Trade-off for heterogeneous distributed storage systems between storage and repair cost

We consider heterogeneous distributed storage systems (DSSs) having flexible reconstruction degree, where each node in the system has nonuniform repair bandwidth and nonuniform storage capacity. In particular, a data collector can reconstruct the file using some $k$ nodes in the system and, for a node failure, the system can be repaired by some set of active nodes. Using min-cut bound, we investigate the fundamental trade-off between storage and repair costs for our model of the heterogeneous DSS. Further, the problem is formulated as bi-objective optimization linear programing problem for various heterogeneous DSSs. For some DSSs, it is shown that the calculated min-cut bound is tight.