FLUCTUATIONS OF TELEPHONE TRAFFIC 973 



as the spectral density function for the N(t) process with constant hold- 

 ing-time, h = ^{a 4- |(3). Similarly, from (15), we note that as the hold- 

 ing-times become singularly normal with mean, h, and variance zero, 

 the covariance function becomes 



f = a{h - t) ^ t ^ h 

 R(r) = \ 



[= T ^ h. 



We can express (16) as 



,2 



/■j-\ .-. j2 /sin -irfh , 



and note that this is exactly like the power spectrum of a random tele- 

 graph wave constructed by choosing values + -s/ah, — -y/ah with equal 

 probability and independently for each interval of length, h. (Cf. Rice,* 

 page 327.) 



REFERENCES 



1. J. L. Doob, Stochastic Processes, John Wiley and Sons, New York, 1953. 



2. C. Palm, Intensitatsschwankungen im Fernsprechverkehr, Ericsson Technics, 



44, pp. 1-189, 1943. 



3. F. W. Rabe, Variations of Telephone Traffic, Elec. Commun., 26, pp. 243-248, 



1949. 



4. S. O. Rice, Mathematical Analysis of Random Noise, B. S.T.J. , 23, pp. 282-332, 



1944, and 24, pp. 46-156, 1945. 



5. J. Riordan, Telephone Traffic Time Averages, B.S.T.J., 30, i)p. 1129-1144, 1951. 



