In Partial Fulfillment of the Requirements for the Degree of
Master of Science
Will defend his thesis
While Markov models are widely used to evaluate the reliability of storage organizations, they have two important limitations. First, they assume that all repair times are distributed according to an exponential law, which is not ture. Second, they typically return the MTTDL of the organization rather that its actual reliability.
We present here the first empirical evaluation of the performance of Markov models applied to storage solutions as simple as mirrored disks and as sophisticated as SSPiRAL arrays. To achieve our goal, we have represented each disk organization by a discrete simulation model that allowed us to compute confidence intervals for the probability that the disk organization would not lose data over a five-year lifetime and compared these intervals with the values predicted by the Markov models of the same organizations.
We found that the confidence intervals obtained assuming that repair times were exponentially distributed were almost always in agreement with the values predicted by the corresponding Markov models. In addition, we found surprisingly little difference between the confidence intervals obtained assuming deterministic repair times and those assuming that repair times were distributed according to an exponential law. The main conclusion of our study is that we have no reason so far to question the accuracy of the reliability figures produced by Markov models for the disk array organizations we investigated.