Hello all,
Here's what I've done to try and validate the new
chooseleaf_descend_once tunable first described in commit
f1a53c5e80a48557e63db9c52b83f39391bc69b8 in the wip-crush branch of
ceph.git.
First I set the new tunable to it's legacy value, disabled,
tunable choose_local_tries 0
tunable choose_local_fallback_tries 0
tunable choose_total_tries 50
tunable chooseleaf_descend_once 0
The map contains one thousand osd devices contained in one hundred hosts
with the following data rule
rule data {
ruleset 0
type replicated
min_size 1
max_size 10
step take default
step chooseleaf firstn 0 type host
step emit
}
I then simulate the creation of one million placement groups using the
crushtool
$ crushtool -i hundred.map --test --min-x 0 --max-x 999999 --num-rep 3
--output-csv --weight 120 0.0 --weight 121 0.0 --weight 122 0.0 --weight
123 0.0 --weight 124 0.0 --weight 125 0.0 --weight 125 0.0 --weight 150
0.0 --weight 151 0.0 --weight 152 0.0 --weight 153 0.0 --weight 154 0.0
--weight 155 0.0 --weight 156 0.0 --weight 180 0.0 --weight 181 0.0
--weight 182 0.0 --weight 183 0.0 --weight 184 0.0 --weight 185 0.0
--weight 186 0.0
with the majority of devices in three hosts marked out. Then in (I)Python
import scipy.stats as s
import matplotlib.mlab as m
data = m.csv2rec("data-device_utilization.csv")
s.chisquare(data['number_of_objects_stored'],
data['number_of_objects_expected'])
which will output
(122939.76474477499, 0.0)
so that the chi squared value is 122939.795 and the p value is, rounded
to, 0.0 and the observed placement distribution statistically differs
from a uniform distribution. Repeating with the new tunable set to
tunable chooseleaf_descend_once 1
I obtain the following result
(998.97643161876761, 0.32151775131589833)
so that the chi squared value is 998.976 and the p value is 0.32 and the
observed placement distribution is statistically identical to the
uniform distribution at the five and ten percent confidence levels,
higher as well of course. The p value is the probability of obtaining a
chi squared value more extreme than the statistic observed. Basically,
from my rudimentary understanding of probability theory, that if you
obtain a p value p < P then reject the null hypothesis, in our case that
the observed placement distribution is drawn from the uniform
distribution, at the P confidence level.
Caleb
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