Calibrating a self-propelled particle model for area-based heterogeneous traffic using quadratic optimisation

This study introduces a traffic modelling framework that treats vehicles as self-propelled particles (SPPs) interacting in a two-dimensional, heterogeneous, and disordered environment. Unlike conventional lane-based models, which assume homogeneity and linear interactions, this approach captures the complexity of real-world traffic where diverse vehicles operate without strict lane discipline. The model employs a synchronous update structure in which each vehicle-agent adjusts its speed and direction based on local interactions, balancing acceleration, alignment, and repulsion forces. A core contribution of this work is a quadratic optimisation-based calibration procedure that fits the self-propelled particle model to large-scale trajectory data while preserving behavioural interpretability. Instead of relying on heuristic tuning, the model parameters are estimated using a constrained quadratic programming (QP) formulation, solved with the Gurobi optimiser. This enables precise, context-sensitive calibration of behavioural parameters, such as speed responsiveness, alignment sensitivity, and directional repulsion, across various unique traffic interaction scenarios defined by vehicle type (6 ×6), relative position (4), and density levels (3), totalling 432 scenarios. The result is a high-fidelity representation of driving behaviour that can adapt to varied traffic compositions and density levels. Beyond motion prediction, the calibrated model offers interpretability and insight into traffic dynamics. It reveals how different vehicle types interact under varied density levels, how risk perception varies across spatial zones, and how local coordination influences flow stability. Importantly, the framework claims to develop a real-time digital twin for proactive safety analysis and efficient operation. By observing variations in behavioural parameters over time, the model can flag early signs of instability or unsafe interactions, enabling timely interventions. The proposed model, formulated as a system of discrete-time equations, presents a scalable solution for modelling disordered traffic systems. It bridges theoretical insights from swarm dynamics with the practical needs of traffic engineering, offering a path forward for simulating, understanding, and improving complex urban mobility, particularly in area-based and heterogeneous traffic environments.