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

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.