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To improve the reliability of data storage systems, certain data placement schemes spread replicas corresponding to data stored on each node across several other nodes. When node failures occur, this enables parallelizing the rebuild process which in turn results in reducing the rebuild times. However, the underlying assumption is that the parallel rebuild process is facilitated by sufficient availability of network bandwidth to transfer data across nodes at full speed. In a large-scale data storage system where the network bandwidth for rebuild is constrained, such placement schemes will not be as effective. In this paper, it is shown through analysis and simulation how the spread of replicas across nodes affects system reliability under a network bandwidth constraint. Efficient placement schemes that can achieve high reliability in the presence of bandwidth constraints are proposed. Furthermore, in a dynamically changing storage system, in which the number of nodes and the network rebuild bandwidth can change over time, the data placement can be accordingly adapted to maintain a high level of reliability.