Optimizing Time-Dependent Network Flows With Environmental Objectives: A Path Controlling Approach Enabled by Automated Vehicles

The autonomy and controllability of automated vehicles (AVs) present new opportunities for regulating the traffic toward system-wide goals. This paper focuses on one aspect that has received increasing attentions in recent years, namely a path control scheme. This study contributes to the ongoing research by extending the path control scheme to a within-day dynamic context, with both system efficiency and environmental objectives taken into consideration. Moreover, it also contributes to the domain of operations research by developing a unified optimization framework to determine the best control strategy. Specifically, we assume that AVs on the roads originally follow the dynamic user equilibrium (DUE) principle and can be controlled as either dynamic system optimum (DSO) users to minimize the total system travel time, or dynamic eco-system optimum (DESO) users to minimize the total emission by the central agent when they depart from origins. We formulate the optimal time-dependent control problem as a single-level optimization program, with the dynamic equilibrium conditions integrated as a gap function-based constraint. A method for evaluating the path marginals is also presented, based on which a Lagrangian relaxation-based heuristic algorithm is proposed to solve the problem. A robust optimization technique is also developed to tackle the non-unique equilibrium flow patterns of the multiclass dynamic traffic assignment problem. Based on the numerical results, it is found that some O-D pairs enjoy higher control priority than others, and theoretically a satisfactory system performance can be achieved by controlling a small fraction of the traffic.