On the maintenance of distributed storage systems with backup node for repair

We consider a hierarchical DSS where the content is stored with coding in storage nodes and without coding in a backup node. We analyze the system where mobile nodes request the content from the storage nodes. Backup node is assumed to be accessible by storage nodes only in the case where repairs are required. Under this scenario, we derive the upper bound on the file size bound as well as establish critical points on the trade-off curve known as Minimum Storage Regenerating (MSR) and Minimum Bandwidth Regenerating (MBR) points. Next, we propose optimal code constructions by utilizing existing regenerating codes. Furthermore, we analyze the statistics of maintenance and data access costs under Poisson model for node failures and data requests. We derive expressions for expected values and variances of both such costs. Finally, numerical results are provided where we show that the most studied points in the literature (MSR and MBR) are not always optimal with respect to total cost. We also point out that variance of maintenance cost may be much important than variance of data access cost.