382 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1953 



Fig. 19 with the abscissa of 2 paths, read to the a = 0.90 curve and find 

 the average delay = 4.25 average holding times = 85 seconds. Or, 

 one may obtain the same answer by substituting in equation (2), 



t = P{>0)h/{c - a) = (0.85)(20)/(2 - 1.80) = 85 seconds. 



Example No. 6 



Suppose in Example 5, an efficient corps of police had been directing 

 traffic toward the exit so that good queueing was maintained. What per 

 cent of the cars would then be delayed more than 5 minutes? 



Solution. We may now refer to other published delay curves for queued 

 operation*, or, more generally, calculate the well known equation (1). 

 In the present case we can read the answer from the ''queued" curve of 

 Fig. 1 as 4.2 per cent. Thus serving customers in the order of arrival 

 nearly halves the occurrence of very long delays. (Note that the average 

 delay for all cars remains unchanged at 85 seconds.) If a partial queueing 

 were maintained the improvement would be intermediate, perhaps com- 

 parable with one of the "limited queueing" distributions shown on 

 Fig. 7. 



The author is indebted to Miss C. A. Lennon for constructing the 

 working delay curves, and to Misses C. J. Durnan and J. C. McNulta 

 for performing the throwdown checks. 



Appendix 



calculation of delay values not found on the working curves 

 of figs. 8-18, for delayed exponential calls served in random 



ORDER 



A master chart. Fig. 20, reproduced from Riordanf, gives in condensed 

 form the proportion F{u) of delayed calls delayed longer than u, where 

 the delay is now expressed in multiples of the h/c (u = ct/h) , and 



c = number of paths (trunks, operators, etc.) provided 



h = average holding time 



t = delay time 



To obtain the probability P{>t/h) of any call being delayed longer than 



*E. C. Molina, Ibid, 

 t Loc. cit. 



