Distributed Storage Allocation for High Reliability

We consider the problem of optimally allocating a given total storage budget in a distributed storage system. A source has a data object which it can code and store over a set of storage nodes; it is allowed to store any amount of data in each storage node, subject to a given total storage budget constraint. A data collector subsequently attempts to recover the original data object by accessing a random fixed-size subset of these storage nodes. Successful recovery of the data object occurs when the total amount of coded data in this subset of storage nodes is at least the size of the original data object. The goal is to determine the amount of data to store in each storage node so that the probability of successful recovery is maximized. We solve this problem in the high recovery probability regime. Our results can be applied to a variety of distributed storage systems, including delay tolerant networks (DTNs), content delivery networks (CDNs), and sensor networks.