Mixed traffic flow of human driven vehicles and automated vehicles on dynamic transportation networks*

Improving the system performance of a traffic network by dynamically controlling the routes of connected and automated vehicles (CAVs) is an appealing profit that CAVs can bring to our society. Considering that there may be a long way to achieve 100% CAV penetration, we discuss in this paper the mixed traffic flow of human driven vehicles (HDVs) and CAVs on a transportation network. We first propose a double queue (DQ) based mixed traffic flow model to describe the link dynamics as well as the flow transitions at junctions. Based on this mixed flow model, we develop a dynamic bi-level framework to capture the behavior and interaction of HDVs and CAVs. This results in an optimal control problem with equilibrium constraints (OCPEC), where HDVs' route choice behavior is modeled at the lower level by the instantaneous dynamic user equilibrium (IDUE) principle and the CAVs' route choice is modelled by the dynamic system optimal (DSO) principle at the upper level. We show how to discretize the OCPEC to a mathematical programming with equilibrium constraints (MPEC) and discuss its properties and solution techniques. The non-convex and non-smooth properties of the MPEC make it hard to be efficiently solved. To overcome this disadvantage, we develop a decomposition based heuristic model predictive control (HMPC) method by decomposing the original MPEC problem into two separate problems: one IDUE problem for HDVs and one DSO problem for CAVs. The experiment results show that, compared with the scenario that all vehicles are HDVs, the proposed methods can significantly improve the network performance under the mixed traffic flow of HDVs and CAVs.