Today efficient traffic management seems to be impossible without the support of the artificial intelligence systems based on mathematical models of traffic flow assignment since a modern road network is a large-scale system with huge amounts of elements. The present paper is devoted to the route-flow traffic assignment problem, which solution is the most valuable from decision-making perspectives. The paper aims to fill the gap in the relation between the column generation process and the uniqueness of the equilibrium route-flow traffic assignment pattern. The independence of routes is showed to be highly significant when travel time functions are arc-additive. Indeed, on the one hand, the independence of routes is proved to guarantee the uniqueness of the equilibrium route-flow traffic assignment pattern. On the other hand, the independence of routes appears to be crucial for column generation when solving the route-flow traffic assignment problem since the equilibrium travel time is proven to be decreased only by adding independent candidate route. Obtained results contribute to the development of algorithms for route-flow traffic assignment based on travel times equilibration procedure.