  A key function of cloud infrastructure is to store and deliver diverse files,
e.g., scientific datasets, social network information, videos, etc. In such
systems, for the purpose of fast and reliable delivery, files are divided into
chunks, replicated or erasure-coded, and disseminated across servers. It is
neither known in general how delays scale with the size of a request nor how
delays compare under different policies for coding, data dissemination, and
delivery.
  Motivated by these questions, we develop and explore a set of evolution
equations as a unified model which captures the above features. These equations
allow for both efficient simulation and mathematical analysis of several
delivery policies under general statistical assumptions. In particular, we
quantify in what sense a workload aware delivery policy performs better than a
workload agnostic policy. Under a dynamic or stochastic setting, the sample
path comparison of these policies does not hold in general. The comparison is
shown to hold under the weaker increasing convex stochastic ordering, still
stronger than the comparison of averages.
  This result further allows us to obtain insightful computable performance
bounds. For example, we show that in a system where files are divided into
chunks of equal size, replicated or erasure-coded, and disseminated across
servers at random, the job delays increase sub-logarithmically in the request
size for small and medium-sized files but linearly for large files.
