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This paper describes an approach to real-time decision-making for quality of service based scheduling of distributed asynchronous data replication. The proposed approach addresses uncertainty and variability in the quantity of data to replicate over low bandwidth fixed communication links. A dynamic stochastic knapsack is used to model the acceptance policy with dynamic programming optimization employed to perform offline optimization. The obtained optimal values of the input variables are used to build and train a multilayer neural network. The obtained neural network weights and configuration can be used to perform near optimal accept/reject decisions in real-time. Offline processing is used to establish the initial acceptance policy and to verify that the system continues to perform near-optimally. The proposed approach is implemented via simulation enabling the evaluation of a variety of scenarios and refinement of the scheduling portion of the model. The preliminary results are very promising.