  This paper shows how particle hopping models fit into the context of traffic
flow theory. Connections between fluid-dynamical traffic flow models, which
derive from the Navier-Stokes-equations, and particle hopping models are shown.
In some cases, these connections are exact and have long been established, but
have never been viewed in the context of traffic theory. In other cases,
critical behavior of traffic jam clusters can be compared to instabilities in
the partial differential equations. Finally, it is shown how this leads to a
consistent picture of traffic jam dynamics.
