How were the weightings in the linux load computation chosen?

Question

In Linux, the load average is said to be on 1min/5min/15min. The formula used by the kernel is actually an Exponential moving average.

If we define cpuload(1)

Answer 1

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

Answer 2

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.