On the Repair Bandwidth and Repair Access of Two Storage Systems: Large-Scale and Uniform Rack-Aware Storage Systems

In this paper, we consider two rack-aware storage systems. First, large-scale rack-aware storage system, which is very common in large-scale storage system, is a rack-aware storage system where all sizes of racks are at least the number of redundant nodes. For such storage system, we prove that any Maximum Distance Separable (MDS) codes can have optimal inter-rack repair bandwidth and give a closed-form representation of all repair schemes with optimal inter-rack repair bandwidth. Furthermore, we show that the optimal repair access and optimal inter-rack repair bandwidth can be attained simultaneously for such storage system. Second, we investigate the rack-aware storage system of all racks with the same size, which is called uniform rack-aware storage system. We prove that, except the trivial cases, we cannot attain optimal inter-rack repair bandwidth and optimal repair access for such storage system at the same time. Specifically, we establish the lower bound of repair access for a repair scheme with optimal interrack repair bandwidth, which is tight for some parameters, and also the tight lower bound of inter-rack repair bandwidth for a repair scheme with optimal repair access.