A five-vertex model interpretation of one-dimensional traffic flow

Here we solve a discrete one-dimensional traffic flow problem by mapping the allowed sets of car trajectories onto a line representation of the five-vertex model configurations. The fundamental flow diagram, obtained previously in a grand canonical ensemble, is rederived. Fluctuations of the flow are described quantitatively and two critical exponents are defined. The zero-density limit is studied by considering an ensemble of single directed self-avoiding loops on a finite torus.