Data-loss models for proactive-tolerance Reed–Solomon storage systems

Proactive fault tolerance increasingly serves as an added protection for data in Reed–Solomon (RS) systems. Compared with declustered placement, grouped placement reduces the failure units and also decreases the repair parallelism, which have the opposite effect on systems reliability. For a RS ($k$, $m$) system, the values of ($k$, $m$) impact storage overhead, fault tolerance and repair traffic. When designing proactive RS storage systems, it is challenging to choose the proper placement scheme and coding scheme.

This paper presents four general reliability equations for estimating the number of data-loss events and the amount of data loss in proactive RS systems using declustered and grouped placement schemes. These equations model the effect of disk/node failures, repair bandwidth, block errors, disk scrubbing, disk/node failure prediction, stripe placement, and coding scheme on the reliability of systems. Moreover, we design a Monte-Carlo based simulator to analyze the reliability of proactive Reed–Solomon systems. The equational results are in good accord with the simulation results, which demonstrates the effectiveness of our proposed equations. Using these mathematical models, we can easily estimate and compare fault tolerant schemes and placement schemes, learn the effect of system parameters on system reliability, facilitating to maintain and design cloud storage systems.