When Context Is Not Enough: Modeling Unexplained Variability in Car-Following Behavior

Chengyuan Zhang, Zhengbing He, Cathy Wu, Lijun Sun
Transportation Research Part B: Methodological (2026).

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Why model driving variability after accounting for traffic context?

Context-dependent predictions and a nonstationary Gaussian process jointly represent the expected acceleration and the evolving temporal structure of residual variability.

Abstract

Modeling car-following behavior is fundamental to microscopic traffic simulation, yet traditional deterministic models often fail to capture the full extent of variability and unpredictability in human driving. While many modern approaches incorporate context-aware inputs (e.g., spacing, speed, relative speed), they frequently overlook structured stochasticity that arises from latent driver intentions, perception errors, and memory effects -- factors that are not directly observable from context alone. To fill the gap, this study introduces an interpretable stochastic modeling framework that captures not only context-dependent dynamics but also residual variability beyond what context can explain. Leveraging deep neural networks integrated with nonstationary Gaussian processes (GPs), our model employs a scenario-adaptive Gibbs kernel to learn dynamic temporal correlations in acceleration decisions, where the strength and duration of correlations between acceleration decisions evolve with the driving context. This formulation enables a principled, data-driven quantification of uncertainty in acceleration, speed, and spacing, grounded in both observable context and latent behavioral variability. Comprehensive experiments on the naturalistic vehicle trajectory dataset collected from the German highway, i.e., the HighD dataset, demonstrate that the proposed stochastic simulation method within this framework surpasses conventional methods in both predictive performance and interpretable uncertainty quantification. The integration of interpretability and accuracy makes this framework a promising tool for traffic analysis and safety-critical applications.

Full abstract from the linked arXiv version, checked 2026-09-13. The bibliographic record above identifies the journal publication; the abstract is the preprint text.

Research summary

Similar gaps and speeds can lead to different acceleration sequences. This work combines a context-dependent mean model with a Gaussian process whose covariance changes with context, using a scenario-adaptive Gibbs kernel.

The useful distinction is between predicting the expected response and modeling how departures from that response persist. The model provides both components for stochastic simulation. Residual variability is defined relative to the inputs and mean model; it does not uniquely identify driver intention or perception error.

How can I use it?

The public implementation includes training, simulation, CSV validation, and a synthetic quickstart. It does not bundle highD data, trained weights, or paper benchmark results. Follow the repository’s data requirements before using your own trajectories.

Research poster · Gaussian processes for time series · Stochastic driving behavior