  A new system model reflecting the clustered structure of distributed storage
is suggested to investigate bandwidth requirements for repairing failed storage
nodes. Large data centers with multiple racks/disks or local networks of
storage devices (e.g. sensor network) are good applications of the suggested
clustered model. In realistic scenarios involving clustered storage structures,
repairing storage nodes using intact nodes residing in other clusters is more
bandwidth-consuming than restoring nodes based on information from
intra-cluster nodes. Therefore, it is important to differentiate between
intra-cluster repair bandwidth and cross-cluster repair bandwidth in modeling
distributed storage. Capacity of the suggested model is obtained as a function
of fundamental resources of distributed storage systems, namely, storage
capacity, intra-cluster repair bandwidth and cross-cluster repair bandwidth.
Based on the capacity expression, feasible sets of required resources which
enable reliable storage are analyzed. It is shown that the cross-cluster
traffic can be minimized to zero (i.e., intra-cluster local repair becomes
possible) by allowing extra resources on storage capacity and intra-cluster
repair bandwidth, according to a law specified in a closed-form. Moreover,
trade-off between cross-cluster traffic and intra-cluster traffic is observed
for sufficiently large storage capacity.
