vdev/pool math with combined raidzX vdevs...

[Jason Usher]

--- On Fri, 7/6/12, Zaphod Beeblebrox <zbeeble at gmail.com> wrote:

> Is there some penalty for not
> googling some basic stats course?  OK.
> This is from memory (hint: you probably should google).


Actually I spent a few hours googling zfs probabilities, and I cannot find any discussion of the changes in failure probability when multiple raidzX are striped in a single pool.

I did not try to google the math and do it myself, as I wouldn't trust my own results.


> Similarly,
> 
> p(12drz2) = 12 * p(f) * 11 * p(f) * 10 * p(f)
> p(12drz3) = 12 * p(f) * 11 * p(f) * 10 * p(f) * 9 * p(f)
> 
> ... again with those assumptions are more complex
> probabilities given
> your replacement strategy.
> 
> ... so, again with simplistic assumptions,
> 
> p(36drz3 --- 12 drives, 3 groups) = p(12drz3) * 3
> 
> A "vanilla" RAID-Z2 (if I make an assumption to what you're
> saying) is:
> 
> p(36drz2) = 36 * p(f) * 35 * p(f)
> 
> ... but I can't directly answer you question without knowing
> a) the
> structure of the RAID-Z2 array and p(f).  If we use a
> 1% figure for
> p(f), then P(36drz3,12,3) = 0.035% and p(36drz2) = 4.3%
> 
> ... that is the raid-Z2 case (one group of 36 drives, two
> redundant
> --- which is crazy) is 4.3% likely to fail where the 3-group
> RAID-Z3
> is only 0.035% likely to fail.  As a more sane
> comparison,
> p(36drz2,12,3) = 3.8%


Ok, you're right - I did not specify the structure of the raidz2 array.

What I meant to compare was the failure probabilities of:

- a single raidz2 vdev made up of 12 disks (10 data, 2 parity)

vs.

- a single raidz3 vdev made up of 12 disks (9 data, 3 parity)

vs.

- a single raidz3 vdev made up of 12 disks (9 data, 3 parity) which ALSO happens to be participating in a stripe with two other identical raidz3 vdevs, all in one zpool.


I can see some probabilites for the first two examples here:

http://hardforum.com/showthread.php?t=1621123

(search for first post on page by "john4200")

as well as your own math, which appears to be the same.


Also, I think we don't need to specify the failure rate, F, since we are merely comparing three scenarios, and can compare results that still contain an 'F' variable in them ... that is, our answers can contain a yet undefined 'F', right ?


As for myself, I have decided that raidz2 is "not enough" for me, and at the same time, would really, really like to combine three raidz3 into a single zpool ... but I don't want to do that if that configuration brings me back to raidz2-ish failure probabilities...