Data is All You Need: Markov Chain Car-Following (MC-CF) Model

Abstract

Car-following behavior is fundamental to traffic flow theory, yet traditional models often fail to capture the stochasticity of naturalistic driving. This paper introduces a new car-following modeling category called the empirical probabilistic paradigm, which bypasses conventional parametric assumptions. Within this paradigm, we propose 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 of the MC-CF model trained on the Waymo Open Motion Dataset (WOMD) demonstrates that its variants significantly outperform physics-based models including IDM, Gipps, FVDM, and SIDM in both one-step and open-loop trajectory prediction accuracy. Statistical analysis of transition probabilities confirms that the model-generated trajectories are indistinguishable from real-world behavior, successfully reproducing the probabilistic structure of naturalistic driving across all interaction types. Zero-shot generalization on the Naturalistic Phoenix (PHX) dataset further confirms the model's robustness. 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 drastically reduces collisions, achieving zero crashes in multiple equilibrium and shockwave scenarios, while successfully reproducing naturalistic and stochastic shockwave propagation. Overall, the proposed MC-CF model provides a robust, scalable, and calibration-free foundation for high-fidelity stochastic traffic modeling, uniquely suited for the data-rich future of intelligent transportation.

Figures (8)

• Figure 1: Open-loop performance comparison of SIDM and MC-CF (stoch) across different interaction types as the number of generated stochastic trajectories (K) increases from 1 to 15. (a), (c), and (e) show SIDM results for AV-following-HDV, HDV-following-AV, and HDV-following-HDV cases, respectively, while (b), (d), and (f) present the corresponding results for MC-CF (stoch).
• Figure 2: Schematic of the ring road simulation geometry ($L = 3,000$ m). The periodic boundary condition ensures that $x = 3,000~m$ and $x = 0~m$ represent the same physical location, creating a closed-loop system for evaluating long-term vehicle interactions.
• Figure 3: Trajectory plots for the Normal Equilibrium test ($N=200$, $v_{start}=5.84$ m/s).
• Figure 4: Ground truth trajectories from the Nagoya Dome ring road experiment (Session 1520, $N=20$). The empirical data exhibits naturalistic speed fluctuations and forward moving shockwaves, contrasting with the rigid uniformity predicted by traditional parametric models.
• Figure 5: Trajectory plots for the Standard Shockwave test. MC-CF models with the conservative mode (e-f) eliminates collisions, while solo data (d-f) ensures proper gap reduction.