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(N D 2) + 1
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of which equation (5.37) becomes a special case of equation (5.43) with Dasyn = 0.
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5.6.2 Active Disk Synchronization
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In deriving the buffer requirement in equation (5.43), we assumed that disks that completed reading a track earlier than others will continue reading the subsequent tracks. While this appears to be making ef cient use of disk time, it is in fact counter-productive. Unlike transaction processing (OLTP) applications, residual disk time in a continuous-media server will not be used for retrieving additional media blocks due to the periodicity of the disk schedule. Therefore, even if there is residual disk time after reading all media blocks and rebuild tracks, the disk will just sit idle until the next service round. This observation motivates us to introduce an active disk synchronization (ADS) scheme to further reduce the buffer requirement in equation (5.43). Speci cally, track retrievals for the surviving disks under ADS are actively synchronized according to the slowest disk. For example, in reading track group i, all disks will start their retrieval for track i at time t = li 1 instead of ti 1, j for disk j as shown in Figure 5.8. Note that the added delay will not affect the normal retrieval process or the rebuild process as they are dimensioned according to the worst-case scenario.
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Figure 5.8 A snapshot of track retrievals at time t = li with Active Disk Synchronization
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Theoretically, with ADS the deviation-bound Dasyn will become zero. In practice, small deviations might still exist because the server is likely to send disk commands serially to each of the surviving disks. Assuming this deviation is small compared to , then Dasyn and the buffer requirement is reduced to Br = (2N D 2) SYmax (5.45) = 1 for Dasyn (5.44)
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5.7 Performance Evaluation
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Using the performance models derived in the previous sections, we present in this section numerical results computed for ve disk drive models to quantitatively compare the studied algorithms. The disks parameters are extracted from the disk speci cations in Ganger et al. [21] and summarized in Table 5.2. Unless stated otherwise, the results are computed using a disk array con guration of four data disks, one parity disk, and one spare disk.
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5.7.1 Comparison of Rebuild Time
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Figures 5.9 and 5.10 show the rebuild time versus server utilization for block-based rebuild and track-based rebuild respectively. We observe that the rebuild time increases modestly until around a utilization of 0.8, after which it increases rapidly due to the limited capacity available for rebuild. For example, rebuild time for the Quantum Atlas-10K disk increases from 44.4 minutes at = 0.5 to 221.9 minutes at = 0.9 for block-based rebuild. Comparing Figure 5.9 with Figure 5.10, it is clear that track-based rebuild signi cantly outperforms blockbased rebuild. With the same disk model, the rebuild time for track-based rebuild is only 12.8 minutes at = 0.5 and 87.7 minutes at = 0.9. This result is encouraging, as rebuilding a failed disk requires less than 1.5 hours even at a server utilization of 0.9. Given that a service provider is likely to dimension a system to operate
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Table 5.2 Parameters of ve disk models Quantum Atlas-III 8057 10 0 ms 0.999 ms 7200 rpm 512 bytes 256 sectors 168 sectors 9.1GB 1.663 ms Quantum Atlas-10K 10042 6 0 ms 0.176 ms 10025 rpm 512 bytes 334 sectors 229 sectors 9.1GB 1.245 ms Seagate Barracuda 5172 5 0 ms 0.1 ms 7200 rpm 512 bytes 186 sectors 119 sectors 2GB 1.943 ms Seagate Cheetah 6581 8 0 ms 0.195 ms 10033 rpm 512 bytes 195 sectors 131 sectors 4.5GB 0.636 ms
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Parameter No. of tracks No. of surfaces Fixed overhead Head-switching time Spinning speed Sector size Max track size Min track size Disk capacity Track-to-track seek
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IBM 9ES 11474 5 0 ms 0.062 ms 7200 rpm 512 bytes 390 sectors 247 sectors 9GB 1.086 ms
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Source: Ganger et al. [21]
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Rebuild Time (minutes)
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Server Utilization
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Quantum Atlas-III Quantum Atlas-10K Seagate Barracuda Seagate Cheetah IBM 9ES
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Figure 5.9 Rebuild time versus server utilization for block-based rebuild (Q = 64KB, N D = 5)