  In this paper we present a theoretical analysis of a recently proposed
two-dimensional Cellular Automata model for traffic flow in cities with the
novel ingredient of turning capability. Numerical simulations of this model
show that there is a transition between a freely moving phase with high
velocity to a jammed state with low velocity. We study the dynamics of such a
model starting with the microscopic evolution equation, which will serve as a
basis for further analysis. It is shown that a kinetic approach, based on the
Boltzmann assumption, is able to provide a reasonably good description of the
jamming transition. We further introduce a space-time continuous
phenomenological model leading to a couple of partial differential equations
whose preliminary results agree rather well with the numerical simulations.
