544 



BELL SYSTEM TECHNICAL JOURNAL 



However, further reference to mathematical studies of telephone traffic 

 indicated that a delay theory based on constant holding times, first developed 



2.0 

 1.5 

 1.0 



0.5 

 



10 II 12 i; 



SIZE OF GROUP 



17 18 19 20 



Fig. 2 — Average circuit delay on all calls (with alternate routes where authorized). 

 Circuit delay = average speed on all calls minus average speed on calls which did not 

 encounter NC. Combined curves based on 16,745 calls. 



by Felix PoUaczek in Germany and amplified by C. D. Crommelin in 

 England, closely approximated the empirical data. This formula^ is: 



d-H 



{awY 





(aiv)"' 



In which 



d — average delay on all calls 



a = average simultaneous calls submitted to a group of c trunks (trunk 



hours) 

 c = number of trunks in group 



It may be quite reasonable that the Pollaczek constant holding time formula 

 should better represent toll delays than an exponential holding time formula 

 since the toll charge and perhaps other factors ordinarily cause these calls 



• C. D. Crommelin, "Delay Probability Formulae," F.O.E.E. Journal, Jan. 1934, p. 266 



