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BELL SYSTEM TECHNICAL JOURNAL 



level of traffic. The traffic engineer would probably decide to schedule his 

 holding time observations during the weeks numbered one to five inclusive. 

 Having determined something as to the character of the holding time 

 trends, if any, with hours of the day, with days of the week, and seasons 

 of the year the traffic engineer is in a better position to lay out a program 

 for sampling. He will especially want to apportion the total sample be- 

 tween the hours or days which show significant differences among them- 

 selves roughly in proportion to the relative traffics flowing at those levels. 

 The less specific the information on the traffic flow characteristics the more 

 important it will be to spread the observations over a variety of hours, 

 days or weeks. 



Ill — A Satisfactory Sample of Directly Measured Holding Times 

 If the standard deviation a of individual call lengths is known, we can 

 estimate the standard error of the average of n measurements as 



a/; 



(2) 



Since n will usually be several hundred we can obtain a good figure for a 

 by calculating the standard deviation, S, of the n observations. As noted 

 before, for exponential calls this will be not far from the average holding 

 time I which may be substituted for a if great accuracy is not required. 

 In fact if the sampling is representatively made from a universe not strictly 

 homogeneous, the better figure for a may be the average i, instead of the 

 standard deviation found in the sample since in so-called Poisson Sampling 

 of stable but nonhomogeneous universes the standard error of the average 

 may be somewhat reduced from S/\/n. 



We may now make the statement that for >! large the probability is P that 

 the true average holding time does not diiTer from that observed by more than 



±s -~— _ seconds, where P and z are given in the table below. 



TABLE II 



For example if we have measured the individual lengths of 900 calls which 

 show an average of 150.3 seconds, we are then W^'f, sure that the true 

 holding time average for the sampled universe lies closely within the range 



150.3 



150.3 ± 2.576 



\/900 



