非MDS码存储系统的通用可靠性模型

General reliability model of the non-MDS coded storage system

为了量化基于非最大距离可分码的分布式存储系统的可靠性,从非最大距离可分码的构造矩阵入手,提出了一种求解采用非最大距离可分码编码的数据对象在丢失若干块后数据对象的可修复概率算法。该算法穷举丢失若干块的所有可能组合,并在生成矩阵中判断每种组合相对应的矩阵是否可逆以计算可恢复的概率。随后采用马尔可夫理论,针对此类系统建立较为通用的度量存储系统可靠性的理论模型。该模型能够量化非最大距离可分码容错配置、存储规模、修复带宽、单节点可靠性、单节点容量对存储系统可靠性的影响。最后采用数值分析的方法,以局部修复码为例验证了模型的正确性,比较了不同因素对存储系统可靠性的影响。本模型为采用非最大距离可分码的存储系统的设计和实现提供了理论基础。

An open problem is how different configurations influence the reliability of a storage system using non-maximum distance separable codes as redundancy strategy.This paper proposes a repairable probability algorithm for solving data objects with non-maximum distance separable code encoding by considering the construction matrix of non-maximum distance separable codes.This algorithm exhaustively loses all possible combinations of several blocks and judges whether the matrix corresponding to each combination is reversible for calculating the probability of recoverability.We propose an analytical model based on the Markov chain to quantify the reliability of the non-maximum distance separable coded storage system.This model could quantify the impact of a series of design factors on the reliability of the storage system,such as the effect of non-maximum distance separable code configuration,the capacity of the storage system,the capacity of the object-based storage device nodes,the repair bandwidth,the mean time to data loss of the object-based storage device nodes and so on.Finally,the numerical analytical method is used to verify the correctness of the model and the influence of different factors on the reliability of the storage system.Our model enables system practitioners to decide the appropriate configuration based on their reliability requirements.