Modeling the Equilibrium Road Network Capacity

The aims of this paper are to present a new model to calculate the maximum equilibrium road network capacity and obtain the associated optimal origin-destination (i.e. OD) flow pattern for a general road network with given network topology and link attributes. First, the Static Congested Traffic Assignment (SCTA) is introduced to describe the network where all used routes are in a congested state. Congested Equilibrium Travel Times (CETTs) between OD pairs obtained by the SCTA model are regarded as the corresponding upper limits of actual equilibrium travel times which are called Uncongested Equilibrium Travel Times (UETTs) and derived from the traditional Static Uncongested Traffic Assignment (SUTA) model. The main idea of modeling is that the total OD flows can be maximized by flexibly scaling and adjusting OD flows of each individual OD pairs to make the UETTs of all OD pairs reach their upper limits (i.e. CETTs). Next, a novel equilibrium road network capacity model is built by combining the SUTA and the SCTA models. Then, the equivalency condition and the solution uniqueness of the proposed model are proved. The paper moves on to provide two solution algorithms together with an analysis of the model characteristics. Finally, through three numerical examples, it is demonstrated that the proposed model can obtain the unique equilibrium network capacity with the given network topology and associated link attributes. The optimal OD flow pattern, which leads to the maximum total OD flows, is thus obtained. The findings in the paper can help to improve the utilization of road networks and contribute to land development planning and control.