Multicritical Behaviours in One-Dimensional Traffic Flow

TL;DR

This paper investigates how the positions of on- and off-ramps affect traffic flow in a one-dimensional cellular automaton model, revealing various phases and multicritical behaviors depending on ramp placement and rates.

Contribution

It introduces a detailed numerical analysis of ramp position effects on traffic phases and uncovers multicritical phenomena in the phase diagrams.

Findings

Multiple traffic phases identified: LDP, IDP, PCP, HDP.

Critical, tricritical, and multicritical behaviors observed.

Ramp positions significantly influence phase transitions.

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.