# An Empirical Markov Chain Car-Following (MC-CF) Model

arXiv: https://arxiv.org/abs/2603.27909 · HTML: https://mlsanity.com/paper/2603.27909/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 42 references that are in the map.
- First posted on arXiv 29 Mar 2026.

## Builds on (most cited first, 13 of 13)

- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Argoverse: 3D Tracking and Forecasting with Rich Maps](https://mlsanity.com/paper/1911.02620/) (2019)
- [Large Scale Interactive Motion Forecasting for Autonomous Driving : The Waymo Open Motion Dataset](https://mlsanity.com/paper/2104.10133/) (2021)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [One Thousand and One Hours: Self-driving Motion Prediction Dataset](https://mlsanity.com/paper/2006.14480/) (2020)
- [WOMD-LiDAR: Raw Sensor Dataset Benchmark for Motion Forecasting](https://mlsanity.com/paper/2304.03834/) (2023)
- [Enhancing Foundation Models for Time Series Forecasting via Wavelet-based Tokenization](https://mlsanity.com/paper/2412.05244/) (2024)
- [Limitations and Improvements of the Intelligent Driver Model (IDM)](https://mlsanity.com/paper/2104.02583/) (2021)
- [Identification of Driving Heterogeneity using Action-chains](https://mlsanity.com/paper/2307.16843/) (2023)
- [Assessing Markov Property in Driving Behaviors: Insights from Statistical Tests](https://mlsanity.com/paper/2501.10625/) (2025)
- [Markov Regime-Switching Intelligent Driver Model for Interpretable Car-Following Behavior](https://mlsanity.com/paper/2506.14762/) (2025)
- [Can the Waymo Open Motion Dataset Support Realistic Behavioral Modeling? A Validation Study with Naturalistic Trajectories](https://mlsanity.com/paper/2509.03515/) (2025)
- [Characterizing Lane-Changing Behavior in Mixed Traffic](https://mlsanity.com/paper/2512.07219/) (2025)

## Abstract (arXiv)

Car-following behavior is fundamental to traffic flow theory, yet traditional models often fail to capture the stochasticity of naturalistic driving. This paper proposes an empirical probabilistic sampling approach to car-following modeling that bypasses conventional parametric assumptions. Under this approach, we introduce the Markov Chain Car-Following (MC-CF) model, which represents state transitions as a Markov process and predicts behavior by randomly sampling accelerations from empirical distributions within discretized state bins. Evaluation on the Waymo Open Motion Dataset (WOMD) demonstrates that MC-CF variants significantly outperform all physics-based baselines (IDM, Gipps, FVDM, and SIDM) across both one-step and open-loop trajectory prediction metrics, and remain competitive with modern data-driven baselines including neural network and Gaussian mixture model approaches. Zero-shot generalization on the Naturalistic Phoenix (PHX) dataset further confirms cross-domain transferability. Finally, microscopic ring road simulations validate the framework's scalability: by incrementally integrating unconstrained free-flow trajectories and high-speed freeway data (TGSIM) alongside a conservative inference strategy, the model substantially reduces collisions across most tested scenarios and successfully reproduces naturalistic and stochastic shockwave propagation, though crashes persist under severe shockwave conditions. Overall, the proposed MC-CF model provides a robust and scalable foundation for simulating population-level stochastic traffic behavior that requires no behavioral parameter calibration, making it well-suited for the data-rich future of intelligent transportation.