Continuum Traffic Model Accounting for Driver Behavior and Lateral Viscosity

Authors

Keywords:

Traffic flow, Continuum traffic model, Viscosity rate, Driver behavior, Higher order models

Abstract

Second-order macroscopic models consist of an LWR continuity equation and a dynamic velocity equation. From a microscopic perspective, this paper proposes a dynamic velocity equation that accounts for cautious and aggressive driving styles, as well as lateral resistance. The model’s stability conditions are determined, providing important insights into traffic behavior under various conditions. The model is further solved numerically, with graphical illustrations of nonlinear traffic phenomena. Although the simulation results are based on a single-pipe scenario, the sensitivity analysis reveals a speed drop due to increased lateral resistance. This effect is evident in the shock and rarefaction wave profiles within the speed space-time and density-space-time domains.

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Author Biographies

  • Gabriel Obed Fosu, Kwame Nkrumah University of Science and Technology, Kumasi-Ghana

    Gabriel is a Lecturer in the Department of Mathematics at Kwame Nkrumah University of Science and Technology (KNUST), Ghana. He holds a PhD in Applied Mathematics and specializes in mathematical modelling and simulation, with a particular focus on vehicular traffic flow theory and the analysis of differential systems. His research integrates theoretical mathematics with practical applications, especially in addressing real-world challenges such as road safety and transportation efficiency. In addition to his academic role, Gabriel is an expositional teacher of the Word of God. His pilgrimage pursuit has been to diligently add to his faith: virtue, knowledge, temperance, patience, godliness, and love, to impact himself and the world around him.

  • Richard Owusu, Kwame Nkrumah University of Science and Technology, Kumasi-Ghana

    Richard holds BSc in Mathematics, MPhil and PhD in Scientific Computing and Industrial Modeling from KNUST. He was appointed to the Department of Mathematics, KNUST, in November 2021, and he is currently ranked Lecturer. His research experience lies in Fluid Dynamics, specifically in the area of Reservoir Modeling and Simulation. His recent developments in the area of Applied Mathematics involve modeling fluid transport in fractured porous domains using up-scaling techniques. Currently, he holds a postdoctoral position with research focus on climate modeling where he employs the coupled atmospheric and land surface dynamics in ICOsahedral Nonhydrostatic (ICON) model with large-eddy simulations (LES) to investigate the influence of moisture extraction on the climate.

  • Ernest Akorly, Kwame Nkrumah University of Science and Technology, Kumasi-Ghana

    Ernest Akorly holds a Bachelor's degree in Mathematics from Kwame Nkrumah University of Science and Technology (KNUST) and a Master's degree from the African Institute for Mathematical Sciences (AIMS), Ghana. He has served as a Teaching and Research Assistant at KNUST and as a tutor with the College of Distance Education at the University of Cape Coast. His research interests lie in mathematical modelling and applied mathematics.

  • Ellen Sarpong, Kwame Nkrumah University of Science and Technology, Kumasi-Ghana

    Ellen is a researcher and student at Kwame Nkrumah University of Science and Technology. Her research focuses on transportation engineering and crystalline porous materials (CPMs) for water purification. With a strong background in mathematics and computational methods, she applies machine learning models to advance these fields.

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Published

2025-07-18

Issue

Vol. 43 No. 2 (2025)

Section

Engineering & Physical Sciences

License

JUST Vol. 43 Number 1 (2025) Copyright and Licensing statement

How to Cite

Continuum Traffic Model Accounting for Driver Behavior and Lateral Viscosity. (2025). Journal of Science and Technology, 43(2), 66-78. https://journal.knust.edu.gh/index.php/just/article/view/2094