New topologies in the fundamental diagram of a one dimensional traffic flow

Abstract

We propose a traffic flow model in which the vehicles are filed from their maximal velocities, the fast cars run with $Vmax{1}$, whereas the slow ones run with $Vmax{2}$. Using new overtaking rules which deals with deterministic NaSch model, it is found that the fundamental diagram exhibits three new topologies, depending on the fractions $f_{fast}$ and $f_{slow}$ of fast and slow vehicles respectively, in which the current profile displays two branches with negative slopes and two branches with positive ones. Moreover, in the second branch of the fundamental diagram, the model exhibits an absorbing phase transitions in which the behaviour of the order parameter $f_{d}$ and the current J is described by the power laws. In this case, it'is found that the system present a universel scaling law. On the other hand, a simple change in the rule of overtaking induce the metastability which depends on the state of the chain instead of external parameters \cite{4,5,6}. Furthermore, in the case of random fractions of vehicles, the fundamental diagrams are similar to the experiments results \cite{7,8}} .