On Thu, Jan 26, 2017 at 7:13 PM, Loic Dachary <loic@xxxxxxxxxxx> 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 ? a joint events of A and B means these two events occur together. Here, A and B are two random variables. so, the notion of P(A && B) or P(A∩B) stands for the probability of the event A and event B happens together. in our case, in our case, "a" denotes the event of "first small", and "b" denotes "first pick not small". so P(a∩b) is the probability of the first pick is not small **and** the resulting pick is not small. maybe you can also reference https://en.wikipedia.org/wiki/Joint_probability_distribution > >> 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 > >> 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 -- Regards Kefu Chai -- 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
