370 THE BELL SYSTEM TECHNia\L JOURNAL, MARCH 1952 



d. Statistical Equilibrium 



Statistical equilibrium may be thought of as the absence of trends in 

 subscriber calling rates or holding times with the passage of time. The 

 effect of trends on switch count accuracy in measuring carried load is 

 very small except where the changes in traffic level are frequent and 

 abrupt with respect to the scan frequency. Such traffic behavior is rare. 



Trends within the busy hour compUcate the problem of estimating the 

 average source load. However, it can be shown that if the trends are small 

 (in the order of 10 per cent to 20 per cent) little error is introduced by 

 assuming that no trend exists. Large trends (in the order of 100 per 

 cent), however, may indicate that the traffic source is so unstable that 

 more hours of traffic data should be taken in order to insure that the 

 sample is representative. 



Trends from day to da}^ do not affect the source load estimates in the 

 same way as \\dthin hour trends. The source loads are seldom exactly the 

 same on any two days although in most offices a load pattern is repeated 

 from week to week. The traffic engineer may be interested in the average 

 source load of either a typical week day in the busy season or, some- 

 times, of the average of the two highest days in the week. As long as the 

 source load of each particular day remains close to the average for that 

 day of the week, the general average for several different days of the 

 week, mil be known with about the same accuracy as if they had all 

 come from a common source. If, however, there is no stable pattern in 

 the source load, a third error in estimating the average is generated. 

 There is some difficulty in determining whether or not variations in load, 

 as indicated by measurements, are due to sampling variations or to an 

 unstable source. Quahty control methods might be used to detect in- 

 stability but gathering and processing sufficient data for such an analysis 

 might prove uneconomical. In general, if a traffic engineer feels that 

 his source load is unstable he \d\\ need more hours of data than indicated 

 by formula (9) to meet a given criterion of reUabihty. 



CONCLUSIONS 



A theoretical approach to the problem of the accuracy of switch count 

 measurements in estimating carried load and average source load has 

 been explored.' It is believed that the assumptions made are satisfied 

 sufficiently often in practice to enable fairly ■s^^de application of the re- 

 sults of this exploration to traffic measurements. However, it should be 

 kept in mind that where the assumptions are clearly not valid, special 

 allowances mil need to be made. In any case, the confidence placed in 



