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Applications in high-speed networks like Grids often require to transfer large volumes of data to remote locations under certain time constraints. This requires a network reservation, mechanism for the large data transfer requests. It is possible that some network capacity is available even after fulfilling the capacity requirements of the requests. The sharing of the available network capacity, called residual capacity, has direct impact on the actual time taken to serve a request. In this paper, we propose a novel weighted capacity sharing model to predict the performance of the deadline-constrained data transfers. A weighted sharing scheme is desirable since a request with higher capacity requirement should get higher share of the residual capacity than that of a request with lower capacity requirement in order to reduce its transfer time. We calculate the blocking probabilities and mean flow time using our scheme and compare the results with an existing scheme of equal residual capacity sharing. The results show that weighted-sharing scheme is better than equal capacity-sharing scheme as it reduces the mean transfer time of requests of a higher capacity requirement class. We also validate the model through simulations.