Cordon Pricing Scheme Based on Macroscopic Fundamental Diagram and Distance

To alleviate traffic congestion in key areas, such as city centers, this study proposes an optimal pricing strategy that is based on the distance that users travel in a given cordon. The proposed strategy is derived from the theory of the macroscopic fundamental diagram (MFD). In this strategy, a non-negative, non-decreasing, and nonlinear distance-toll function is defined by a piecewise linear approximation method. A bi-level programming model is then constructed on the basis of the toll charge function and the characteristics of the MFD. The upper model considers the overall operating efficiency of the system and aims to maximize the outflow of the road network. The lower model assumes that users' route choice behavior complies with Wardrop's first principle to formulate a user equilibrium model under a fixed demand. In view of the non-additive property of path cost imposed by the nonlinear distance-toll function, the network transformation technique is used to realize the conversion between real networks and virtual networks. The Frank-Wolfe algorithm based on road segments is then used to solve the lower model. The verification of the reasonable feasibility of the pricing model and algorithm reveals that the implementation of cordon pricing schemes based on distance can make the outflow of the border area maintain the best level. Moreover, the obtained optimal charge function makes the system run efficiently. These results prove that the nonlinear optimal toll charge function is realistic and effective.