PhD Final Defense – Sungyong Chung

Stochastic and Quantum Modeling of Microscopic Tra=ic Flow Dynamics

Advisor: Professor Alireza Talebpour

Abstract

Traditional microscopic tra/ic modeling has relied on parametric, physics-based equations that attempt to

capture driver behavior through calibrated parameters. While these models provide theoretical insights, their

simplified assumptions constrain their capacity to exploit modern large-scale trajectory datasets and capture

the stochastic nature of human driving. This dissertation proposes a probabilistic, empirically grounded

frameworks based on four central ideas: (i) driving behavior is inherently stochastic, meaning observed

trajectories represent samples from a range of plausible outcomes rather than fixed, deterministic results; (ii)

Markov chain o/ers the appropriate mathematical framework for modeling the driver behavior; (iii) real-world

interactions exhibit correlations that are well suited to quantum formalism; and (iv) quantum computation

provides native structural inductive biases that classical continuous-space architectures do not natively

possess.

The dissertation makes six interconnected contributions. First, we introduce OpenCF, a standardized

benchmarking framework with 32,559 car-following events and automated evaluation, revealing that

traditional models struggle to simultaneously achieve prediction accuracy, safety, and naturalistic behavior.

Second, we propose the Markov Chain Car-Following (MC-CF) model, an empirical probabilistic sampling

approach that learns state transitions directly from data and achieves competitive or superior performance

relative to physics-based models across multiple evaluation metrics while reproducing the probabilistic

structure of naturalistic driving. Third, we introduce the Universal Quantum Transformer (UQT), a

parameterized quantum circuit that achieves mathematically exact, deterministically stable generalization, a

regime we define as crystallization, across cyclic modular arithmetic, non-Abelian group algebra, and

systematic linguistic compositionality using only 551 to 1,650 parameters, and confirm these results on IBM

Quantum NISQ hardware. Fourth, we extend the UQT to car-following through the Universal Quantum

Transformer Car-Following model (UQT-CF), which introduces Fourier positional encoding for continuous

driving states and interprets Born rule measurement probabilities directly as a non-parametric acceleration

distribution, achieving competitive open-loop trajectory accuracy and near-zero crash rates in ring-road

simulation with only 1,170 parameters. Fifth, we apply evolutionary game theory to 7,636 lane-changing

events, identifying social dilemmas in mixed tra/ic and demonstrating that repeated interactions consistently

increase cooperation. Sixth, we introduce quantum game theory to resolve a fundamental inconsistency:

classical models predict full cooperation while real-world data shows stable 42% cooperation rates. Using

the Marinatto-Weber quantization scheme, we calibrate a human entanglement parameter that accurately

reproduces observed mixed equilibria and demonstrate that human adaptation critically depends on

underlying AV algorithms.

Collectively, these studies establish that with appropriate mathematical structures (Markov chains, empirical

distributions, quantum circuits, and quantum formalism), we can move beyond classical parametric

assumptions to better characterize the stochastic nature of microscopic tra/ic dynamics in the data-rich era

of automated vehicles.