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 > 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
