PURPOSES : This study verifies the stability and uniqueness of the traffic assignment algorithm. METHODS : The traffic assignment step of the four-phase traffic demand model is an important step in determining the traffic volume of the link in the process of distributing the O/D traffic volume on each link. In this step, primarily, a link-based algorithm based on user equilibrium has been used. The typical link-based algorithm, FWA, is known to provide uniqueness and stability, in theory, regarding traffic assignment results. However, recent studies have raised the controversy that, in reality, the FWA is less stable and unique depending on the termination criterion applied to the FWA in the traffic assignment step. Stability tests and proportionality tests were conducted for the application of algorithms to widely used commercial software (for example, EMME, CUBE, and TransCAD). RESULTS : According to this study, the uniqueness and stability of the FWA were not followed in the process of actual traffic assignment, unlike the theory. CONCLUSIONS : The traffic assignment model has essentially the same result when the optimum level is reached, irrespective of the program and traffic allocation techniques used. Therefore, efforts will be required to recognize limitations in practice and to produce stable results at an appropriate level when predicting traffic demand, traffic volume, benefits, and feasibility studies using a traffic allocation model.