Carmen Mezquita-Nieto

arXiv2026

A multi-class kinetic traffic flow model: discrete-velocity formulation and diffusively-corrected macroscopic limits

This paper introduces a multi-class extension of a discrete-velocity kinetic traffic flow model based on a non-local Prigogine-Herman framework. We derive a hyperbolically scaled system of equations from a continuous kinetic formulation describing interactions between different vehicle classes through braking and relaxation terms. The model is then discretized with respect to the velocity variable for an arbitrary number of vehicle classes, and the structural properties of the resulting formulation are analyzed. In particular, we prove hyperbolicity and total linear degeneracy. Due to the non-conservative structure of the model, we employ a path-conservative finite volume scheme for the numerical approximation of the system. Finally, we derive the corresponding diffusively-corrected macroscopic multi-class model, investigate its stability and present numerical simulations on a single-lane road to illustrate the theoretical findings.

math.NA↗

arXiv2026

Discrete adjoint gradient computation for multiclass traffic flow models on road networks

This paper applies a discrete adjoint gradient computation method for a multi-class traffic flow model on road networks. Vehicle classes are characterized by their specific velocity functions, which depend on the total traffic density, resulting in a coupled hyperbolic system of conservation laws. The system is discretized using a Godunov-type finite volume scheme based on demand and supply functions, extended to handle complex junction coupling conditions -- such as merges and diverges -- and boundary conditions with buffer lengths to account for congestion spillback. The optimization of different travel-related performance metrics, including total travel time and total travel distance, is formulated as a constrained minimization problem and is accomplished through the use of an adjoint gradient approach, allowing for an efficient computation of sensitivities with respect to the chosen time-dependent control variables. Numerical simulations on a sample network demonstrate the efficiency of the proposed framework, particularly as the number of control parameters increases. This approach provides a robust and computationally efficient solution, making it suitable for large-scale traffic network optimization.

math.AP↗