Competitive Parallel Disk Prefetching and Buffer Management

Abstract

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 COMPETITIVE PARALLEL DISK PREFETCHING 153 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 ' Ž . hold up to M disk blocks, we derive a lower bound of ⍀ D on the competitive Ž . 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 Ž . contrast, using only local lookahead results in an ⍀ 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. ᮊ

PC-OPT: optimal offline prefetching and caching for parallel I/O systems

“…Such blocks have the adverse effect of choking the buffer and reducing the parallelism in fetching more immediate blocks. In earlier works [7], [15], we showed that, even when the problem is reduced to just prefetching decisions, it is not trivial: In this case, when each block is accessed exactly once, the problem of deciding which blocks to fetch in an I/O is non-intuitive. In the general case considered here, the buffer manager has to deal with the additional complexity of deciding which blocks to cache and which to evict, in conjunction with prefetching.…”

“…The problem of online scheduling of read-once reference strings in a multiple-disk system was first addressed in [7]. A lower bound of ð ffiffiffiffi D p Þ on the competitive ratio of any prefetching algorithm with M-block lookahead was established and a greedy prefetching algorithm was shown to attain the bound.…”

“…For read-once reference strings, analysis of algorithms exploiting a randomized data placement was studied in [6], [7], [20], [21]. In a generalization of the stall model to parallel disks, [17] designed a sophisticated offline approximation algorithm to service read-many reference strings.…”

“…The interrelation between prefetching and caching decisions makes designing effective buffer management policies challenging. Applying these techniques to parallel I/O systems is fundamentally different from that in systems with a single disk [7], [17], [22]. Intuitively appealing greedy prefetching policies that are suitable for single-disk systems can have poor worst-case and averagecase performance for multiple disks [7], [21].…”

“…Applying these techniques to parallel I/O systems is fundamentally different from that in systems with a single disk [7], [17], [22]. Intuitively appealing greedy prefetching policies that are suitable for single-disk systems can have poor worst-case and averagecase performance for multiple disks [7], [21]. Similarly, traditional caching strategies do not account for parallelism in the I/O accesses and, consequently, may not perform well in a multiple-disk system.…”