Multicritical Behaviours in One-Dimensional Traffic Flow

Abstract

The effect of the on-ramp and off-ramp positions $i_1$ and $i_2$, respectively, on the one dimensional-cellular automaton traffic flow behaviour, is investigated numerically. The on-ramp and off-ramp rates at $i_1$ and $i_2$ are ${\alpha }_0$ and ${\beta }_0$, respectively. However, in the open boundary conditions, with injecting and extracting rates $\alpha$ and $\beta$ and using parallel dynamics, several phases occur, depending on the position of $i_1$ by respect to $i_2$. Namely, low density phase (LDP), intermediate density phase (IDP), plateau current phase (PCP) and high density phase (HDP). Furthermore, critical, tricritical and multicritical behaviours take place in the $(i_1,{\alpha }_0)$ phase diagrams.