RELIABILITY OF TRAFFIC MEASUREMENTS 359 



2. Even if the load carried during a measurement period were known 

 very accurately, it is still only a sample of the many loads that might be 

 offered l)y the same source of traffic inider statist ically identical con- 

 ditions. Therefore, the average of several load readings may be expected 

 to be somewhat in error as an estimate of the true average of the traffic 

 source. The latter aWU be referred to as the source load to distinguish it 

 from the carried load. 



Mechanical and human errors are likely to be present as well but, since 

 they are not inherent in the switch count method, they will be neglected 

 here. 



SWITCH COUNT ERROR 



As shown in the Appendix, for periods of observation w^hich are rela- 

 ti^•ely long with respect to average holding time made on traffic with 

 certain assumed characteristics, the average error of switch counts in 

 estimating traffic load carried in the same period is zero. The coefficient 

 of variation of the error, which is the standard deviation of the error 

 expressed in per cent of the traffic load carried, is given by: 



V:, = 100 



rctnh( ^ ) - 2 



t (p) 



a' NT 



/r\ _ 1 + e "^ _ , , ,. , . ,. r 



ctnhl - ) = = hyperbolic cotangent of 



V2/ 1 - e-"- 2 



re = T/i > 20 



where /■ = ratio of scan interval to holding time 



I = average hokhng time 



a' = carried load in erlangs 



c = number of switch counts 



T = length of observation period 



N = number of observation periods 



and where the following assumptions are made: 



a. Calls originate individually and collectively at random.! 



b. Holding times are exponentially distributed. 



c. Congestion loss from the group is neghgible. 



* I have recently learned that these carried load formulas have been published 

 hy ConnyFalm mTekniska Medelandenf ran Kungl. T'elegrafstyrelsen, 1941. nr. 7-9. 



t See T. C. Fry, Probability and lis Engineering Uses, D. van Nostrand Co. 

 Inc., New York, p. 216, for a definition of this condition. 



