# FastScale: Accelerate RAID Scaling by Minimizing Data Migration

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3 D New data is filled in D Figure 2: RAID scaling from 3 disks to 5 using, where m n. into one region. In Figure 2, different regions are separated with a wavy line. For different regions, the ways to data migration and data filling are exactly identical. In a region, all of the data blocks within a parallelogram will be moved. The base of the parallelogram is 2, and the height is 3. In other words, 2 data blocks are selected from each old disk and migrated to new disks. The 2 blocks are sequential, and the start address is disk no. Figure 2 depicts the moving trace of each migrating block. For one moving data block, only its physical disk number is changed while its physical block number is unchanged. As a result, the five columns of two new disks will contain 1, 2, 2, 1, and migrated data blocks, respectively. Here, the data block in the first column will be placed upon disk 3, while the data block in the fourth column will be placed upon disk 4. The first blocks in columns 2 and 3 are placed on disk 3, and the second blocks in columns 2 and 3 are placed on disk 4. Thus, each new disk has 3 data blocks. After data migration, each disk, either old or new, has 3 data blocks. That is to say, regains a uniform data distribution. The total number of data blocks to be moved is 2 3 = 6. This reaches the minimal number of moved blocks, (5 3) (2/(3 + 2)) = 6. We can claim that the RAID scaling using can satisfy Requirement 1 and Requirement 2. Let us examine whether can satisfy Requirement 3, i.e., fast data addressing. To consider how one logical data block is addressed, we divide all the data space in the RAID into three categories: original and unmoved data, original and migrated data, and new data. A conclusion can be drawn from the following description D New data is filled in D Figure 3: RAID scaling from 2 disks to 5 using, where m < n. that the calculation overhead for the data addressing is very low. The original and unmoved data can be addressed with the original addressing method. In this example, the ordinal number of the disk holds one block x can be calculated: d = x mod 3. Its physical block number can be calculated: b = x/3. The addressing method for original and migrated data can be obtained easily from the above description about the trace of the data migration. b = x/3. For those blocks in the first triangle, i.e., blocks, 3, and 4, we have d = d + 3. For those blocks in the last triangle, i.e., blocks 7, 8, and 11, we have d = d + 2. Here, d is their original disk. Each region can hold 5 2 = 1 new blocks. In one region, how those new data blocks are placed is shown in Figure 2. If block x is a new block, it is the y th new block, where y = x Each stripe holds 2 new blocks. So, we have b = y/2. The first two new blocks in each region are placed on Blocks of Disk and 4. For the other blocks, d = (y mod 2) + (b mod 5) 1. Example 2: In the above example, the number of the old disks m and the number of the new disks n satisfy the condition: m n. In the following, we inspect the case when m < n. Take RAID scaling from 2 disks to 5 as an example. Here, m = 2 and n = 3. Likewise, in a region, all of the data blocks within a parallelogram will be moved. The base of the parallelogram is 3, and the height is 2. 3 consecutive data blocks are selected from each old disk and migrated to 3

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