Dynamic congestion pricing has attracted increasing attentions during the recent years. Nevertheless, limited research has been conducted to address the dynamic tolling scheme at the network level, such as to cooperatively manage two alternative networks with heterogeneous properties, e.g., the two-layer network consisting of both expressway and arterial network in the urban areas. Recently, the macroscopic fundamental diagram (MFD) developed by both field experiments and simulation tests illustrates a unimodal low-scatter relationship between the mean flow and density network widely, providing the network traffic state is roughly homogeneous. It reveals traffic flow properties at an aggregated level and sheds light on dynamic traffic management of a large network. This paper proposes a bilevel programming toll model, incorporating MFD to solve the unbalanced flow distribution problem within the two-layer transportation networks. The upper level model aims at minimizing the total travel time, while the lower level focuses on the MFD-based traffic assignment, which extends the link-based traffic assignment to network wide level. Genetic algorithm (GA) and the method of successive average were adopted for solving the proposed model, on which an online experimental platform was established using VISSIM, MATLAB, and Visual Studio software packages. The results of numerical studies demonstrate that the total travel time is decreased by imposing the dynamic toll, while the total travel time savings significantly outweigh the toll paid. Consequently, the proposed dynamic toll scheme is believed to be effective from both traffic and economic points of view.
Marginal cost congestion pricing based on the network fundamental diagram
