not usually distinguish). 

 Some information on re-trial times was assembled in 1944 by C. Clos by 

 observing the action of customers who received the busy signal on 1,100 

 local calls in the City of New York. As seen in Fig. 6, the return times, 

 after meeting "busy," exhibit a marked tendency toward the exponential 

 distribution, after allowance for a minimum interval required for re- 

 dialing. 



An exponential distribution with average of 250 seconds has been 

 I fitted by eye on Fig. 6, to the earlier ■ — and more critical — customer re- 

 turn times. This may seem an unexpectedly long wait in the light of indi- 

 vidual experience; however it is probably a fair estimate, especially 

 since, following the collection of the above data, it has become common 

 practice for American operating companies in their instructional lit- 

 erature to advise customers receiving the busy signal to "hang up, wait 

 a few minutes, and try again." 



The mathematical representation of the situation assuming exponen- 

 I tial return times is easily formulated. Let there be .r actual trunks, and 



