THEORIES FOR TOLL TRAFFIC ENGINEERING IN THE U. S. A. 457 



the agreement, of course, is poor since the non-randomness of the over- 

 flow here is marked, having an average of 1.88 and a variance of 3.84. 



Comparison of Negative Binomial with Overflow Distributions Observed 

 hi/ llirowdoivns and on Actual Trunk Groups 



Fig. 18 shows a comparison of the negative binomial with the over- 

 How distributions from four direct groups as seen in throwdown studies, 

 'ilie agreement over the range of group sizes from one to fifteen trunks is 

 seen to be excellent. The assumption of randomness (Poisson) as shown 

 by the dot values is clearly unsatisfactory for overflows beyond more 

 than two or three trunks. 



A number of switch counts made on the final group of an operating 

 toll alternate routing system at Newark, New Jersey, during periods 

 when few calls were lost, have also shown good agreement with the neg- 

 ative binomial distribution. 



7.2.2. A Probability Distribution for Combined Overflow Traffic Loads 



It has been shown in Section 7.2.1 that, at least for load ranges of wide 

 interest, the negative binomial with but two parameters, chosen to agree 



Fx(§n) 



0.01 



0.001 



TION 



OMIAL 

 BUTION 



I 2 3 4 5 6 7 8 9 10 11 12 13 14 15 

 n= NUMBER OF SIMULTANEOUS CALLS 



Fig. 15 — Probability distributions of overflow traffic with 5 erlangs offered to 

 1, 2, 5, and 10 trunivs, when all trunks are busy; fitted by negative binomial. 



