  The propagation of traffic congestion along roads is a commonplace nonlinear
phenomenon. When many roads are connected in a network, congestion can spill
from one road to others as drivers queue to enter a congested road, creating
further nonlinearities in the network dynamics. This paper considers the node
model problem, which refers to methods for solving for cross-flows when roads
meet at a junction. We present a simple hybrid dynamic system that, given a
macroscopic snapshot of the roads entering and exiting a node, intuitively
models the node's throughflows over time. This dynamic system produces
solutions to the node model problem that are equal to those produced by many
popular node models without intuitive physical meanings. We also show how the
earlier node models can be rederived as executions of our dynamic system. The
intuitive physical description supplied by our system provides a base for
control of the road junction system dynamics, as well as the emergent network
dynamics.
