Mathematical modeling of traffic flow for connected and automated vehicles

The development of connected and automated vehicle (CAV) technologies motivate modeling efforts and studies to understand CAVs' collective behaviors on public roads. In this thesis, we study CAV traffic flows through macroscopic models under two mathematical frameworks: the nonlocal conservation laws and the mean field games.The nonlocal conservation law models incorporate traffic information in a nonlocal range into each vehicle's driving control. We study one such model with a finite spatial nonlocal range, and demonstrate that proper use of the nonlocal information will offer better traffic stability. We also discuss numerical computation of the model that is robust under the changes of the nonlocal range. The mean field game models consider strategic interactions between CAVs, assuming each vehicle anticipates future traffic conditions and plans its driving control to minimize a predefined driving cost. A systematic approach is developed to derive the model, solve the model, and test the equilibrium solution. We take this approach in several traffic scenarios for CAVs on a single road or on a network, and demonstrate that proper design of the CAV driving cost function can lead to more efficient and stable traffic flows than human traffics. The established results in the thesis will bring more mathematical understandings on the proposed and studied models. The results may also provide insights on how to utilize the vehicle connectivity and automation to improve the overall traffic, and help to the CAV driving algorithm design.