# Storing Data: Disks and Files 723 Levels of Redundancy in Software Make Data Matrix 2d barcode in Software Storing Data: Disks and Files 723 Levels of Redundancy

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since the disk wears out Failures do not occur independently either: consider a re in the building, an earthquake, or purchase of a set of disks that come from a bad manufacturing batch) Reliability of a disk array can be increased by storing redundant information If a disk failure occurs, the redundant information is used to reconstruct the data on the failed disk Redundancy can immensely increase the MTTF of a disk array When incorporating redundancy into a disk array design, we have to make two choices First, we have to decide where to store the redundant information We can either store the redundant information on a small number of check disks or we can distribute the redundant information uniformly over all disks The second choice we have to make is how to compute the redundant information Most disk arrays store parity information: In the parity scheme, an extra check disk contains information that can be used to recover from failure of any one disk in the array Assume that we have a disk array with D disks and consider the rst bit on each data disk Suppose that i of the D data bits are one The rst bit on the check disk is set to one if i is odd, otherwise it is set to zero This bit on the check disk is called the parity of the data bits The check disk contains parity information for each set of corresponding D data bits To recover the value of the rst bit of a failed disk we rst count the number of bits that are one on the D 1 nonfailed disks; let this number be j If j is odd and the parity bit is one, or if j is even and the parity bit is zero, then the value of the bit on the failed disk must have been zero Otherwise, the value of the bit on the failed disk must have been one Thus, with parity we can recover from failure of any one disk Reconstruction of the lost information involves reading all data disks and the check disk For example, with an additional 10 disks with redundant information, the MTTF of our example storage system with 100 data disks can be increased to more than 250 years! What is more important, a large MTTF implies a small failure probability during the actual usage time of the storage system, which is usually much smaller than the reported lifetime or the MTTF (Who actually uses 10-year-old disks ) In a RAID system, the disk array is partitioned into reliability groups, where a reliability group consists of a set of data disks and a set of check disks A common redundancy scheme (see box) is applied to each group The number of check disks depends on the RAID level chosen In the remainder of this section, we assume for ease of explanation that there is only one reliability group The reader should keep in mind that actual RAID implementations consist of several reliability groups, and that the number of groups plays a role in the overall reliability of the resulting storage system
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Storing Data: Disks and Files 723 Levels of Redundancy
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Throughout the discussion of the di erent RAID levels, we consider sample data that would just t on four disks That is, without any RAID technology our storage system would consist of exactly four data disks Depending on the RAID level chosen, the number of additional disks varies from zero to four
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Level 0: Nonredundant
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A RAID Level 0 system uses data striping to increase the maximum bandwidth available No redundant information is maintained While being the solution with the lowest cost, reliability is a problem, since the MTTF decreases linearly with the number of disk drives in the array RAID Level 0 has the best write performance of all RAID levels, because absence of redundant information implies that no redundant information needs to be updated! Interestingly, RAID Level 0 does not have the best read performance of all RAID levels, since systems with redundancy have a choice of scheduling disk accesses as explained in the next section In our example, the RAID Level 0 solution consists of only four data disks Independent of the number of data disks, the e ective space utilization for a RAID Level 0 system is always 100 percent
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