STATISTICS FOR A SIMPLE TELEPHONE EXCHANGE MODEL 953 



1.0 



0.8 



0.6 



0.4 



0.2 



i-e-'" 



c = ~ — 



6 8 



r 



10 



12 



14 



Fig. 2 — C as a function of r. 



From Entry 3 of Table II it can be seen that K is distributed as 

 2u + V, where u and v follow independent Poisson distributions with the 

 respective parameters aT{l — C) and 2aTC. The probability that K = 

 n for an interval of equilibrium is 



r„ = exp {aTiC - 1)} £ (^ _ 2^)! Jl ' 



where the sum is over j's for which ^ 2j ^ n. 



The estimator di for a is equal to K/2T, and has mean and variance 

 given by 



E{di} = a, 

 var {d,} = ^ (2 - C). 



The distribution of di is given by 



pr{di ^ x} = X) ''" , 



the summation being over /( ^ 2Tx. 



From (9.2) one can obtain, by substitution of the stationary n distribu- 

 tion for [pn], and subsecjuent differentiation, the means, variances, 

 covariances, and correlation coefficients of the sufficient statistics, for 



