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THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



50 



60 



70 



80 



120 



Fig. 1 — Delay curves for random service. F{u) = conditional probability of 

 delay at least u; u = ct/h, c = no. trunks, h = av. holding time, a = call input 

 in time h, a = a/c. 



a, the delay curves for order of arrival and random service include the 

 same area, which is in fact equal to the mean delay (of calls delayed), 

 (1 — a)~ . Since F{0) = 1 for both, and the random service curve 

 decreases more slowly for large u, the curves must intersect at some 

 point, say for u = iio ;ior u < Uo , the o.a. curve must be above the ran- 



Table I — Delay-Time and Random Service 



Delay Times, w, for given F(u) and a and for order of arrival (o.a.) and ran- 

 dom service. 



