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BELL SYSTEM TECHNICAL JOURNAL 



Newark group). Their true average holding time was 131.45 seconds. 

 The mean error was found to be + 1 .84 seconds and the standard deviation 

 25.55 seconds. The corresponding theoretical distribution is found to have 

 a standard deviation of 24.56 seconds with a mean, of course, of zero. The 

 theoretical distribution is superposed on the data of Fig. 15 and is seen to 

 give quite a good fit . 



It is interesting that the theoretical average error for each of these three 

 widely dissimilar holding time distributions should be zero, while their 

 standard deviations and analytical forms assume quite different characteris- 



3 0.08 



o 

 o 



O 0.06 



>- 



5 0.04 

 < 



in 

 O 

 tr 

 Q- 0.02 



THEORY 



I^ 



-1.0 -0.8 -0.6 -0.4 -0.2 0.2 0.4 0.6 0.8 1.0 



ERROR IN MULTIPLES OF INTERVAL I 



Fig. 15 — Distribution of call measurement errors for exponential holding times 



tics.^ A comparison of the a's obtained from equations (19), (23) and (27) 

 for a typical choice of values, / = 145 seconds, i = 60 seconds, gives 



(7x constant h.t. = 29.58 seconds, 



(Xx "Equally likely" h.t. = 24.48 seconds, 



ai Exponential h.t. — 24.03 seconds. 



The cTj constant h.t. is largely a function of whether /" is closely a whole 

 multiple of i; comparing the values for the other two (Ti's indicates it is 

 slightly advantageous that most of the variable holding time calls to be 

 switch counted in practice are of a roughly exponential form. 



The Total Error on n Calls 



We shall now attempt to combine the errors from the three sources just 



discussed and formulate some general conclusions for making the most 



^ It may readily be shown that the average error will be zero for any assumed holding 

 time distribution, by noting that each length of call therein may momentarily be segre- 

 gated and considered under paragraph "a" as a constant holding time. 



