  A new system model reflecting the clustered structure of distributed storage
is suggested to investigate interplay between storage overhead and repair
bandwidth as storage node failures occur. 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, node storage capacity, intra-cluster repair bandwidth and cross-cluster
repair bandwidth. The capacity is shown to be asymptotically equivalent to a
monotonic decreasing function of number of clusters, as the number of storage
nodes increases without bound. Based on the capacity expression, feasible sets
of required resources which enable reliable storage are obtained in a
closed-form solution. Specifically, 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 the law specified in the closed-form. The network
coding schemes with zero cross-cluster traffic are defined as intra-cluster
repairable codes, which are shown to be a class of the previously developed
locally repairable codes.
