Traffic flow phase transition phenomena based on the kinetic approach

To study the phase transition phenomenon in traffic flow, we propose a discrete Boltzmann model that integrates Boltzmann dynamics with the Cellular Automata framework. This approach combines the theoretical power of the Boltzmann equation with the computational simplicity of Cellular Automata. By examining traffic flows at mesoscopic scales, the model captures the dynamical behavior of traffic in phase space and provides insights into the mechanisms driving phase transitions.

The model can also be interpreted as dynamics on a graph. Numerical simulations, conducted under the assumption of a uniform or heterogeneous vehicle density distribution, yield results that align well with observed empirical phenomena. The model allows for the analysis of various parameters influencing traffic flow and serves as a robust tool for studying the global properties of systems governed by complex motion dynamics.