Reliable and Fault-Tolerant Storage Systems in Visual Studio .NET

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Reliable and Fault-Tolerant Storage Systems
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rebuild the disk that failed. Nevertheless, this is equivalent to the case without failure prediction and hence will not degrade rebuild performance. For simplicity, we will not make use of this failure prediction feature in the rest of the chapter.
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5.4.1 Sparing Scheme
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To support automatic data rebuild, a dedicated spare disk is reserved to store data reconstructed in the rebuild process. The spare disk is connected to the server at all times but is not used during normal mode and degraded mode of operation. In this sparing scheme, the recomputed data will be stored in the spare disk, which will replace the failed disk once the rebuild process is completed. Note that human intervention is still required to replace the failed disk with another spare disk to cater for another disk failure but this is less time-critical.
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5.4.2 Rebuild Algorithm
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The challenge of automatic rebuild is to proceed with the rebuild process without interrupting user services. Speci cally, all retrievals in a disk service round must nish within Tr seconds and the addition of rebuild requests must not violate this limit. Clearly, we can only utilize unused disk capacity to serve rebuild requests. Once rebuild blocks from the surviving disks are retrieved into memory, the server can then perform an erasure-correction computation to reconstruct the lost media blocks and store them to the spare disk. This process repeats until all the media blocks lost in the failed disk are reconstructed to the spare disk, which then simply replaces the failed disk to bring the system back into normal mode of operation. The failed disk will later be replaced or repaired manually and a new spare disk will be reinserted into the system to prepare for the next rebuild cycle.
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5.4.3 Analysis of Rebuild Time
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A key performance metric in evaluating automatic data rebuild algorithms is rebuild time, de ned as the time required to completely rebuild data in the failed disk to the spare disk. For a server with N D disks (one of which has failed) and one spare disk, the rebuild process consists of reading (N D 1) blocks for each parity group from the surviving (N D 1) disks and reconstructing the lost media block for storage in the spare disk. Note that this is true even if the failed disk happens to be the parity disk because all (N D 1) data blocks in a parity group are required to recompute the parity block for storage in the spare disk. Let u, 0 u K , be the number of active streams in the server. We de ne a server utilization , 0 1, as follows: = u K (5.19)
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Now the number of rebuild blocks retrieved by a working disk in a service round, denoted by n b , will be given by nb = K u (5.20)
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which is the same for all disks. Given that there are (N D 1) working disks, the rate at which rebuild data are retrieved, denoted by Rrb , is then given by Rrb = (N D 1)n b Q (N D 1)n b Q = Tr (N D 1)(Q/Rv ) (5.21)
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= n b Rv
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where the numerator is the total amount of rebuild data retrieved in a service round, and the denominator is the length of a service round. Note that if Rrb is only the rate at which rebuild data are retrieved, the reconstruction process will consume (N D 1) rebuild blocks to reconstruct one lost media block. Therefore, the rebuild rate Rrebuild , de ned as the rate at which lost data are reconstructed, can be computed from Rrb : Rrebuild = n b Rv Rrb = (N D 1) (N D 1) (5.22)
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Using equations (5.19) and (5.20), we can simplify equation (5.22) into Rrebuild = (K u)Rv (N D 1) (1 ) KRv = (N D 1)
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(5.23)
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Equation (5.23) computes the achievable rebuild rate under a given server utilization. Let G be a disk s storage capacity. Assuming storage in the entire disk array is fully utilized, we can then calculate the rebuild time from Trebuild = G G(N D 1) = Rrebuild KRv (1 ) (5.24)
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