360 THE BELL SYSTEM TECHNICAL JOURXAL, MARCH 1952 



As shown ill the Appendix, this formula simplifies, when r < 2, to 



T = M / 1 



^ c'tV CWNTl ^^^ 



where c T = rate of scan in cycles per time unit. From equation (2) it 

 is apparent that if the scan interval is of the order of a holding time, the 

 error of an estimate of ti-aiSc carried is inversely proportional to the rate 

 of scan and inversely proportional to the sfjuare root of avei'age load, 

 holding time and hours of observation. For example, take the case where 

 switch counts are made dui'ing the busy hour, five minutes apart on a 

 trunk group carrying calls with an average holding time of 3 minutes 

 and an average load of 5 erlangs (180 CCS). What is the error in the 

 estimated load carried if the readings for ten days are averaged? (As- 

 sume conditions (a), (b) and (c) are met.) We have 



A^ = 10 observation periods 



T = 1 hour 



t = 1/20 hour 



a' = 5 erlangs 



c = 12 scans per observation period 



re — T t = 20 average holding times per observation period 



From equation (2) since T / = 20 and r = T ci = 1.7 



T' - iQQ,/ 1 -0150/ 



* ^ " 12^ r 6-O-10-M/20 " -^''/^ 



If, as proposed in the Appendix, it is assumed that the error has a 

 normal distribution, there is 90 per cent assurance that observed values 

 ■s\'ill fall within 1.64 F^ , or in the example within 3.52 per cent, of the true 

 average*. Note that this error limit would be halved if the rate of scan 

 were doubled or if four times as many hours of observation were taken. 



The coefficient of variation of the SAAdtch count error for constant values 

 of T/t as a function of r is plotted on Fig. 1 for one observation period 

 of a one erlang load. For loads other than one erlang the coefficient of 

 variation is found by dividing by \/a'N- Thus in the example we have, 

 using the dotted curve. 



* This assumes that a sufficient number of observations are taken so that a 

 priori information maj- be neglected in making an estimate of the universe. 



