118 THE BELL SYSTEM TECHNICAL JOURNAL, JANUARY 1953 



Table V — Approximations to Delay Function F{u) for Random 



Service 



Two Exponentials 



Three Exponentials 



7. numerical results 



Table V gives both two-exponential and three-exponential 4 decimal 

 approximations to the delay function F(u) for 



and for 



a = 0.1(0.1)0.9(0.1 to 0.9 in steps of 0.1) 



u{l - a) = 1(1)2(2)14, 



in the same abbreviated notation.* The variable v = u(l — a) is in- 

 troduced to reduce the spread of these tables. It will be noticed that, 

 as expected, the two orders of approximation agree closely for small 

 values of a; indeed, only for the three largest values of a are the dif- 

 ferences appreciable from the engineering standpoint. 



♦ The results for two exponentials, some of those for three-exponentials, and 

 all special results given below, have been obtained by Miss Marian Darville, 

 whom I also thank for her careful drawing of the curves. The entire three-exponen- 

 tial table has been computed independently by Miss Lennon. 



