RELIABILITY OF TRAFFIC MEASUREMENTS 371 



usage measurements by a traffic engineer is a function of his experience 

 and judgment. It is hoped that tlie lesuhs of this study will add to the 

 knowledge essential to sound (lallic ciigincciing. 



APPENDIX 



DERIVATION OF SAVITCH COUNT ERROR IN ESTIMATING CARRIED LOAD — 

 WITH EXPONENTIAL HOLDING TIMES 



This derivation is based on a similar deiix'ation by R. I. Wilkinson'. 

 However, since load rather than holding time is of interest here, the em- 

 phasis has been somewhat shifted. 



Assume^ that switch count measurements are being taken on traffic 

 with : 



a. Calls originated indi\'idually and collectively at random 



b. Exponentially distributed holding times 



c. Negligible loss 



Let i = interval between scans 

 t = average holding time 

 a' = traffic carried, in erlangs 

 T = length of observation pei'iod 



r - ^ = number of holding times in a scan interval 

 t 



T 



c = . = number scans in observation period 

 I 



T 



re = . = number of holding times in observation period 



N = number of observation periods. 



Consider that the observation period begins with the first scan and 

 ends i time units after the last scan. It is desired to find the error in esti- 

 mating the true load carried by averaging the number of circuits found 

 busy on each scan. Following Wilkinson's method we will first estimate 

 the error of the switch count method in measuring the contribution of a 

 single call to total usage and then modify it to take account of n calls. 

 Calls of two types must be considered, those originating outside the in- 

 terval and extending into it, Type I, and those originating within the 

 interval, Type II. Both types may be subdivided depending on whether 

 or not they extend beyond the end of the observation period. These are 



