![]() This organization with n parity disks will have n(n− 1)/2 data disks. The second, " complete " organization corresponds to a closer weave, where all parity stripes intersect and each intersection contains a parity disk. Hence a square layout organization with n 2 data disks will have 2n parity disks. The first, " square " organization is a traditional square layout where data disks are formed into a square and the parity stripes are formed by the rows and columns in the square. To illustrate the power of our method, we apply it to two distinct, archival two-dimensional array organizations. The overall probabilities that a given number n of disk failures will cause a data loss is then given by the ratio of the total number of fatal disk failures involving n disks over the total number of possible failures of n disks. ![]() ![]() ![]() We then use this representation to identify and enumerate minimal sets of disk failures, say, triple failures, quadruple failures and so forth, that will cause a data loss. We start by representing each array organization by a graph where each parity stripe, and its associated parity disk, is represented by a node and each data disk by an edge. We present a general method for estimating the risk of data loss in arbitrary two-dimensional RAID arrays where each data disk belongs to exactly two single-parity stripes. Our results show that rectangular layouts are significantly more reliable than layouts based on the most basic Pyramid codes, but that they also require more disk accesses to recover from disk failures. We compare the two layouts by measuring their robustness to data loss, their one-year survival rate, and the expected number of number of disks that must be involved to recover from both single and multiple disk failures. In this variant, a stripe has a Q-parity calculated from the data disks in the stripe, but the data disks are also organized into smaller groups where each group has a separate P-parity calculated as the exclusive-or of the data disks in the group. We can view this layout as an example RAID Level 6 variant. Our second layout is based on the most basic pyramid code. Recovery from a disk failure proceeds by preferring columns when reconstructing lost data, and thereby has fewer reads than the parity overhead would normally suggest. Our first organization is a flat XOR code that organizes the data disks into a rectangle with fewer rows than columns, and adds a simple parity disk to each row and column. We investigate two two-failure tolerant disk layouts that have lower parity overhead than the number of disks read (and hence powered-on) for recovering data on lost drives would suggest. Of all such tasks, reconstructing data after a disk failure is the one that is likely to have the highest energy footprint and the most impact on the overall power consumption of the array, because it typically involves powering up all the disks belonging to the same reliability stripe as the failed disk and keeping them running for considerable time at each occurrence. The best strategy for such systems is to keep their disks powered-off unless they have to be powered up to access their contents, to reconstruct lost data, or to perform other disk maintenance tasks. Archival data storage systems contain data that must be preserved over long periods of time but which are often unlikely to be accessed during their lifetime.
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