We propose a cellular automata rule for modeling road traffic in an urban environment. We consider a generalization of Wolfram's rule 184 (used for single lane traffic models) to account for two-dimensional (north, south, east and west) car displacements. Road crossings are naturally implemented as rotary junctions.
We consider the traffic in a Manhattan-like city and study the flow diagram (average velocity versus number of cars) and the car density profile along road segments.
We may identify four regimes: (i) free traffic, (ii) maximum flow, (iii) partially jammed and (iv) completely jammed (deadlock) regimes. Besides, traffic in the street network self-organizes in three regions, of fixed car density: queues that form in front of a crossing, the rotaries and, finally the road segments right after the junctions. Increasing the number of car increases the queue length but does not change the car density in these three regions.
The length of the car queues obeys a complex dynamics and is the key to the description of the transition from one traffic regime to another. The drivers' behavior at crossings is determinant for the global properties of the system, as well as the length of the street between two junctions.