Optimal Congestion Pricing with Day-to-Day Evolutionary Flow Dynamics: A Mean–Variance Optimization Approach

This paper investigates the optimal congestion pricing problem that considers day-to-day evolutionary flow dynamics. Under the circumstance that traffic flows evolve from day to day and the system might be in a non-equilibrium state during a certain period of days after implementing (or adjusting) a congestion toll scheme, it is questionable to use an equilibrium-based index under steady state as the objective to measure the performance of a congestion toll scheme. To this end, this paper proposes a mean–variance-based congestion pricing scheme, which is a robust optimization model, to consider the evolution process of traffic flow dynamics in the optimal toll design problem. More specifically, in the mean–variance-based toll scheme, travelers aim to minimize the variance of expected total travel costs (ETTCs) on different days to reduce risk in daily travels, while the average ETTC over the whole planning period is restricted to being no larger than a predetermined target value set by the authorities. A metaheuristic approach based on the whale optimization algorithm is designed to solve the proposed mean–variance-based day-to-day dynamic congestion pricing problem. Finally, a numerical experiment is conducted to validate the effectiveness of the proposed model and solution algorithm. Results show that the used 9-node network can reach a steady state within 18 days after implementing the mean–variance-based congestion pricing, and the optimal toll scheme can be also obtained with this toll strategy.

A Two-Layer Network Dynamic Congestion Pricing Based on Macroscopic Fundamental Diagram

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.