My research focuses on the study of traffic-flow models and their applications. Macroscopic and microscopic models are the two main approaches: macroscopic models describe the spatial quantities of traffic, such as density, velocity and flux; while microscopic models simulate the behavior of individual cars based on their interaction. For the macroscopic model, we study the Lighthill-Whitham equation, and account for multiple traffic scenarios by modifying the original Lighthill-Whitham equation. We also study several microscopic car-following models: the optimal velocity model, the full velocity difference model, the modified GHR model and the intelligent driver model. The main research work include: 1 Investigate the collision behavior of the microscopic car-following model. We theoretically prove the collision-free property of several car-following models through fast-slow system technique, and also carry out numerical simulations to provide a valid reference to the dynamics of traffic collisions. 2 Apply data assimilation technique (ensemble Kalman filter and particle filter) to estimating the traffic states and uncertain parameters. An augmented approach is proposed to simultaneously assimilate the Eulerian sensor data and Lagrangian GPS data. 3 Study the phenomenon of capacity discharge in the lane-drop scenario. Macroscopically, we model the lane-drop scenario with inhomogeneous Lighthill-Whitham equation, and then proposed two controlling strategies to guide vehicles smoothly through the bottleneck: (1) change driving habit through fundamental diagram; (2) merge vehicles in advance through virtual lane usage.
"Traffic-flow models: analysis, estimation and control"
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.