Re: revisiting uneven CRUSH distributions

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It is working, with straw2 (your cluster still is using straw).

For instance for one host it goes from:

        ~expected~  ~objects~  ~over/under used %~  ~delta~  ~delta%~
~name~
osd.24         149        159                 6.65     10.0      6.71
osd.29         149        159                 6.65     10.0      6.71
osd.0           69         77                11.04      8.0     11.59
osd.2           69         69                -0.50      0.0      0.00
osd.42         149        148                -0.73     -1.0     -0.67
osd.1           69         62               -10.59     -7.0    -10.14
osd.23          69         62               -10.59     -7.0    -10.14
osd.36         149        132               -11.46    -17.0    -11.41

to

        ~expected~  ~objects~  ~over/under used %~  ~delta~  ~delta%~
~name~
osd.0           69         69                -0.50      0.0      0.00
osd.23          69         69                -0.50      0.0      0.00
osd.24         149        149                -0.06      0.0      0.00
osd.29         149        149                -0.06      0.0      0.00
osd.36         149        149                -0.06      0.0      0.00
osd.1           69         68                -1.94     -1.0     -1.45
osd.2           69         68                -1.94     -1.0     -1.45
osd.42         149        147                -1.40     -2.0     -1.34

By changing the weights to

[0.6609248140022604, 0.9148542821020436, 0.8174711575190294, 0.8870680217468655, 1.6031393139865695, 1.5871079208467038, 1.8784764188501162, 1.7308530904776616]

And you could set these weights on the crushmap, there would be no need for backporting.


On 05/01/2017 08:06 PM, Stefan Priebe - Profihost AG wrote:
> Am 01.05.2017 um 19:47 schrieb Loic Dachary:
>> Hi Stefan,
>>
>> On 05/01/2017 07:15 PM, Stefan Priebe - Profihost AG wrote:
>>> That sounds amazing! Is there any chance this will be backported to jewel?
>>
>> There should be ways to make that work with kraken and jewel. It may not even require a backport. If you know of a cluster with an uneven distribution, it would be great if you could send the crushmap so that I can test the algorithm. I'm still not sure this is the right solution and it would help confirm that.
> 
> I've lots of them ;-)
> 
> Will sent you one via private e-mail in some minutes.
> 
> Greets,
> Stefan
> 
>> Cheers
>>
>>>
>>> Greets,
>>> Stefan
>>>
>>> Am 30.04.2017 um 16:15 schrieb Loic Dachary:
>>>> Hi,
>>>>
>>>> Ideally CRUSH distributes PGs evenly on OSDs so that they all fill in
>>>> the same proportion. If an OSD is 75% full, it is expected that all
>>>> other OSDs are also 75% full.
>>>>
>>>> In reality the distribution is even only when more than 100,000 PGs
>>>> are distributed in a pool of size 1 (i.e. no replication).
>>>>
>>>> In small clusters there are a few thousands PGs and it is not enough
>>>> to get an even distribution. Running the following with
>>>> python-crush[1], shows a 15% difference when distributing 1,000 PGs on
>>>> 6 devices. Only with 1,000,000 PGs does the difference drop under 1%.
>>>>
>>>>   for PGs in 1000 10000 100000 1000000 ; do
>>>>     crush analyze --replication-count 1 \
>>>>                   --type device \
>>>>                   --values-count $PGs \
>>>>                   --rule data \
>>>>                   --crushmap tests/sample-crushmap.json
>>>>   done
>>>>
>>>> In larger clusters, even though a greater number of PGs are
>>>> distributed, there are at most a few dozens devices per host and the
>>>> problem remains. On a machine with 24 OSDs each expected to handle a
>>>> few hundred PGs, a total of a few thousands PGs are distributed which
>>>> is not enough to get an even distribution.
>>>>
>>>> There is a secondary reason for the distribution to be uneven, when
>>>> there is more than one replica. The second replica must be on a
>>>> different device than the first replica. This conditional probability
>>>> is not taken into account by CRUSH and would create an uneven
>>>> distribution if more than 10,000 PGs were distributed per OSD[2]. But
>>>> a given OSD can only handle a few hundred PGs and this conditional
>>>> probability bias is dominated by the uneven distribution caused by the
>>>> low number of PGs.
>>>>
>>>> The uneven CRUSH distributions are always caused by a low number of
>>>> samples, even in large clusters. Since this noise (i.e. the difference
>>>> between the desired distribution and the actual distribution) is
>>>> random, it cannot be fixed by optimizations methods.  The
>>>> Nedler-Mead[3] simplex converges to a local minimum that is far from
>>>> the optimal minimum in many cases. Broyden–Fletcher–Goldfarb–Shanno[4]
>>>> fails to find a gradient that would allow it to converge faster. And
>>>> even if it did, the local minimum found would be as often wrong as
>>>> with Nedler-Mead, only it would go faster. A least mean squares
>>>> filter[5] is equally unable to suppress the noise created by the
>>>> uneven distribution because no coefficients can model a random noise.
>>>>
>>>> With that in mind, I implemented a simple optimization algorithm[6]
>>>> which was first suggested by Thierry Delamare a few weeks ago. It goes
>>>> like this:
>>>>
>>>>     - Distribute the desired number of PGs[7]
>>>>     - Subtract 1% of the weight of the OSD that is the most over used
>>>>     - Add the subtracted weight to the OSD that is the most under used
>>>>     - Repeat until the Kullback–Leibler divergence[8] is small enough
>>>>
>>>> Quoting Adam Kupczyk, this works because:
>>>>
>>>>   "...CRUSH is not random proces at all, it behaves in numerically
>>>>    stable way.  Specifically, if we increase weight on one node, we
>>>>    will get more PGs on this node and less on every other node:
>>>>    CRUSH([10.1, 10, 10, 5, 5]) -> [146(+3), 152, 156(-2), 70(-1), 76]"
>>>>
>>>> A nice side effect of this optimization algorithm is that it does not
>>>> change the weight of the bucket containing the items being
>>>> optimized. It is local to a bucket with no influence on the other
>>>> parts of the crushmap (modulo the conditional probability bias).
>>>>
>>>> In all tests the situation improves at least by an order of
>>>> magnitude. For instance when there is a 30% difference between two
>>>> OSDs, it is down to less than 3% after optimization.
>>>>
>>>> The tests for the optimization method can be run with
>>>>
>>>>    git clone -b wip-fix-2 http://libcrush.org/dachary/python-crush.git
>>>>    tox -e py27 -- -s -vv -k test_fix tests/test_analyze.py
>>>>
>>>> If anyone think of a reason why this algorithm won't work in some
>>>> cases, please speak up :-)
>>>>
>>>> Cheers
>>>>
>>>> [1] python-crush http://crush.readthedocs.io/
>>>> [2] crush multipick anomaly http://marc.info/?l=ceph-devel&m=148539995928656&w=2
>>>> [3] Nedler-Mead https://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method
>>>> [4] L-BFGS-B https://docs.scipy.org/doc/scipy-0.18.1/reference/optimize.minimize-lbfgsb.html#optimize-minimize-lbfgsb
>>>> [5] Least mean squares filter https://en.wikipedia.org/wiki/Least_mean_squares_filter
>>>> [6] http://libcrush.org/dachary/python-crush/blob/c6af9bbcbef7123af84ee4d75d63dd1b967213a2/tests/test_analyze.py#L39
>>>> [7] Predicting Ceph PG placement http://dachary.org/?p=4020
>>>> [8] Kullback–Leibler divergence https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence
>>>>
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>>
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-- 
Loïc Dachary, Artisan Logiciel Libre
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