Inbound traffic capture link-design problem independent of assumptions on users’ route choices

In some traffic management situations, a cordon (a set of points at which traffic flows into a given area) is set in a road network to establish a reference for the location of equipment to implement traffic measurements and controls (e.g., traffic volume surveys and congestion charging). However, few studies have focused on the optimum location of a cordon. We devise a problem denoted the inbound traffic capture link-design problem to select the optimum combination of links for inclusion in a cordon. We regard this combination as the minimum number of links that can capture traffic on all routes, under the condition that there is a path between nodes inside the cordon that is not captured. We formulate this model by employing the graph theory concept of the minimum cut, and use the concept of a Steiner tree with auxiliary network flows to express the constraint of ensuring that there is an uncaptured path inside a cordon. After a basic formulation, to obtain an identical cordon, we devise two subsidiary schemes. In addition, we perform a linear relaxation of our method to reduce its computational cost. The results of computational experiments confirm that our model selects the optimal cordon location formed by a combination of capturing links and also outputs an identical cordon as a boundary line of an area. As the model is computationally feasible, even when applied on a large network, we believe it will have a wide range of practical applications. •A new mathematical model to optimize a closed cordon location is devised.•We formulate the model using the concept of minimum cut and Steiner tree in graph theory.•Our model provides a robust solution that does not depend on assumptions about users' route-choice behaviors.•We confirm the computational feasibility of our model through experiments on a large-scale road network.