# Modeling self-consistent multi-class dynamic traffic flow

Hsun-Jung Cho, Shih Ching Lo*

*Corresponding author for this work

Research output: Contribution to journalArticle

12 Scopus citations

### Abstract

In this study, we present a systematic self-consistent multiclass multilane traffic model derived from the vehicular Boltzmann equation and the traffic dispersion model. The multilane domain is considered as a two-dimensional space and the interaction among vehicles in the domain is described by a dispersion model. The reason we consider a multilane domain as a two-dimensional space is that the driving behavior of road users may not be restricted by lanes, especially motorcyclists. The dispersion model, which is a nonlinear Poisson equation, is derived from the car-following theory and the equilibrium assumption. Under the concept that all kinds of users share the finite section, the density is distributed on a road by the dispersion model. In addition, the dynamic evolution of the traffic flow is determined by the systematic gas-kinetic model derived from the Boltzmann equation. Multiplying Boltzmann equation by the zeroth, first- and second-order moment functions, integrating both side of the equation and using chain rules, we can derive continuity, motion and variance equation, respectively. However, the second-order moment function, which is the square of the individual velocity, is employed by previous researches does not have physical meaning in traffic flow. Although the second-order expansion results in the velocity variance equation, additional terms may be generated. The velocity variance equation we propose is derived from multiplying Boltzmann equation by the individual velocity variance. It modifies the previous model and presents a new gas-kinetic traffic flow model. By coupling the gas-kinetic model and the dispersion model, a self-consistent system is presented.

Original language English 342-362 21 Physica A: Statistical Mechanics and its Applications 312 3-4 https://doi.org/10.1016/S0378-4371(02)00868-3 Published - 15 Sep 2002

### Keywords

• Boltzmann equation
• Macroscopic traffic equations
• Multiclass traffic flow
• Multilane traffic flow
• Poisson equation