THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 461 



Table I — Comparison of Parameters of a Fitting 



Negative Binomial to the Convolution of 



Three Negative Binomials 



Semi-Invariants A, Skewness \/pi , and Kurtosis ^2 , of Sum Distributions 



Fig. 22 shows the corresponding comparisons of the overflow loads in 

 the other two trunk arrangements of Fig. 20. Again good agreement 

 with the negative binomial is seen. 



7.3. Equivalent Random Theory for Prediction of Amount of Traffic Over- 

 flowing a Single Stage Alternate Route, and Its Character, with Lost 

 Calls Cleared 



As discussed in Section 7.2, when random traffic is offered to a limited 

 number of trunks x, the overflow traffic is well described (at least for 

 traffic engineering purposes) by the two parameters, mean a and variance 

 V. The result can readily be applied to a group divided (in one's mind) 

 two or more times as in Fig. 23. 



Employing the a and v curves of Figs. 12 and 13, and the appropriate 

 numbers of trunks a;i , Xi + 0:2 , and Xi + X2 + x^ , the pairs of descrip- 

 tive parameters, ai , vi , ao , vo and a-s , v-a can be read at once. It is clear 

 then that if at some point in a straight multiple a traffic with parameters 

 ai , Vi is seen, and it is offered to .r2 paths, the overflow therefrom will 

 have the characteristics 012 , vo . To estimate the particular values of a-y 

 and v-i , one would first determine the values of the equivalent random 



