Reliability of erasure coded storage systems: A geometric approach

We consider the probability of data loss in an erasure coded distributed storage system. Data loss in an erasure coded system depends on the repair duration and the failure probability of individual disks. This dependence on the repair duration complicates the data loss probability analysis. In previous work, the data loss probability of such systems has been studied under the assumption of exponentially distributed disk life and disk repair durations, using well-known analytic methods from the theory of Markov processes. Here, we assume that the repair duration is a constant and derive an upper bound on the probability of data loss by calculating the volumes of specific polytopes that are determined by the code. Closed form bounds are exhibited for some example codes.