KELIAHILITY OF H()IJ)1.\G TIME \rj-:ASrRr..\fK.\TS 399 



sense conclusions since, as previously sugj^esterl, when the observation ])eriocl 

 is increased by a factor k, 



a. The "sampling" error decreases as — , since we are looking at k 



\/k 



times as many calls, 



b. The error of measurement on the indix'idual calls decreases also as 



l/\/^, and for the same reason, and 



c. The "end effect" errors are unchanged in actual magnitude but are 



now prorated over k times as many calls; hence, the effect of this 

 element decreases as \/k. 

 'Jlie overall effect then as k increases is for <Toa to decrease faster than 

 Csampiing as we have just seen in the example. Thus not only is the sampling 

 error decreased by lengthening the observation period, but the overall 

 error decreases even faster. It is clear then that an observation period 

 as long as is consistent with a "controlled" universe of holding times is to be 

 preferred. 



Further important deductions may be drawn from a study of Fig. 19. 

 If we wish to minimize the effect of errors introduced by a use of the switch 

 count method we shall need to select our observation interval i so that it 

 will be relatively small compared with the average holding time. Appar- 

 ently we should do well to keep- ^ 1.5; the higher this ratio the better, 



although the improvement beyond, say, 2.0, is slow. Roughly, for commonly 

 observed local subscriber holding times if the holding time is at least twice 

 the observation interval the increase in error occasioned by the switch count 

 method over the stop watch method need not exceed 7 per cent. 



Fig. 19 has been constructed for use when / is estimated as /' from equa- 

 tion (35), 



-, ^ {s — S n, -\- sji ^ i 



II 



1 - e-1 



35) 



in which 5 is the sum of r -|- 1 switch counts (which includes counts at both 

 the extreme ends of the period), m is the count at the beginning, and w 

 the count at the end of the period. 



It will be of interest to estimate something of the enlarged error when /' 

 is found merely by taking 



/' = ^' - "'^' (41) 



n 



which entirely neglects the special information contained in the tirst and 



last switch counts. ( If only ''( = .- ) counts are made they should be at the 



