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Rebuild Time (minutes)
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0.4 0.6 Server Utilization
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Figure 5.10 Rebuild time versus server utilization for track-based rebuild (Q = 64KB, N D = 5)
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well below such a high utilization to minimize blocking, the rebuild time in practice is likely to be even shorter.
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5.7.2 Sensitivity to Server Utilization
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Figure 5.11 plots the reduction in rebuild time by track-based rebuild versus server utilization. We observe that track-based rebuild consistently achieves signi cant rebuild-time reductions over a wide range of server utilization. This result demonstrates that performance gain of the track-based rebuild algorithm is stable with respect to server utilization.
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5.7.3 Sensitivity to Media Block Size
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In Figure 5.12, we plot the rebuild time versus the media block size at three server utilizations of 0, 0.25 and 0.5 respectively. We observe that rebuild time for block-based rebuild decreases with increases in media block size as larger block size increases the overall disk ef ciency. By contrast, rebuild time for track-based rebuild is relatively insensitive to the media block size used as retrievals are done in whole tracks instead of blocks. Figure 5.13 plots the reduction in rebuild time versus the media block size. As expected, the reduction decreases for increases in media block size as rebuild performance for block-based
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80 Reduction in Rebuild Time (%)
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Server Utilization
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Figure 5.11 Comparison of rebuild time reduction by track-based rebuild (Q = 64KB, N D = 5)
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rebuild improves. However, even at a very large block size of 640KB, track-based rebuild still outperforms block-based rebuild by about 30%.
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5.7.4 Buffer Requirement
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We plot the buffer requirement for the studied algorithms versus number of disks in Figure 5.14 for the Quantum Atlas-10K disk model. We observe that track-based rebuild without buffer sharing has the largest buffer requirement as expected. However, even with buffer sharing track-based rebuild still requires more buffers than block-based rebuild. This is due to the fact that the block size (64KB) used is smaller than the track size (varies from 114.5KB to 167KB) and hence the rebuild buffers dominate the buffer requirement. By contrast, the pipelined rebuild algorithm has only a slightly larger buffer requirement than the best scheme block-based rebuild with buffer sharing. For a ve-disk server, pipelined rebuild requires only 0.7MB to 1.5MB more buffers than block-based rebuild with buffer sharing (see Table 5.3). Note that block-based rebuild with buffer sharing is already optimal because the same server will require just as much buffer without the rebuild option. Therefore, with pipelined rebuild, we can achieve a signi cant gain in rebuild performance through track rebuild and at the same time avoid the large buffer requirement.
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Scalable Continuous Media Streaming Systems
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40 Rebuild Time (minutes)
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Media Block Size (KB)
Block-based Rebuild (0% Utilization) Track-based Rebuild (0% Utilization) Block-based Rebuild (25% Utilization) Track-based Rebuild (25% Utilization) Block-based Rebuild (50% Utilization) Track-based Rebuild (50% Utilization)
Figure 5.12 Rebuild time versus media block size (Quantum Atlas-10K)
5.8 Summary
In this chapter we have investigated two algorithms for rebuilding data lost in a failed disk to a spare disk automatically and transparently. We rst presented a block-based rebuild algorithm derived from the conventional CSCAN disk scheduler and analyzed its performance. A buffersharing scheme was then introduced to eliminate the additional buffer requirement during rebuild. Next, we presented a track-based rebuild algorithm that can reduce the rebuild time by 70 80%. The large buffer requirement incurred in track-based rebuild is then reduced to insigni cant levels by a novel pipelined rebuild algorithm. Numerical results show that it is feasible to completely rebuild a failed disk using the presented rebuild algorithms in a practical amount of time without causing any performance degradation to the media server. While the algorithms presented in this chapter are designed for media servers serving CBR media streams, they can also be extended to media servers serving variable-bit-rate (VBR) media streams. One possibility is to replace xed-size block retrievals with variable-size block retrievals, with the block size corresponding to the video bit-rate. As long as the sizes of the blocks to be retrieved in a disk round is known, we can use the same worst-case analysis as in Section 5.5 to determine how much disk time to allocate for rebuild. The rest of the rebuild process will be similar.
80 Reduction in Rebuild Time (%)
Media Block Size (KB)