A probabilistic limit on the virtual size of replicated disk systems

Recently, there has been considerable interest in parallel disk drive systems, in which full or partial replication of the stored data is used for both fault tolerance and enhanced performance. The performance-enhancement derives both from the ability to do parallel reads, and from the reduction of seek time which results from being able to assign a read to whichever drive will produce the shortest seek. Although earlier work implied that for a k-drive system, mean seek distance for read converges to 0 as k→α, a refined analysis is presented which shows that this limit is actually nonzero. It is further shown that the system behaves probabilistically as if k were small, no matter how large the physical value of k is