2017-02-06 16:18 GMT+08:00 Loic Dachary <loic@xxxxxxxxxxx>: > Hi, > > On 02/06/2017 04:08 AM, Jaze Lee wrote: >> It is more complicated than i have expected..... >> I viewed http://tracker.ceph.com/issues/15653, and know that if the >> replica number is >> bigger than the host we choose, we may meet the problem. >> >> That is >> if we have >> host: a b c d >> host: e f g h >> host: i j k l >> >> we only choose one from each host for replica three, and the distribution >> is as we expected? Right ? >> >> >> The problem described in http://tracker.ceph.com/issues/15653, may happen >> when >> 1) >> host: a b c d e f g >> >> and we choose all three replica from this host. But this is few happen >> in production. Right? >> >> >> May be i do not understand the problem correctly ? > > The problem also happens with host: a b c d e f g when you try to get three replicas that are not on the same disk. You can experiment with Dan's script Yes, I mean why we choose three from one host ? In production the host number is ALWAYS more than replica number..... root rack-0 host A host B rack-1 host C host D rack -2 host E host F when choose pg 1.1 for osd, it will always choose one from rack-0, one from rack-1, one from rack-2. any pg will cause one be choosed from rack-0, rack-1, rack-2. The problem is happened when we want to choose more than one osd from a bucket for a pg, right ? > > https://gist.github.com/anonymous/929d799d5f80794b293783acb9108992 > > Cheers > > >> >> >> >> >> >> >> >> >> >> >> 2017-02-04 2:54 GMT+08:00 Loic Dachary <loic@xxxxxxxxxxx>: >>> >>> >>> On 02/03/2017 04:08 PM, Loic Dachary wrote: >>>> >>>> >>>> On 02/03/2017 03:47 PM, Sage Weil wrote: >>>>> On Fri, 3 Feb 2017, Loic Dachary wrote: >>>>>> On 01/26/2017 12:13 PM, Loic Dachary wrote: >>>>>>> Hi Sage, >>>>>>> >>>>>>> Still trying to understand what you did :-) I have one question below. >>>>>>> >>>>>>> On 01/26/2017 04:05 AM, Sage Weil wrote: >>>>>>>> This is a longstanding bug, >>>>>>>> >>>>>>>> http://tracker.ceph.com/issues/15653 >>>>>>>> >>>>>>>> that causes low-weighted devices to get more data than they should. Loic's >>>>>>>> recent activity resurrected discussion on the original PR >>>>>>>> >>>>>>>> https://github.com/ceph/ceph/pull/10218 >>>>>>>> >>>>>>>> but since it's closed and almost nobody will see it I'm moving the >>>>>>>> discussion here. >>>>>>>> >>>>>>>> The main news is that I have a simple adjustment for the weights that >>>>>>>> works (almost perfectly) for the 2nd round of placements. The solution is >>>>>>>> pretty simple, although as with most probabilities it tends to make my >>>>>>>> brain hurt. >>>>>>>> >>>>>>>> The idea is that, on the second round, the original weight for the small >>>>>>>> OSD (call it P(pick small)) isn't what we should use. Instead, we want >>>>>>>> P(pick small | first pick not small). Since P(a|b) (the probability of a >>>>>>>> given b) is P(a && b) / P(b), >>>>>>> >>>>>>> >From the record this is explained at https://en.wikipedia.org/wiki/Conditional_probability#Kolmogorov_definition >>>>>>> >>>>>>>> >>>>>>>> P(pick small | first pick not small) >>>>>>>> = P(pick small && first pick not small) / P(first pick not small) >>>>>>>> >>>>>>>> The last term is easy to calculate, >>>>>>>> >>>>>>>> P(first pick not small) = (total_weight - small_weight) / total_weight >>>>>>>> >>>>>>>> and the && term is the distribution we're trying to produce. >>>>>>> >>>>>>> https://en.wikipedia.org/wiki/Conditional_probability describs A && B (using a non ascii symbol...) as the "probability of the joint of events A and B". I don't understand what that means. Is there a definition somewhere ? >>>>>>> >>>>>>>> For exmaple, >>>>>>>> if small has 1/10 the weight, then we should see 1/10th of the PGs have >>>>>>>> their second replica be the small OSD. So >>>>>>>> >>>>>>>> P(pick small && first pick not small) = small_weight / total_weight >>>>>>>> >>>>>>>> Putting those together, >>>>>>>> >>>>>>>> P(pick small | first pick not small) >>>>>>>> = P(pick small && first pick not small) / P(first pick not small) >>>>>>>> = (small_weight / total_weight) / ((total_weight - small_weight) / total_weight) >>>>>>>> = small_weight / (total_weight - small_weight) >>>>>>>> >>>>>>>> This is, on the second round, we should adjust the weights by the above so >>>>>>>> that we get the right distribution of second choices. It turns out it >>>>>>>> works to adjust *all* weights like this to get hte conditional probability >>>>>>>> that they weren't already chosen. >>>>>>>> >>>>>>>> I have a branch that hacks this into straw2 and it appears to work >>>>>>> >>>>>>> This is https://github.com/liewegas/ceph/commit/wip-crush-multipick >>>>>> >>>>>> In >>>>>> >>>>>> https://github.com/liewegas/ceph/commit/wip-crush-multipick#diff-0df13ad294f6585c322588cfe026d701R316 >>>>>> >>>>>> double neww = oldw / (bucketw - oldw) * bucketw; >>>>>> >>>>>> I don't get why we need "* bucketw" at the end ? >>>>> >>>>> It's just to keep the values within a reasonable range so that we don't >>>>> lose precision by dropping down into small integers. >>>>> >>>>> I futzed around with this some more last week trying to get the third >>>>> replica to work and ended up doubting that this piece is correct. The >>>>> ratio between the big and small OSDs in my [99 99 99 99 4] example varies >>>>> slightly from what I would expect from first principles and what I get out >>>>> of this derivation by about 1%.. which would explain the bias I as seeing. >>>>> >>>>> I'm hoping we can find someone with a strong stats/probability background >>>>> and loads of free time who can tackle this... >>>>> >>>> >>>> It would help to formulate the problem into a self contained puzzle to present a mathematician. I tried to do it last week but failed. I'll give it another shot and submit a draft, hoping something bad could be the start of something better ;-) >>> >>> Here is what I have. I realize this is not good but I'm hoping someone more knowledgeable will pity me and provide something sensible. Otherwise I'm happy to keep making a fool of myself :-) In the following a bin is the device, the ball is a replica and the color is the object id. >>> >>> We have D bins and each bin can hold D(B) balls. All balls have the >>> same size. There is exactly X balls of the same color. Each ball must >>> be placed in a bin that does not already contain a ball of the same >>> color. >>> >>> What distribution guarantees that, for all X, the bins are filled in >>> the same proportion ? >>> >>> Details >>> ======= >>> >>> * One placement: all balls are the same color and we place each of them >>> in a bin with a probability of: >>> >>> P(BIN) = BIN(B) / SUM(BINi(B) for i in [1..D]) >>> >>> so that bins are equally filled regardless of their capacity. >>> >>> * Two placements: for each ball there is exactly one other ball of the >>> same color. A ball is placed as in experience 1 and the chosen bin >>> is set aside. The other ball of the same color is placed as in >>> experience 1 with the remaining bins. The probability for a ball >>> to be placed in a given BIN is: >>> >>> P(BIN) + P(all bins but BIN | BIN) >>> >>> Examples >>> ======== >>> >>> For instance we have 5 bins, a, b, c, d, e and they can hold: >>> >>> a = 10 million balls >>> b = 10 million balls >>> c = 10 million balls >>> d = 10 million balls >>> e = 1 million balls >>> >>> In the first experience with place each ball in >>> >>> a with a probability of 10 / ( 10 + 10 + 10 + 10 + 1 ) = 10 / 41 >>> same for b, c, d >>> e with a probability of 1 / 41 >>> >>> after 100,000 placements, the bins have >>> >>> a = 243456 >>> b = 243624 >>> c = 244486 >>> d = 243881 >>> e = 24553 >>> >>> they are >>> >>> a = 2.43 % full >>> b = 2.43 % full >>> c = 2.44 % full >>> d = 2.43 % full >>> e = 0.24 % full >>> >>> In the second experience >>> >>> >>>>> sage >>>>> >>>>> >>>>>> >>>>>>> >>>>>>>> properly for num_rep = 2. With a test bucket of [99 99 99 99 4], and the >>>>>>>> current code, you get >>>>>>>> >>>>>>>> $ bin/crushtool -c cm.txt --test --show-utilization --min-x 0 --max-x 40000000 --num-rep 2 >>>>>>>> rule 0 (data), x = 0..40000000, numrep = 2..2 >>>>>>>> rule 0 (data) num_rep 2 result size == 2: 40000001/40000001 >>>>>>>> device 0: 19765965 [9899364,9866601] >>>>>>>> device 1: 19768033 [9899444,9868589] >>>>>>>> device 2: 19769938 [9901770,9868168] >>>>>>>> device 3: 19766918 [9898851,9868067] >>>>>>>> device 6: 929148 [400572,528576] >>>>>>>> >>>>>>>> which is very close for the first replica (primary), but way off for the >>>>>>>> second. With my hacky change, >>>>>>>> >>>>>>>> rule 0 (data), x = 0..40000000, numrep = 2..2 >>>>>>>> rule 0 (data) num_rep 2 result size == 2: 40000001/40000001 >>>>>>>> device 0: 19797315 [9899364,9897951] >>>>>>>> device 1: 19799199 [9899444,9899755] >>>>>>>> device 2: 19801016 [9901770,9899246] >>>>>>>> device 3: 19797906 [9898851,9899055] >>>>>>>> device 6: 804566 [400572,403994] >>>>>>>> >>>>>>>> which is quite close, but still skewing slightly high (by a big less than >>>>>>>> 1%). >>>>>>>> >>>>>>>> Next steps: >>>>>>>> >>>>>>>> 1- generalize this for >2 replicas >>>>>>>> 2- figure out why it skews high >>>>>>>> 3- make this work for multi-level hierarchical descent >>>>>>>> >>>>>>>> sage >>>>>>>> >>>>>>>> -- >>>>>>>> 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 >>>>>>>> >>>>>>> >>>>>> >>>>>> -- >>>>>> Loïc Dachary, Artisan Logiciel Libre >>>>>> -- >>>>>> 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 >>>>>> >>>> >>> >>> -- >>> Loïc Dachary, Artisan Logiciel Libre >>> -- >>> 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 >> >> >> > > -- > Loïc Dachary, Artisan Logiciel Libre -- 谦谦君子 -- 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
