DELAYS E.XCOUNTERED BY TOLL OPERATORS 



545 



to exhibit considerably less percentage deviation from their average than 

 is found in the exponential distribution. 



In order to compare the empirical data with the PoUaczek formula it was 

 necessar}^ to assume a holding time per attempt since the formula expresses 

 the delays in terms of the average interval of use whenever the circuit is in 

 use. The average holding time as reported by the companies for the groups 

 included in the study was 8.3 minutes per message. Recent data show 1.42 

 attempts per call disposed of. Relating this figure to the 8.3 minutes re- 

 sults in an average holding time per circuit use of 5.85 minutes. Six 



7 8 9 



SIZE OF GROUP 



Fig. 3 — Average circuit delay on all calls. 

 Comparison of empirical data (with alternate routes) and Pollaczek formula (no alter- 

 nate routes) u?ing a 6 minute holding time. 



minutes is therefore well within the limits of accuracy required for this 

 purpose. 



Curves were prepared from the Pollaczek formula for various levels of 

 usage at a 6-minute holding time per attempt. The corresponding curves 

 derived from the empirical data were then superimposed for comparative 

 purposes as shown in Fig. 3. It will be seen that the shape and levels of the 

 curv-es are very similar except for the smaller groups on which the effect of 

 alternate routes tends to reduce the average length of delay. 



As a further check on the validity of the Pollaczek formula, the delay 

 data from the Cleveland (1929-1930) study were expressed in terms of hold- 



