Competitive Parallel Disk Prefetching and Buffer Management

Abstract

We provide a competitive analysis framework for online prefetching and buffer management algorithms in parallel I/O systems, using a read-once model of block references. This has widespread applicability to key I/O-bound applications such as external merging and concurrent playback of multiple video streams. Two realistic lookahead models, global lookahead and local lookahead, are defined. Algorithms NOM and GREED, based on these two forms of lookahead are analyzed for shared buffer and distributed buffer configurations, both of which occur frequently in existing systems. An important aspect of our work is that we show how to implement both of the models of lookahead in practice using the simple techniques of forecasting and flushing.Given a D-disk parallel I/O system and a globally shared I/O buffer that can hold up to M disk blocks, we derive a lower bound of Ω(D) on the competitive ratio of any deterministic online prefetching algorithm with O(M) lookahead. NOM is shown to match the lower bound using global M-block lookahead. In contrast, using only local lookahead results in an Ω(D) competitive ratio. When the buffer is distributed into D portions of M/D blocks each, the algorithm GREED based on local lookahead is shown to be optimal, and NOM is within a constant factor of optimal. Thus we provide a theoretical basis for the intuition that global lookahead is more valuable for prefetching in the case of a shared buffer configuration, whereas it is enough to provide local lookahead in the case of a distributed configuration. Finally, we analyze the performance of these algorithms for reference strings generated by a uniformly-random stochastic process and we show that they achieve the minimal expected number of I/Os. These results also give bounds on the worst-case expected performance of algorithms which employ randomization in the data layout.