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A cost-effective approach to building up scalable video-on-demand (VoD) servers is to couple a number of VoD servers together in a cluster. In this article, we study a crucial video replication and placement problem in a distributed storage VoD cluster for high quality and high availability services. We formulate it as a combinatorial optimization problem with objectives of maximizing the encoding bit rate and the number of replicas of each video and balancing the workload of the servers. It is subject to the constraints of the storage capacity and the outgoing network bandwidth of the servers. Under the assumption of single fixed encoding bit rate for all videos, we give an optimal replication algorithm and a bounded-placement algorithm for videos with different popularities. To reduce the complexity of the replication algorithm, we present an efficient algorithm that utilizes the Zipf-like video popularity distributions to approximate the optimal solution. For videos with scalable encoding bit rates, we propose a heuristic algorithm based on simulated annealing. We conduct a comprehensive performance evaluation of the algorithms and demonstrate their effectiveness via simulations over a synthetic workload set.