Department of Mathematics

The kinematic wave theory, originally proposed by (Lighthill and Whitham, 1955b; Richards, 1956), has been a good candidate for studying vehicular traffic. In this dissertation, we study kinematic wave models of network traffic, which are expected to be theoretically rigorous, numerically reliable, and computationally efficient. For traffic systems with inhomogeneous links, merges, diverges, or mixed-type vehicles, we study the kinematic waves in their Riemann solutions and develop numerical solution methods of the Godunov type and the supply-demand type. For a network traffic system, we propose a multi-commodity kinematic wave (MCKW) model and an implementation of it. The model observes First-In-First-Out principle in the order of a time interval and is numerically convergent. Further, we apply this simulation model to study equilibrium states and periodic waves in road networks. Finally, we summarize our work and discuss future research directions.