Re: What is the point of RAID?

On Wednesday 12 November 2008, lee <lee@xxxxxxxxxxxxxxx> wrote about 'Re:
What is the point of RAID?':
On Wed, 12 Nov 2008 09:59:09 -0600

"Boyd Stephen Smith Jr." <bss03@xxxxxxxxxxxxxx> wrote:
So what is the optimal number of disks in a raid 5 and a raid 1?

If by optimal, you mean, least chance of failure:

Not exactly; I was wondering if there is a breaking point, as in
"adding more drives only increases the chances of the whole array to
fail" beyond that point, and "adding more drives reduces the chances of
the whole array failing" before that point.

Um, that's exactly what I mean by least chance of failure.

Under the assumption of "hard disk n" fails events being,
mathematically, "independent events":

RAID-1 always grows in redundancy, and doesn't fail until all the drives
fail. At n drives, the chance of failure of the array is p^n, for
probabilities less than 100% (or 1), p^(n+1) < p^n for any n > 0, so
adding a drive always reduces the chance of failure. [aleph-sub-naught is
the first countable infinity.]

RAID-5 always grows in storage not redundancy, and fails as soon as any two
(or more) drives file. At n drives the chance of failure of the array
is ... something I'd have to look up ... but where (for n drives) < (for
n+1 drive) for any n >= 2. So 3 drives (the minimum in RAID-5), provides
the least chance of failure.

Wouldn't it be useful if that breaking point was known for all kinds of
raid setups?

Under the "independent events" assumption, it is. I'm not sure anyone just
has a table you can look it up with, but basic combinatorial maths will
get you the answer.

The calculation would have to consider the chances of
several drives failing at (about) the same time.

You could do that, and the failure probabilities would be different but in
the same relative order, until you varied two much from the "independent
events" assumption, for example: making two of the drive completely
dependent on one another; when one fail so does the other and vice-versa.

For something that takes into account that recovery/rebuild takes some
time, during when redundancy is decreased or lost entirely, well I'm
pretty sure the maths exists, I just haven't studied it at all.

The problem is that redundancy isn't the whole story. Sure 5 drives in a
RAID-1 is very safe compared to 5 drives in a RAID-5, but the RAID-5 has 4
times the storage for the same cost. You have to consider the array's
cost, usable storage, chance of failure, and performance. Small
trade-offs in one of those values can change the other a lot.

RAID-5 might not be the fastest or least risky way to store data across
5x(1 TB) drives, but it wins because it gives a lot of space (4 TB) at an
acceptable level of redundancy -- I challenge anyone to come up with a
scheme that gives the same performance and at least 3 1/3 TB of space with
ANY redundancy.

RAID-6 might not perform as well as RAID-5/0 or even RAID-5, but it stays
up no matter which two drives go down and doesn't require an even number
of drives.

RAID is "old school"/"old guard", but it works very well. I'm not a big
believer in ZFS, because I believe a separation between the filesystem and
block-device management makes the whole system for flexible and useful.
--
Boyd Stephen Smith Jr. ,= ,-_-. =.
bss03@xxxxxxxxxxxxxx ((_/)o o(\_))
ICQ: 514984 YM/AIM: DaTwinkDaddy `-'(. .)`-'
http://iguanasuicide.org/ \_/

Attachment: signature.asc
Description: This is a digitally signed message part.

Relevant Pages

  • Re: backup archive format saved to disk
    ... everything, not just some things, in case of failure. ... You then create 10M of redundancy ... You use par2 to reconstruct the archive, ... If drives are atomic in this way, it seems that the only way to achieve ...
    (Debian-User)
  • Re: backup archive format saved to disk
    ... everything, not just some things, in case of failure. ... You then create 10M of redundancy ... You use par2 to reconstruct the archive, ... If drives are atomic in this way, it seems that the only way to achieve ...
    (Debian-User)
  • Re: backup archive format saved to disk
    ... everything, not just some things, in case of failure. ... You then create 10M of redundancy ... You use par2 to reconstruct the archive, ... If drives are atomic in this way, it seems that the only way to achieve ...
    (Debian-User)
  • Re: FYI: RAID5 unusably unstable through 2.6.14
    ... add disks the probability of a single failure is grows linearly, but the probability of double failure grows much more slowly. ... If 1 disk has a 1/1000 chance of failure, ... After the first drive fails you have no redundancy, the chance of an additional failure is linear to the number of remaining drives. ...
    (Linux-Kernel)
  • Re: FYI: RAID5 unusably unstable through 2.6.14
    ... add disks the probability of a single failure is grows linearly, but the probability of double failure grows much more slowly. ... I was speaking in the case of a RAID-5 set, where the minimum is 3 drives, so every additional drive increases the chance of a double fault condition. ...
    (Linux-Kernel)
Loading