The paper deals with simulation of congested road networks through dynamic traffic assignment models and presents a new quasi-dynamic traffic assignment model that improves realism and effectiveness of both usual static traffic assignment models and other quasi-dynamic models recently introduced in the literature, as it simulates flow progression onto the network by moving link flows according to the link speed at every time step. The new model has been applied to the real large-scale road network of the town of Rome and has provided a comparable fit of real data with that obtained in a different application by a much more sophisticated simulation-based dynamic traffic assignment model, although it requires much lower calibration effort and smaller computation time.