380 



THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1953 



0.01 

 8 



0.001 



0.0001 



2.50 



Fig. 

 = 100 



0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 

 t/h = DELAY IN MULTIPLES OF AVERAGE HOLDING TIME 



18 — Delayed traffic served in random order, exponential holding times, 



minute, what per cent of the cars will be delayed more than 5 minutes? 

 What will be the average delay for all cars? 



Solution. Assume there is no traffic supervision and cars converge on 

 the gate from many directions. Service in random order (or worse) 

 among those delayed might then be approximated. Also the distribution 

 of times for calculating and collecting the charge might be roughly 

 exponential. We have then, 



c = 2 paths 



a = (5.4)(20)/(60)(2) = 0.90 



t/h = 



5(60) 

 20 



= 15 



Enter Fig. 9 at t/h = 15, read to the a = 0.90 curve, opposite which find 

 P = 0.069. Hence 7 per cent of the cars would be expected to have to 

 wait 5 minutes or more. To obtain the average delay for all cars, enter 



