Diverging junctions are important network bottlenecks, and a better
understanding of diverging traffic dynamics has both theoretical and practical
implications. In this paper, we first introduce a continuous multi-commodity
kinematic wave model of diverging traffic and then present a new framework for
constructing kinematic wave solutions to its Riemann problem with jump initial
conditions. In supply-demand space, the solutions on a link consist of an
interior state and a stationary state, subject to admissible conditions such
that there are no positive and negative kinematic waves on the upstream and
downstream links respectively. In addition, the solutions have to satisfy
entropy conditions consistent with various discrete diverge models. In the
proposed analytical framework, kinematic waves on each link can be uniquely
determined by the stationary and initial conditions, and we prove that the
stationary states and boundary fluxes exist and are unique for the Riemann
problem of diverge models when all or partial of vehicles have predefined
routes. We show that the two diverge models by Lebacque and Daganzo are
asymptotically equivalent. We also prove that the supply-proportional and
priority-based diverge models are locally optimal evacuation strategies. With
numerical examples, we demonstrate the validity of the analytical solutions of
interior states, stationary states, and corresponding kinematic waves. This
study presents a unified framework for analyzing traffic dynamics arising in
diverging traffic and could be helpful for developing emergency evacuation
strategies.