We provide a competitive analysis framework for online prefetching and buffer management algorithms in parallel IrO systems, using a read-once model of block references. This has widespread applicability to key IrO-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 IrO system and a globally shared IrO buffer that can hold up to M disk blocks, we derive a lower bound of V '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 V D. competitive ratio. When
the buffer is distributed into D portions of MrD 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 IrOs. These results also give bounds on the worst-case expected performance of algorithms which employ randomization in the data layout.
1 A preliminary version of this paper has appeared in the Proceedings of the ACM Fifth
Annual Workshop on IrO in Parallel and Distributed Systems.
2 Supported in part by an IBM graduate fellowship. Part of this work was done while the
author was visiting Lucent Technologies, Bell Laboratories, Murray Hill, NJ.
3 Supported in part by a grant from the Schlumberger Foundation and by the National
Science Foundation under Grant CCR-9704562.
4 Supported in part by the National Science Foundation under Grant CCR-9522047 and by
Army Research Office MURI Grant DAAH04-96-1-0013. Part of this work was done while
the author was visiting Lucent Technologies, Bell Laboratories, Murray Hill, NJ.