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In this arrangement, each data block is protected by two parity blocks:
one interdisk parity block on a different disk and on intradisk parity block
on the same disk.
This approach may reduce a disk's eective nonrecoverable read error
rate because if one block in an extent is lost, it can be recovered from the
remaining sectors and parity on the disk. Of course, if multiple blocks in
the same extent are lost, the system must rely on redundancy from other
disks.
(a) Assuming that a disk's nonrecoverable read errors are independent
and occur at a rate of one lost 512 byte sector per 10 15 bits read,
what is the effective nonrecoverable read error rate if the operating
system stores one parity block per seven data blocks on the disk?
Hint: You may find the bc or dc arbitrary-precision calculators use-
ful. These programs are standard in many Unix, Linux, and OSX
distributions. See the man pages for instructions.
(b) Why is the above likely to significantly overstate the impact of intra-
disk redundancy?
9. Many RAID implementations allow on-line repair in which the system
continues to operate after a disk failure, while a new empty disk is inserted
to replaced the failed disk, and while regenerating and copying data to the
new disk.
Sketch a design for a 2-disk, mirrored RAID that allows the system to
remain on-line during reconstruction, while still ensuring that when the
data copying is done, the new disk is properly reconstructed (i.e., it is an
exact copy of other disk.)
In particular, specify (1) what is done by a recovery thread, (2) what is
done on a read during recovery, and (3) what is done on a write during
recovery. Also explain why your system will operate correctly even if a
crash occurs in the middle of reconstruction.
10. Suppose you are willing to sacrice no more than 1% of a disk's bandwidth
to scrubbing. What is maximum frequency at which you could scrub a
1 TB disk with 100 MB/s bandwidth?
11. Suppose a 3 TB disk in a mirrored RAID system crashes. Assuming the
disks used in the system can sustain 100MB/s sequential bandwidth, what
is the minimum mean time to repair that can be achieved? Why might a
system be configured to perform recovery slower than this?
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