Optimal Read-Once Parallel Disk Scheduling

An optimal prefetching and I/O scheduling algorithm L-OPT, for parallel I/O systems, using a read-once model of block references is presented. The algorithm uses knowledge of the next $L$ references, $L$-block lookahead, to create a minimal-length I/O schedule. For a system with $D$ disks and a buffer of capacity $m$ blocks, we show that the competitive ratio of L-OPT is $Theta(sqrt{mD/L})$ when $L geq m$, which matches the lower bound of any prefetching algorithm with $L$-block lookahead. Tight bounds for the remaining ranges of lookahead are also presented. In addition we show that L-OPT is the optimal offline algorithm: when the lookahead consists of the entire reference string, it performs the absolute minimum possible number of I/Os. Finally, we show that L-OPT is comparable with the best online algorithm with the same amount of lookahead; the ratio of the length of its schedule to the length of the optimal schedule is always within a constant factor.