376 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1952 



and for r < 2 



Therefore 



3 45 



rctnh(0-2 + J 



The error in carried load may be considered as the sum of a large num- 

 ber of independent errors. Its distribution may, therefore, be expected 

 to approach the normal distribution. Comparison of the third and fourth 

 moments of the normal distribution with those of the error distribution 

 (which may be obtained from equation (13)) show good agreement for 

 values of a' greater than 1. 



DERIVATION OF SWITCH COUNT ERROR IN ESTIMATING CARRIED LOAD WITH 

 CONSTANT HOLDING TIMES 



Wilkinson has sho^\^l^ that, for constant holding time, swdtch count 

 error in measuring the holding time of one call has an average 



X = 



and standard deviation 



<Tx = yj — X\X-i 



where T » I 

 T»i 



Xi = negative error 

 X2 = positive error 

 Divide the problem into two parts: 

 1. For r > 1 

 Xi = —t 

 X2 = i — t 

 <xx = Vti - P = iVr - 1 (17) 



