364: THE BELL SYSTEM TECHXICAL J(jrRXAL, MARCH 1952 



is evident. Such a refinement would probably change the etiuation for 

 standard deviation only slightly from that derived for the intlependent 

 case; therefore independence will be assumed. The standard deviation 

 of the sum of two independent variables is the square root of the sum oi 

 the squares of the component standai'd deviations: 



0". = Val + al 0) 



rctnh! 



ta' 2ta (Q\ 



S'f ^ NT 



a . 

 Assuming -— is approximatelv iniity, that is, that carried load is approxi- 

 a 



mately eciual to source load, 



Vs = 100 a/^ rctnhf ^) (9) 



anT \2 



In the example given, 



K = 4 



There is, then, 90 per cent assurance that the source average is within 

 1.64 X 4.96 = 8.1 per cent of the observed average. Note that doubling 

 the switch count rate (which halves the switch count error) reduces the 

 total error only to 7.6 per cent (about 6.7 per cent improvement), while 

 doubling the number of hours of observations reduces the error to 5.9 

 per cent (about 30 per cent improvement). Plots of the coefficient of 

 variation of a one hour observation of a one erlang load versus scan rate 

 for various average holding times are given in Fig. 3 for a wide range of 

 holding times. The coefficient of variation of error in estimating other 

 loads may be found from Fig. 3 by dividing the unit load coefficient 

 by -s/aNT. In the example, the unit load coefficient is found, by entering 

 Fig. 3 with l = 3 minutes and rate of scan = c/T = 12/1 scan cycles per 

 hour, to be 35.0 per cent. Dividing by \/5-l-10 gives a coefficient of 

 variation of 4.96 per cent as before. It is evident from Fig. 3 that in- 

 creasing scan rates is not a universal way to improve the accuracy of 

 source load estimates. 



CHOICE OF SCAN RATES 



What then governs the choice of scan rate? Evidently increasing the 

 rate increases the accuracy of carried load estimates to any point de- 



