TITLE:
A Nonlinear Mathematical Model for Dynamic Traffic Flow Optimization: A Stem Innovation
AUTHORS:
Marc Bigirimana, Fulgence Nahayo, Mounir Haddou, Abraham Niyongere
KEYWORDS:
Traffic Fluidity Function, Mass Variation, AMPL, IPOPT, Inter-Coupled Differential Equations, RK4 Discretization, Heat-Powered Vehicle
JOURNAL NAME:
Open Journal of Optimization,
Vol.14 No.4,
October
29,
2025
ABSTRACT: This paper aims to develop a model of road traffic dynamics. The Heat-powered vehicle is modeled as a highly complex, controlled dynamic system whose 3D motion considers kinematic, dynamic, and rotational contributions. An objective function to optimize traffic flow is proposed. An additional assumption of mass variation of the thermal vehicle in motion is added to the fundamental principle of dynamic mechanics formulated by Sir Isaac Newton. A set of constraints related to dynamics, kinematics, control, and comfort is taken into consideration. A set of intercoupled nonlinear differential equations governs the formulation of this problem. A Runge-Kutta discretization RK4 is required to solve the problem. A Mathematical Programming Language AMPL and the Interior Point OPTimizer IPOPT solver are used to extract solutions. The numerical results confirm the assumption of mass variation and a considerable improvement in traffic fluidity.