460 



THE BELL SYSTEM TECHNICAL JOUENAL, MARCH 1956 



parities in the higher semi-invariants, the agreement for practical traffic 

 purposes is very good indeed. 



Numerous throwdown checks confirm that the negative binomial em- 

 ploying the calculated sum-overflow mean and variance has a wide range 

 over which the fit is quite satisfactory for traffic description purposes. 

 Fig. 20 shows three such trunking arrangements selected from a con- 

 siderable number which have been studied by the simulation method. 

 Approximate!}^ 5,000, 3,500, and 580 calls were run through in the three 

 examples, respective!}' . Tlie overflow parameters obtained !)y experiment 

 are seen to agree reasonably well with the theoretical ones from (28) 

 and (29) when the numbers of calls processed is considered. 



On Fig. 21 are sliown, for the first arrangement of Fig. 20, distributions 

 of simultaneous offered calls in each subgroup of trunks compared with 

 the corresponding Poisson; the agreement is satisfactory as was to be 

 expected. The sum distribution of the overflows from the eight subgroups 

 is given at the foot of the figure. The superposed Poisson, of course, is a 

 poor fit; the negative binomial, on the other hand, appears quite accept- 

 able as a fitting curve. 



1.0 

 0.8 

 0.6 



P 2n 



1 TRUNK- a = \.22 



3 TRUNKS- a = 2.24 



0.4 - 



0.2 ■ 



1.0 



0.8 - 



0.6 

 0.4 

 0.2 



234501 234 



n=NUMBER OF SIMULTANEOUS CALLS 





P^n 



9 TRUNKS- a = 6.21 



THEORY OBSD 

 ( -) ( ) 



AVG 0.52 0.46 



VAR 1.00 1.48 



. RANDOM TRAFFIC 

 a = 0.52 



4 68 10 024 68 



n=NUMBER OF SIMULTANEOUS CALLS 



10 



12 



Fifj;. 18 — Ovorflow (li.-<t ril)utioiis from diroct interoffice trunk groups; negative 

 binomial theory versus thrgwclowji observations. 



