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The end-to-end traffic volume between source and destination nodes in a telecommunication carrier network is essential traffic information for computing the necessary link capacity for the network's primary and backup paths. However, the end-to-end traffic volumes are not frequently measured because it puts additional loads onto the network equipment, and the measuring devices are too expensive to install on all the links of the network. Under these circumstances, network carriers must estimate the link capacity under limited available traffic information. We propose a link-capacity design model for shared protection to meet this demand. Shared protection is effective for economically constructing networks; however, it complicates network design. In this model, we formulate the link-capacity design as a series of linear programming problems. Since the algorithm for solving the model is time-consuming, we modified it to accelerate computation. We evaluated the proposed model from the viewpoint of the gap between computational and actual bandwidths in several networks and the proposed algorithms from the viewpoint of computing time.