Continuous limit of the Nagel-Schreckenberg model

A generalized version of the Nagel-Schreckenberg model of traffic flow is presented that allows for continuous values of the velocities and spatial coordinates. It is shown that this generalization reveals structures of the dynamics that are masked by the discreteness of the original model and thus helps to clarify the physical interpretation of the dynamics considerably. It is shown numerically that the transition leading from the free how regime to the congested flow regime bears strong similarities with a first-order phase transition in equilibrium thermodynamics. A similar behavior is observed in more complicated microscopic models and in hydrodynamical descriptions of traffic flow, putting the model within a broader context of other models of traffic flow. An additional advantage of this continuous model is that it is much easier to calibrate with empirical data, only slightly decreasing numerical efficiency.