Macroscopic arc performance models with capacity constraints for within-day dynamic traffic assignment

In this paper, we present a new nonstationary link-based macroscopic arc performance model with capacity constraints, derived from an approximate solution to the simplified kinematic wave theory which based on the assumption, often introduced in the algorithms solving Dynamic Traffic Assignment, that the arc inflows are piecewise constant in time. Although the model does not require to introduce any spatial discretization, it is capable of taking implicitly into account the variability of the flow state along the arc accordingly to any concave fundamental diagram. To appreciate the effect of the approximation introduced, the model has been compared in terms of efficiency and effectiveness with three typical existing models, which have been to this end suitably modified and enhanced.