Optimal Routing Policy for a Mixed Traffic Flow of Connected Vehicles and Regular Vehicles with En-route Information

Travelers often acquire traffic information and update their route choices en-route. This study examines travelers' decision-making (regarding information acquisition and routing) and impacts of information, when travel times are uncertain in a road network with a mixed traffic flow of connected vehicles (CVs) and regular vehicles (RVs). CVs are equipped with onboard communication systems, which allows CV users to acquire en-route information efficiently at no additional cost, while RV users may choose to purchase en-route information via route-guidance systems. We examine two types of routing behaviors, i.e., the user-optimal routing and the system-optimal routing. The user-optimal routing behavior applies when road users aim to minimize their individual expected travel costs when they determine whether to acquire en-route information and what is the optimal routing policy. We characterize decisions of RV and CV users as a mixed-flow user equilibrium with recourse (MUER), which is first formulated as a policy-based variational inequality problem. To solve the problem efficiently, we further derive an equivalent convex optimization program. We propose a solution framework, where a tailored bi-conjugate Frank-Wolfe algorithm is embedded with a TS-OSP algorithm designed to find the optimal routing policy in our problem. The system-optimal routing behavior, which minimizes the expected system travel time, is also examined in the mixed traffic flow environment. We propose a linear program (LP) and prove an anonymous System Optimum (SO) toll scheme, can be obtained by solving the proposed LP. A column generation procedure is adopted to find the SO tolls. We test our model and algorithms on both the Braess network and the Sioux Falls network. The numerical results show that higher penetration of CVs does not necessarily reduce congestion. Meanwhile, improving RVs' information technology can help to achieve SO with mild tolls