376 



THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1953 



1.0 



8| 



Q. 0.001 



0.0001 



2.5 



5.0 7.5 tO.O 12.5 15.0 17.5 20.0 22.5 



t/h = DELAY IN MULTIPLES OF AVERAGE HOLDING TIME 



25.0 



Fig. 14 — Delayed traffic served in random order, exponential holding times, 



Example No. 3 



Suppose in Example 2, the second requirement had been that no more 

 than one of 1000 customers should be required to wait over 3 minutes. 

 Would 8 operators then suffice? 



Solution. Reading on Fig. 14, with a = 0.78 and t/h = 180/100 = 1.8, 

 P{>t/h) = 0.027. Thus 27 in 1000 calls would be expected to experience 

 delays over 3 minutes, and therefore more than 8 operators will be 

 required. Consulting the c = 10 curves of Fig. 15, we find that with 

 a = 0.625, and t/h = 1.8, P(>3 minutes delay) = 0.0012 which closely 

 meets the one in a thousand requirement. Ten operators would then be 

 needed; and this would, of course, (from Fig. 19) reduce the average 



