How were the weightings in the linux load computation chosen?

Consider a particular load sample active(K), and how much that sample contributes to cpuload(K+d), for increasing values of d. There are a few key observations:

• active(K) is multipled by some weight W(d) to determine its contribution to cpuload(K+d).
• W(d) is always less than one.
• W(d) decreases exponentially as d increases.
• computer arithmetic has finite precision.

Together, these points mean that there is some dmin such that, for d>dmin, active(K)W(d)=0 and so active(K) has no influence on cpuload(K+d). In short, cpuload(n) is only influenced by dmin previous samples.

Another way to look at this is that cpuload(n) forgets data after a time defined by

• the decay exponent, which defines dmin, and
• the sampling frequency.

This final interpretation gives the meaning of the 1-minute, 5-minute, and 15-minute load averages. The decay and the sampling interval are chosen so that these load averages forget the past after 1, 5, and 15 minutes respectively.

I'm guessing they wanted the mean lifetime of the contribution of a running process to be one minute.