Traffic model with an absorbing phase transition

Abstract

The contribution of Nagel and Schreckenberg (NaSch) model in study of traffic models is remarkable. First of all it is the first model based on cellular automata, the update rules is quite simple but one of them has a special importance: the randomization process. This step introduces a stochastic parameter, the probability p, in the system capable of reproduce some features quite common in real traffic, e.g., the transition between free flow to jammed state. In original NaSch model the randomization process produces a lot of unusual behaviours, for instance we have the exaggerated decelerations due the addition of randomization process to the slowing down one. We propose a slight modification in randomization step that produces two kinds of drivers behaviours: The stochastic and deterministic. The first one, as an original model, the drivers can deceleration in the randomization process with probability p. The second one cannot. Despite of simplicity, this new model produces interesting results as phase transition, hystereses and absorbing state. The plane p-p is divided in three different regions. The first one represents an absorbing state, all conductors have deterministic behaviour. The second one the state which both sort of behaviours coexists and the system never evolves to absorbing state, and the third one, in which the state of a system depends on its initially configuration: some distributions can evolve to absorbing states and others cannot.