PhD Final Defense – Yanlin Zhang

Uncertainty-Aware Characterization and Modeling of Mixed-Autonomy Traffic: From Driver Behavior to Stochastic Traffic Flow

Advisor: Associate Professor Alireza Talebpour

Abstract

Mixed-autonomy traffic is shaped by uncertainty at several levels: human drivers respond

heterogeneously to automated vehicles (AVs), naturalistic data omit counterfactual behavior,

occlusions hide portions of motion, and microscopic fluctuations aggregate into stochastic traffic

waves. Rather than treating these sources as residual error, this dissertation develops methods to

characterize, infer, and propagate them. Five studies span four information regimes: fully observed

behavior, examined through two microscopic studies; missing counterfactual behavior; partially

observed motion; and stochastic macroscopic flow.

The first study examines controlled human car-following behind human-driven and automated

leaders under matched conditions. Dynamic Time Warping (DTW) compares full trajectories of

speed, acceleration, relative speed, spacing, and time headway. Spacing most clearly separates the

leader regimes, whereas calibrated parameters of the deterministic Intelligent Driver Model (IDM)

do not. A stochastic IDM extension identifies a substantially lower calibrated acceleration-noise

parameter when the leader is automated. In this setting, the distinction between leader conditions

is therefore expressed more clearly through response variability than through deterministic meanresponse

parameters.

The second study moves from controlled longitudinal response to naturalistic two-dimensional

maneuvering. Discretionary lane changes extracted from the Third Generation Simulation (TGSIM)

dataset are represented by time series of lead and lag gaps and relative speeds. Pairwise DTW

distances and Affinity Propagation clustering reveal recurring interaction patterns without

predefined driver classes. Gap-based clusters describe asymmetric aggressive, neutral, and

cautious strategies toward target-lane leaders and followers, while relative-speed clusters

distinguish overtaking-like maneuvers from transitions into speed-compatible traffic. These

groups describe the observed sample rather than universal driver types, but they translate trajectory

heterogeneity into interpretable maneuver categories.

The first two studies characterize uncertainty when the relevant trajectories are observed. The third

addresses what observational data omit: the trajectory that would have occurred under an

alternative condition. Classical synthetic control estimates this counterfactual from weighted

donor trajectories, but large, correlated donor pools can produce many nearly equivalent pre2

intervention fits with unstable weights. Graph-Regularized Synthetic Control builds a donorsimilarity

graph from pre-intervention behavior and combines sparse selection with graph-

Laplacian smoothing to favor coherent solutions among similar donors. Theory characterizes the

resulting stability--bias tradeoff, while semi-synthetic experiments, a standard policy benchmark

based on California Proposition 99, and an AV-exposure application using the Waymo Open

Motion Dataset evaluate fit and donor-pool sensitivity. The method stabilizes an observational

comparison; without an appropriate identification design, it does not itself establish causal AV

effects.

A different form of missingness arises when the trajectory itself, rather than its counterfactual, is

unobserved. The fourth study represents short empirical trajectory clips as nodes in a

compositional motion graph and feasible transitions as directed edges. Hidden motion is inferred

as a posterior over graph walks, preserving multiple dynamically plausible explanations instead of

reducing an occluded interval to one interpolated curve. Given only a pre-occlusion prefix, the

framework generates controllable alternative futures; when post-occlusion tracks are available, it

jointly selects the matching identity and reconstructs the missing path. Experiments on the Waymo

Open Motion Dataset and TGSIM evaluate generation, association, imputation, and uncertainty.

They demonstrate the interpretability of clip-based hypotheses while identifying endpointconditioned

regimes in which simpler interpolation remains more accurate than the current graphwalk

implementation.

The final study changes scale from individual trajectories to stochastic first-order traffic flow. For

a concave fundamental diagram, it establishes that if the initial spatial density is a strong Markov

process with upward jumps, the entropy solution remains Markov at later times. Compatible spatial

and temporal generators yield kinetic equations for rarefaction drift, shock intensity, and shock

merging, providing a closed description of stochastic traffic-wave interactions. A finite-state

approximation admits an isospectral Lax evolution, while signalized-road and periodic-highway

examples illustrate queue and spillback probabilities, shock-front intensity, total variation, and

merging-time distributions. These Monte Carlo studies illustrate the framework's probabilistic

outputs rather than calibrate the kinetic closure to field data.

Taken together, the five studies form a progression from empirical characterization to structured

inference and stochastic propagation across scales. Under complete observation, uncertainty is

characterized through response variability and maneuver heterogeneity that deterministic averages

can conceal. When a counterfactual or trajectory segment is missing, it is represented through

regularized donor weights or posterior motion hypotheses. After aggregation, it evolves through

probability laws for interacting traffic waves. The dissertation therefore contributes a coherent

strategy for matching the representation of uncertainty to the available information and analytical

scale, while identifying causal design, posterior calibration, and empirical vehicle-to-flow

mapping as essential next steps.