Relations Between Entity Sizes and Error-Correction Coding Codewords and Effective Data Loss

Erasure-coding redundancy schemes are employed in storage systems to cope with device and component failures. Data durability is assessed by the Mean Time to Data Loss (MTTDL) and the Expected Annual Fraction of Entity Loss (EAFEL) reliability metrics. In particular, the EAFEL metric assesses losses at an entity, say file, object, or block level. This metric is affected by the number of codewords that entities span. The distribution of this number is obtained analytically as a function of the size of the entities and the frequency of their occurrence. The deterministic and the random entity placement cases are investigated. It is established that for certain deterministic placements of variable-size entities, the distribution of the number of codewords that entities span also depends on the actual entity placement. To evaluate the durability of storage systems in the case of variable-size entities, we introduce the Expected Annual Fraction of Effective Data Loss (EAFEDL) reliability metric, which assesses the fraction of stored user data that is lost by the system annually at the entity level. The MTTDL, EAFEL, and EAFEDL metrics are assessed analytically for erasure-coding redundancy schemes and for the clustered, declustered, and symmetric data placement schemes. It is demonstrated that an increased variability of entity sizes results in improved EAFEL, but degraded EAFEDL. It is established that both reliability metrics are adversely affected by the size of the erasure-coding symbols.