The paper presents a comparison between three approaches to solving the length-bounded maximum multicommodity flow problem with unit edge-lengths. Following the first approach, Garg and Könemann’s, we developed an improved fully polynomial-time approximation scheme for this problem. As the second alternative, we considered the well-known greedy approach. The third approach is the one that yields exact solutions by means of a standard LP solver applied to an LP model on the time-expanded network. Computational experiments are carried out on benchmark graphs and the graphs that model software defined satellite networks, to compare the proposed algorithms with an exact linear programming solver. The results of the experiments demonstrate a trade-off between the computing time and the precision of algorithms under consideration.