  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.
