Reliability-bandwidth tradeoffs for distributed storage allocations

We consider the allocation of coded data over nodes in a distributed storage system under a budget constraint. A system with failed nodes can recover the original data of unit size if the amount of data in the active nodes is at least a unit. Building on the work of Leong et al. [1], we introduce the concepts of tight allocations and repair bandwidth in this distributed setting. For tight allocations, the amount of data in the failed nodes gives a lower bound to the repair bandwidth required to put the system back to its original state. Using this bound, we define the Minimum Expected Repair Bandwidth (MERB) to study the tradeoffs between reliability and repair bandwidth, both empirically and by proving bounds on MERB in terms of the reliability. We show that even computing MERB for a general allocation is #P-Hard and suggest a simpler objective function to optimize it approximately. Finally, we study the asymptotic behavior of MERB for large systems and show two distinct optimal allocation regimes depending on the failure probability of the storage nodes.