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 >>> >> -- >> To unsubscribe from this list: send the line "unsubscribe ceph-devel" in >> the body of a message to majordomo@xxxxxxxxxxxxxxx >> More majordomo info at http://vger.kernel.org/majordomo-info.html >> > -- To unsubscribe from this list: send the line "unsubscribe ceph-devel" in the body of a message to majordomo@xxxxxxxxxxxxxxx More majordomo info at http://vger.kernel.org/majordomo-info.html
