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BELL SYSTEM TECHNICAL JOURNAL 



b. Errors at the End of the Observation Period 



If switch counts have been made at regular intervals i so that the r + 1st 

 count occurs at the exact end of the period for which the number of originat- 

 ing calls has been registered, then the situation closely resembles that at 

 the start of the period. The r + 1st observation tells us immediately how 

 many calls are continuing into the next hour. A particular one of these 

 calls may extend to the areas to i, i to 2i, 2i to 3i, etc., measured beyond 

 the end of the period as in Fig. 8. A call ending in the interval 2/ to 3i, 



LAST*! 

 SWITCH 

 COUNT 



I 2L 31 



TIME FROM END OF PERIOD 



41 



Fig. 8 — Diagram of switch counts at the end of the period 



for instance, would fail to have two switch counts marked up if the counting 

 stopped at 0. Then the probability of losing exactly zero switch counts is 



Po = Pi<i) = K>0) - Pi>U) = I - e i, 



and in general 



vi 



p, = P(>vi) - P\>(v -\- \)i] =-- e~i - 



(v+l)t 



-l)t vi / i\ 



I~ = f~I (^1 - e~^) 



= c'e i (7) 



where v varies from o to oo . The average and standard deviation of a 

 single variable will be^ 



V = ^ vp„ = 



e t 



\ — e 1 



(8) 



'•• The value v is one less than ft shown in equation (3) after neglecting the minute cor- 

 rection factor, since each call there received a switch count at time which is omitted here. 

 The standard deviation is identical with equation (4) w'ithout the correction factor, since 

 a constant deduction has simj^ly lieen made on each call. 



