Benchmarking intra-driver heterogeneity car-following models using a behavioural and numerical evaluation framework

Intra-driver heterogeneity significantly impacts traffic dynamics yet remains poorly understood and insufficiently assessed in existing car-following models. Whilst various modelling approaches have been proposed, the lack of a unified benchmarking framework has obscured their limitations, particularly regarding behavioural soundness and intra-driver heterogeneity recovery. This study benchmarks four well-established car-following models (Intelligent Driver Model, Optimum Velocity Model, Full Velocity Difference Model, and Newell) using four methods for incorporating intra-driver heterogeneity. We propose a benchmarking methodological framework to comprehensively evaluate these models from both numerical and behavioural perspectives. Six experiments are performed: (i) evaluating traditional models without heterogeneity, (ii) testing heterogeneity models on heterogeneity-free data, (iii) analysing simplified scenarios excluding the standstill regime, (iv) assessing models’ ability to recover heterogeneity in controlled data, (v) evaluating traditional models with real-world data, and (vi) testing heterogeneity models with real-world data. Numerical evaluation (using Percentage Parameter Estimation Error, Root Mean Square Error, and Percentage of Intra-driver Heterogeneity Error) and behavioural consistency (e.g., unrealistic accelerations, oscillations, and concavity of oscillations growth) are used for comparison. Results indicate that some traditional models struggle with behavioural soundness, whereas incorporating intra-driver heterogeneity improves certain aspects but introduces new challenges. Among model-method combinations, combining the Langevin method with the Intelligent Driver Model is promising for capturing realistic intra-driver heterogeneity behaviour and fewer behavioural issues. Yet the variable parameter method is generally robust in reproducing the concave growth curve of oscillations when integrated with any model. The proposed benchmarking framework offers a comprehensive approach for rigorously evaluating intra-driver heterogeneity models.