  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.
