Methods for the optimal allocation of bandwidth among a plurality of video-on-demand (VOD) programs available on each link of a VOD tree network, where a server at the root node of the tree network broadcasts the multiple VOD programs. Each node in the network has demands for a subset of the programs and each link connecting nodes in the network has a limited amount of available bandwidth capacity. The available bandwidth is allocated on each link optimally among all programs that are carried on that link. The bandwidth allocated to a specific program may be different on different links of the network, as the bandwidth allocated may be decreased, but not increased, from one link to the next along the paths from the root node to the destination nodes. The methods use equitable resource allocation models with a lexicographic minimax objective function. The first method finds optimal solutions while satisfying the capacity constraints on all links, tree-like ordering constraints for the bandwidth allocated to each of the programs, and lower and upper bounds on bandwidth allocation for each program. The second method finds optimal solutions to a more restrictive scheme that imposes additional constraints which require equal bandwidth allocation for a specific program on all relevant links emanating from the same node.
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