Distributed Storage Allocations for Optimal Service Rates

Redundant storage maintains the performance of distributed systems under various forms of uncertainty. This paper considers the uncertainty in node access and download service. We consider two access models under two download service models. In one access model, a user can access each node with a fixed probability, and in the other, a user can access a random fixed-size subset of nodes. We consider two download service models. In the first (small file) model, the randomness associated with the file size is negligible. In the second (large file) model, randomness is associated with both the file size and the system's operations. We focus on the service rate of the system. For a fixed redundancy level, the systems' service rate is determined by the allocation of coded chunks over the storage nodes. We consider quasi-uniform allocations, where coded content is uniformly spread among a subset of nodes. The question we address asks what the size of this subset (spreading) should be. We show that in the small file model, concentrating the coded content to a minimum-size subset is universally optimal. For the large file model, the optimal spreading depends on the system parameters. These conclusions hold for both access models.