Mirrored Disk Organization Reliability Analysis

Disk mirroring or RAID level 1 (RAID1) is a popular paradigm to achieve fault tolerance and a higher disk access bandwidth for read requests. We consider four RAID1 organizations: basic mirroring, group rotate declustering, interleaved declustering, and chained declustering, where the last three organizations attain a more balanced load than basic mirroring when disk failures occur. We first obtain the number of configurations, A(n, i), which do not result in data loss when i out of n disks have failed. The probability of no data loss in this case is A(n, i)/matrix of(n, i). The reliability of each RAID1 organization is the summation over 1 les i les n/2 of A(n, i)rn-i (1 - r) i, where r denotes the reliability of each disk. A closed-form expression for A(n, i) is obtained easily for the first three organizations. We present a relatively simple derivation of the expression for A(n, i) for the chained declustering method, which includes a correctness proof. We also discuss the routing of read requests to balance disk loads, especially when there are disk failures, to maximize the attainable throughput