  Fundamental to many transportation network studies, traffic flow models can
be used to describe traffic dynamics determined by drivers' car-following,
lane-changing, merging, and diverging behaviors. In this study, we develop a
deterministic queueing model of network traffic flow, in which traffic on each
link is considered as a queue. In the link queue model, the demand and supply
of a queue are defined based on the link's fundamental diagram, and its in- and
out-fluxes are computed from junction flux functions corresponding to
macroscopic merging and diverging rules. We demonstrate that the model is well
defined and can be considered as a continuous approximation to the kinematic
wave model on a road network. From careful analytical and numerical studies, we
conclude that the model is physically meaningful, computationally efficient,
always stable, and mathematically tractable for network traffic flow. As an
addition to the multiscale modeling framework of network traffic flow, the
model strikes a balance between mathematical tractability and physical realism
and can be used for analyzing traffic dynamics, developing traffic operation
strategies, and studying drivers' route choice and other behaviors in
large-scale road networks.

Dynamical Systems;Classical Analysis and ODEs