PURPOSES : This study aims to investigate the factors that affect the practical condition of the convergence and convergence behaviors of the asymmetric transportation equilibrium problem (ATEP). METHODS : To achieve this objective, a real network experiment is critical because the crux of the problem associated with the ATEP is the difficulty of verifying the unique condition in real networks owing to asymmetric modeling. The study employed a numerical approach to deal with this problem because analytical derivation based on small networks has a limitation in extending its findings to practical applications. The study addressed the problems using large real networks and different types of interactions, including links and modes. An investigation of the factors that have the potential to affect the convergence of the problem was conducted with the solution algorithm, which is the double projection method. RESULTS : The study presented a partial answer to the question of whether the ATEP's convergence condition is too strong. In link interactions, demand intensities and symmetric features within the cost function along with the network configuration were determined to relax the convergence condition. In mode interactions, the degree of overlap of the route composition and the controlled asymmetric interactions in the cost function were determined to affect the convergence condition. CONCLUSIONS : The results suggested that the modeling of link interactions for a more complicated transportation system design enabled the modeling of complex asymmetric interactions as long as the demand intensity of the network was not strong. In the case of mode interactions, whereas it was not possible to control the route composition, it was considered possible to a degree where the use of a distinct route was observed for each class (for example, designated truck lanes).