I need to understand
groups, especially the difference between a 3+1 vs. a 7+1 parity group. Does one offer more protection than the other or is the difference really more in the way parity is calculated?
There is a lot of discussion and some debate about using smaller
(parity) groups vs. larger ones, particularly when using high-capacity
disk drives. Depending on your application performance and workload characteristics, some things to consider that impact performance and parity calculation in general are that a 7+1 will have a lower cost from a storage overhead standpoint than a 3+1. However, for write-intensive environments, there would be more parity contention with a 7+1 and possibly improved read performance given more drives in the stripe.
On the other hand, a 3+1 offers less exposure to a drive failure in a RAID group than a 7+1. However I'm sure you could come up with a mathematical or statistical analysis to prove otherwise. So, in general, take a look at your application read and write characterize as well as I/O size and patterns and factor those into your decision to use a 3+1 or 7+1 or some other variation of a RAID parity group.
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