Rebuild Algorithm in .NET

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5.5.1 Rebuild Algorithm
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Figure 5.5 depicts the track-based rebuild algorithm. In reading data from the data disks, playback data are still retrieved in xed-size blocks but rebuild data are retrieved in tracks. This allows the elimination of rotational latency during rebuild data retrieval. Speci cally, in block-based retrieval, the disk head must wait for the required disk sector to rotate to beneath the disk head before data transfer can begin. In the worst case where the required sector has just passed over the disk head after searching is complete, the disk will have to wait for one complete round of rotation before beginning data transfer. By contrast, under track-based retrieval, the disk head can start data transfer as soon as seeking is completed because the entire track is to be retrieved. Clearly, the reading time is
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Figure 5.5 Track-based automatic data rebuild.
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simply the time for one disk rotation, i.e., W 1 . After reading the corresponding tracks from all (N D 1) disks, the server can then reconstruct the lost track and write it to the spare disk. Additionally, the rebuild process rebuilds tracks sequentially starting from one end of the disk surface with all track retrievals performed back-to-back in one go. For example, let yi , i = 0, 1, . . . , (u 1) and yi y j for i < j, be the track numbers for the u data blocks to be retrieved for playout in a round. Suppose that the next track to rebuild is track number x and a total of v tracks are to be rebuilt. Then the order of retrievals will be y0 , y1 , . . . , yi , x, y j , . . . , yu 1 , where yi x y j . In other words, all v tracks are retrieved in one go between the retrievals of block i and j. Consequently, the seek time between track retrievals is reduced to tseek (1). The rebuild process will retrieve as many tracks as possible in a round for rebuild as long as retrieval performance for normal data blocks can still be guaranteed.
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5.5.2 Analysis of Rebuild Time
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To model the rebuild process, let u (u K ) be the number of media blocks to retrieve for playback and v be the number of tracks to retrieve for rebuild in a service round. Using the
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disk model in Section 5.3.3, the modi ed service round length is bounded from above by tr (u, v) = u + f seek (Ntrk /(u + 2)) + + + Q Q thsw + SYmin SYmin Nsuf f seek (1)
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Q W 1 + f seek (Ntrk /(u + 2)) + v + thsw + W 1 SYmin v 1 tseek (1) + f seek (Ntrk /(u + 2)) Ns (5.30)
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The rst term is the service time for reading u media blocks; the second term is the additional seek time due to rebuild; the third term is the time for reading v tracks, the fourth term is the track-to-track seek time for reading rebuild tracks, and the last term is the head-repositioning delay. Now invoking the continuity condition in equation (5.17), we can determine the maximum number of tracks that can be retrieved for rebuild given there are already u data requests in a round, denoted by V (u), from V (u) = max v|tr (u, v) (N D 1)Q , v = 0, 1, . . . Rv (5.31)
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Given a disk with Nsuf recording surfaces and Ntrk tracks per surface, the rebuild time can then be computed from Trebuild = Ntrk Nsuf (N D 1)Q V (u) Rv (5.32)
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5.5.3 Buffer Requirement
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Under track-based rebuild, tracks retrieved in a service round will be consumed by the reconstruction process to compute the lost tracks for writing to the spare disk in the next service round. With a sector size of S bytes and up to Ymax sectors per track, the maximum buffer requirement for rebuild can be obtained from Br = V (0)(N D 1) SYmax + V (0) SYmax (5.33)
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where the rst term is the buffer for reading from the (N D 1) working disks and the second term is the buffer for writing to the spare disk. Without buffer sharing, the total buffer requirement would be the sum of equations (5.2) and (5.33): Bsum = B p + Br = K (2N D 1)Q + V (0)N D SYmax (5.34)
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Using buffer-sharing technique, we can compute the combined buffer requirement at a given server utilization from Bshare (u) = u(2N D 1)Q + V (u)N D SYmax (5.35)
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