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New Topologies in the Fundamental Diagram of a Cellular Automata Traffic Flow Model

We propose a traffic flow model in which vehicles are fixed at their maximal velocities, the fast cars run with V(subscript max1), whereas the slow ones run with V(subscript max2). Using new overtaking rules which deal with the deterministic NaSch model, it is found that the fundamental diagram exhibits three new topologies, depending on the fractions f(subscript fast) and f(subscript 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 transition in which the behaviour of the order parameter f(subscript d) and the current J is described by power laws. In this case, it is found that the system presents a univeral scaling law. On the other hand, a simple change in the rule of overtaking induces a metastability, which depends on the state of the chain instead of the external parameters [4-6]. Furthermore, in the case of random fractions of vehicles, the fundamental diagrams are similar to the experimental results [7, 8].