more below...
Ed Gould wrote:
On Jul 18, 2006, at 8:58, Richard Elling wrote:
Jeff Bonwick wrote:
For 6 disks, 3x2-way RAID-1+0 offers better resiliency than RAID-Z
or RAID-Z2.
Maybe I'm missing something, but it ought to be the other way around.
With 6 disks, RAID-Z2 can tolerate any two disk failures, whereas
for 3x2-way mirroring, of the (6 choose 2) = 6*5/2 = 15 possible
two-disk failure scenarios, three of them are fatal.
For the 6-disk case, with RAID-1+0 you get 27/64 surviving states
versus 22/64 for RAID-Z2. This accounts for the cases where you could
lose 3 disks and survive with RAID-1+0.
It seems to me that a useful resiliency calculation must include the
probability of the failures. Just because there are more potential
failure states for RAID-Z doesn't mean, in practical terms, at least,
that it is less resilient. Yes, there is one case of 3-disk failure
that the 3x2 arrangement will survive that RAID-Z2 won't, but there are
(as Jeff pointed out) three 2-disk failures that are fatal to 3x2.
Three different 2-failure scenarios total a much more likely occurrence
than than the net five (all requiring three or more failures) scenarios
that would be fatal to RAID-Z2 but not 3x2.
A combinatorial resiliency analysis has no concept of time. To consider
reliability, you need to consider time. Ergo, the combinatorial analysis
is only suitable when the reliability of the components are the same, such
as the JBOD disk case.
As usual, we also do a large number of models for data availability and
MTTDL which are based on reliability, recovery, spares, etc. Nevertheless,
there are some valid cases where the combinatorial analysis is particularly
useful: those where you cannot service or cannot service for long periods
of time. As you would expect, those cases also tend towards triple
redundant (3-way RAID-1) designs.
It is worth noting that RAID-Z2 is more resilient than 2-way RAID-1 when
the number of disks is <= 5, but not as the number of disks grows beyond 6.
This is in line with Roch's performance optimization observations, where
we may recommend something like 2x6-way RAID-Z2 over 12-way RAID-Z2 for
performance and resiliency, sacrificing space.
-- richard
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