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       PDP calculation explanation - PDP inner calculation logics with an example by Tianpeng Xia


       This article explains how PDP are calculated in a detailed yet easy-to-understand way,
       with an example.

Refreshing some basics about PDP

   Fundamental knowledge
       If you have not read the tutorials or man pages either on the official site or those by
       others, then I strongly encourage you to do so.  As said in the description, this article
       will only explain how a PDP is calculated, but not the definition of it.  So please read
       the following materials to get a basic understanding of PDP:

       <> - By Alex van den Bogaerdt. This article
       explained PDP in a very detailed and clear way, however, it does not explain the
       "normalization process" in its "Normalize interval" section in the right way( as opposed
       to the official version I confirmed with @oetiker himself). The flaw can be easily seen in
       the bar charts, discussed in the "Calculation logics" section.

       <> - This one is on the official site.
       Actually it's the manual page for "rrdcreate", and it reveals what's under the hood with
       regard to PDP calculation in its "The HEARTBEAT and the STEP" section.

       The text graph by Don Baarda provides a vivid explanation on how UNKOWN data are produced
       and how heartbeat value can influence in the sampling. Unfortunately, it fails to give a
       clear method by which PDPs are calculated.

       <> - Another detailed official
       tutorial by Alex van den Bogaerdt. Similarly, it only provides examples with data evenly
       and exactly distributed according to the step set.

       If you don't like doing experiments or care about the inner mechanics that much, you can
       just stop here and give more attention to more practical topics like graph exports or
       command manual. But if you are the sort of people like me who just care as much about the
       calculation logics, please read on.

Calculation logics

       Here begins the core part of this article. In the following content of this section, I
       would like to give two versions of calculation methods, one by Alex van den Bogaerdt and
       the other by @eotiker.

       To provide an ASCII-friendly explanation, I will explain both versions with the char below
       instead of a real image.

         |    (v1)
         | _______                        (v4)  (v5)
         | |     |           (v3)        ____________
         | |     |        ______________|     ||   |
         | |     |        |            ||     ||   |
         | |     |        |            ||     ||   |
         | |     |   (v2) |            ||     ||   |
         | |     |________|            ||     ||   |
         0 1     3        7            17     20   21

       The X axis means time slots( each second denotes one slot) and the Y axis means the value.

       Let's make everything a little clearer:

       - The step is 5

       - each PDP gets updated only if a value arrives at or after the last slot of the PDP, for
       instance, the last slot of the PDP from 16 to 20 is 20

       - The heartbeat is 20, so the samples during the entire 7-17 period is not discarded

       - At second 3, the first value comes in as v1, and so on

       - Second 0 is the origin, and it does not count as a sample

   Bogaerdt version
       As can be seen on this page: <>, after all the
       primary data are transformed to rates( except for GAUGE, of course), they have to go
       through a normalization process if they are not distributed exactly according to the step
       or on well-defined boundaries in time, in the words of the author.

       What does that mean? Basically, if all the known (as opposed to an unknown value) data
       make up at least 50% of all slots during a period, then a PDP is calculated from them.

       This version seems to go well until we reach the bar chart part.

       According to the ASCII bar chart, we have the following results:

       From second 1 on, the PDP of each period( 1-5,6-10, ...) is computed by averaging all the
       values within it.

       So: - the PDP from 1 to 5 is (v1*3+v2*2)/5

       - the PDP from 6 to 10 is (v2*2+v3*3)/5

       - the PDP from 11 to 15 is (v3*5)/5, since all the values in slots 11, 12, 13, 14 and 15
       are the same, which is v3

       - ...

   The official version( also @oetiker version):
       Using the same chart, this version suggests the following:

       - the PDP from 1 to 5 is (v1*3+v2*2)/5

       - the PDPs from 6 to 10 and 11 to 15 are the SAME, which is (v2*2+v3*8)

       - ...

   A Comparison and some explanation
       So we have seen the above two versions and their PDPs from 6 to 10 and 11 to 15 do not
       comply with each other.

       Why is that?

       Because the difference between the official version and Bogaerdt version stems from the
       way they do the calculation for PDP(6-10) and PDP(11-15).

       Let's discuss this in more detail using the above bar chart.

       Bogaerdt's version,

       PDPs are always computed individually no matter how values arrive.

       For example, the value at slot 17 comes after the last slot of PDP(11-15). Also, the
       immediate previous value before slot 17 is at 7. All the slots from 7 to 17 are assigned
       v3. Since each PDP is computed individually, PDP(6-10) is (v2*2+v3*3)/5 while the
       PDP(11-15) is (v3*5)/5.

       The official version

       PDPs are always computed in terms of the steps which the next update spans, be it 1 step,
       2 steps or n steps; in other words, PDPs may be computed together.

       For example, the update at slot 17 spans PDP(6-10) and PDP(11-15) because the immediate
       previous value is at 7 and 7 is within 6 and 10 , and 17 is after 15. PDP(1-5) and
       PDP(16-20) are not included since the update at slot 7 has already triggered the
       calculation for PDP(1-5) and the update at slot 17 comes before the last slot of
       PDP(16-20) which is 20.

       That's the reason why PDP(6-10) and PDP(11-15) have the same value, (v2*2+v3*8).

An example

       If you are still confused, don't worry, an example is here to help you.

       Let's get our hands dirty with some commands

        rrdtool create target.rrd --start 1000000000  --step 5 DS:mem:GAUGE:20:0:100 RRA:AVERAGE:0.5:1:10
        rrdtool update target.rrd 1000000003:8 1000000006:1 1000000017:6 \
        1000000020:7 1000000021:7 1000000022:4 \
        1000000023:3 1000000036:1 1000000037:2 \
        1000000038:3 1000000039:3 1000000042:5
        rrdtool fetch target.rrd AVERAGE --start 1000000000 --end 1000000045

       Basically, the above codes contain 3 commands: create, update and fetch. First create a
       new rrd file, and then we feed in some data and last we fetch all the PDPs from the rrd.

   Focus on single steps
       In order to provide a detailed explanation, each the calculation process of each PDP is

       Below is the output of the commands above:

        1000000005: 5.2000000000e+00
        1000000010: 5.5000000000e+00
        1000000015: 5.5000000000e+00
        1000000020: 6.6000000000e+00
        1000000025: 1.7333333333e+00
        1000000030: 1.7333333333e+00
        1000000035: 1.7333333333e+00
        1000000040: 2.8000000000e+00
        1000000045: nan
        1000000050: nan

       NOTE: 1000000005 means the PDP from 1000000001 to 1000000005, and so on. For concision and
       readability, we use only the last two digits, so 05 denotes 1000000005. We choose the type
       of the data source as gauge because original values will be treated as rates, no
       additional transformation is needed, see this article
       <> for detail.

       05: 5.2 = (8*3+1*2)/5

       10: 5.5 = (1*1+6*9)/10

       15: the same as the previous one

       20: 6.6 = (6*2+7*3)/5

       25: 1.73333 = (7+4+3+1*12)/15


       45: nan, as the last value is at 42,which does not trigger the calculation for PDP(41-45)

       50: nan, why this unknown PDP is shown is explained in this article


       All that said, I hope you get a clear understanding of the inner calculation "magic" for

   Other References
       ·   A great PowerShell shell script for generating ASCII bar charts:

       ·   <>