On Mon, 13 Feb 2017, Loic Dachary wrote: > Hi, > > Dan van der Ster reached out to colleagues and friends and Pedro > López-Adeva Fernández-Layos came up with a well written analysis of the > problem and a tentative solution which he described at : > https://github.com/plafl/notebooks/blob/master/replication.ipynb > > Unless I'm reading the document incorrectly (very possible ;) it also > means that the probability of each disk needs to take in account the > weight of all disks. Which means that whenever a disk is added / removed > or its weight is changed, this has an impact on the probability of all > disks in the cluster and objects are likely to move everywhere. Am I > mistaken ? Maybe (I haven't looked closely at the above yet). But for comparison, in the normal straw2 case, adding or removing a disk also changes the probabilities for everything else (e.g., removing one out of 10 identical disks changes the probability from 1/10 to 1/9). The key property that straw2 *is* able to handle is that as long as the relative probabilities between two unmodified disks does not change, then straw2 will avoid moving any objects between them (i.e., all data movement is to or from the disk that is reweighted). sage > > Cheers > > 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), > > > > 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. 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 > > 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 > >
