# The Math

### The Basics

At first glance, the way collectl calculates its numbers is pretty straight forward. It looks at successive intervals of counters, calculates their differences and normalizes the result by dividing by the interval, the result of which is the counter's rate/second. If -on is specified collectl does not divide by the interval and simply reports the difference. However, one occasionally may see numbers that don't make sense, such as a 1Gb network reporting rates almost double what it is capable of or other anomolous numbers.

### The Interval Time Stamps

By design, collectl takes one time stamp at the start of each monitoring interval and associates that time with all the samples taken during that interval. This has been done for one major reason - there needs to be a single time associated with all data points, especially if you want to plot the data. The overhead in collecting the data is fairly constant and therefore the interval for that sample is fairly consistent and so the rates reported are also consistent.

However, there can be a problem that is important to understand and has been seen in the past. A device had the wrong firmware level and under some conditions caused a long delay in the middle of the collection interval. Some samples were collected close the the starting time of that interval while all that followed the delay were actually collected at a time much later than was being reported.

Consider the following in which we're looking at raw data collected for 2 subsystems, call them XXX and YYY. Let's also assume that the counters we're monitoring are increasing at a steady rate of 100 units/sec. In this example, during the 10:00:01 interval there was a 10 second hang in collecting the YYY sample. The XXX sample was correctly recorded, but by the time the YYY sample was collected, 1000 units were recorded. As we move to the next interval which was delayed by 10 seconds, the sample for XXX has accumulated 1000 units and the sample for YYY is 100.

    TYPE            XXX     YYY
    10:00:00        100     100
    10:00:01        200     1100
    10:00:11        1200    1200
    10:00:12        1300    1300

The problem here is when reporting the 2 rates at 10:00:01, we'll see a rate of 1000 units/sec for YYY because based on the timestamp that interval only appears to be 1 second long. Conversely, the rate reported for that same subsystem at 10:00:11 will be 10 units/sec because this interval is reported as 10 seconds long. Also note that for this interval the counter for XXX has been incremented correctly and the resultant rates are reported correctly. This is because the sampling occured before the delays. If one were to move the timestamp to the end of the interval, it would fix the problem with YYY, but then move it to XXX.

It IS important to understand that this is only a problem if the delay is during the data collection itself. If there is a system delay that causes all data collection to be delayed but once started runs as expected, and this has been seen to be the typical case, the intervals may be longer but the counters will have increased proportionaly and the results consistent.

The only real answer to this problem would be to timestamp individual samples, however it is also felt that this problem is rare enough as to not be of serious concern and changing the methodology of timestamping would cause more problems than it solves.

### The Counter Update Rate

This is a problem that is very real and worth understanding even it if you never personally see it. If the rate at which a counter is updated is too coarse, especially if it is close to the monitoring interval, the reported numbers will be off. For most of the data collectl reports on, this is not a problem because these counters ARE updated frequently. However, it turns out that some network drivers only updated about once a second and in early versions of the 2.6 kernel (and may the one you're currently running on), you may see some very strange anomolies in the output if you look at 1-second data samples. See this page for more details.

### Normalization

As described elsewhere, collectl divides counter values by the interval between samples and then rounds off the results. When run interactively with a default interval of 1 second, this is not an issue. However, for data collected in deamon mode this can actually be of significance. Consider a network that has 1-4 errors over a 10 second period. This will normalize to a value of <5 and be rounded off to 0! The same is true for values reported for process/slab statistics, where these are typically measured over 60 seconds. Normalization in these cases can be even more dramatic.

One other thing to consider is that when selecting only non-zero values be reported, one might be occasionally be surprised by see values of 0 being reported. This will occur if there is a non-zero value that is then nomalized to 0.

If you think you might need to see these close to 0 values, you should include -on which tells collectl not to normalize its output before reporting.

### In conclusion

As they say, garbage in, garbage out and so if the number you're seeing look wrong, it's worth trying to understand why and you shouldn't necessary take them as face value.

updated Feb 21, 2011