Numerical Simulation of a Macroscopic Multilane Traffic Flow Model Based on Linear Velocity-Density Function

Abstract

Our present world is based on communication. Transportation is a major component of communication. For overpopulated countries in the world, a large number of vehicles are required for transportation, which causes traffic congestion. Traffic congestion is a critical issue in urban areas worldwide, particularly on multilane roadways where the complexity of interactions between vehicles can lead to significant delays, accidents, and reduced efficiency. Multilane traffic flow models have emerged as powerful tools to simulate and analyze traffic dynamics under various conditions. In this paper, we assume a macroscopic multilane traffic flow model based on a linear velocity-density relationship, which yields a non-linear first-order system of hyperbolic partial differential (PDE) equations as an initial boundary value problem (IBVP). Since the analytical solution of the macroscopic multilane traffic flow model for two lanes is very complicated, there is a demand for efficient numerical methods to solve the macroscopic multilane traffic flow model. Due to the complexity of the analytical solution, we explore numerical solutions using the finite difference method, specifically the first-order Explicit Upwind Scheme, the Lax-Friedrich Scheme, and the second-order Lax-Wendroff Scheme. We determine the well-posedness and the stability analysis, and finally compare the three numerical schemes. The goal of this research is to contribute to the development of more efficient traffic management systems by providing insights into the movement and interaction of vehicles on multilane roads.

GANITJ. Bangladesh Math. Soc. 46.3 (2026) 082–090