Tradeoff for Heterogeneous Distributed Storage Systems between Storage and Repair Cost

In this paper, we consider heterogeneous distributed storage systems (DSSs) having flexible reconstruction degree, where each node in the system has dynamic repair bandwidth and dynamic storage capacity. In particular, a data collector can reconstruct the file at time $t$ using some arbitrary nodes in the system and for a node failure the system can be repaired by some set of arbitrary nodes. Using $min$-$cut$ bound, we investigate the fundamental tradeoff between storage and repair cost for our model of heterogeneous DSS. In particular, the problem is formulated as bi-objective optimization linear programing problem. For an arbitrary DSS, it is shown that the calculated $min$-$cut$ bound is tight.