]{i;mability of tuaffic mkasurements 



3G5 



sired. This is fai' tVom true if source load is l)(>iiij>; (vstimated. If the cost 

 of maivinj>; a scan is constant, inci-easinji; the number of observation 

 periods and decreasing the scan rate will iinproxc accui'acy of source 

 load estimates M'ithout changini;- measurement costs. Tiie mmiber of 

 hours axailahle for measuiina;, of course, limits this procedure, while 

 the increase in accuracy becomes nej>;lioible as r be(H)mes large. On the 

 other hand, if the cost of each obsei'vation is only slightly affected by the 

 cost of making additional scans, a high scan rate might be justified. 



In ai)iilying the abo\-e relationships to traffic measurements, the 

 usual cjuestion raised by the traffic engineer will be cither how many 

 hours of data need he take to l)e reasonably- suic of his estimate or, 

 conversely, how sure is he of an estimate based on available data. 

 Assuming as before that the error distribution is normal, the per cent 

 plus or minus error limits within which a proportion, P^ , of the estimates 

 will fall is given by zVs ; the value of z corresponding to any selected 

 P; may be found from tables of the normal probability distribution. 

 "Reasonably sure" is often taken to mean that there is 90 per cent 

 assurance that the error does not exceed 5 per cent. When P^ is 0.90, 

 z is 1.64, so that under this condition 1.647s = 0.05, or Vs = 0.0305. 

 Given scan rate and holding time, Vs is proportional to l/s/aNT accord- 

 ing to equation (9) or Figure 3. When Vs is held constant, aNT is con- 

 stant so that the plot of log NT against log a is linear, as shown in 

 Figs. 4 and 5. The number of hours needed to meet any chosen reliability 



100 

 80 



<S 20 



u. o; 

 lU < . 



10 20 40 60 100 200 400 1000 2000 4000 



SCAN IN CYCLES PER HOUR 



Fig. 3 — l^fficiency of switcli covnits for usage measuromciit. 



10,000 



