A semi-analytical method based on alternate projections on a linear vector space is used to construct a service matrix from a traffic matrix, where the traffic matrix represents the bandwidth requested by the edge nodes and the service matrix represents how the bandwidth will be distributed by the core of an optical star network that operates in a Time Division Multiplexing mode. The algorithm iterates over a mathematical expression of complexity O(N^2), where N denotes the number of edge nodes. The complexity of the method is therefore O(kN^2) where k denotes the number of iterations needed to converge. With N large enough one observes that k\le\leN and hence this expression tends to O(N^2). Results show that the service matrices obtained with this projection method have very high measures of similarity to the original traffic matrix, with an average similarity greater than 95% for N \geqslant 32 . The method is robust to inadmissible/bursty traffic and yields equal or improved delay performance in the optical network compared to other allocation methods.