Risk-Averse Stochastic User Equilibrium on Uncertain Transportation Networks

Abstract

Extreme weather events, like flooding, disrupt urban transportation networks by reducing speeds and capacities, and by closing roadways. These hazards create regime-dependent uncertainty in link performance and travel-time distribution tails, challenging conventional traffic assignment that relies on the expectation of cost or mean excess of cost summation. This study develops a risk- and ambiguity-aware traffic assignment framework coupling stochastic supply driven by hazard impacts, endogenous route choice with choice set truncation, and tail-risk management within a tractable convex truncated stochastic user equilibrium (TSUE) formulation. Travelers' perceived costs use a normalized mean-CVaR certainty equivalent encoding tail sensitivity into two interpretable parameters ($\alpha$ and $\lambda$) while preserving convexity. We propose two complementary treatments. TSUE-Stochastic Programming (TSUE-SP) optimizes a nominal risk-aware TSUE balancing average performance and adverse-tail outcomes. TSUE-Distributionally Robust Optimization (TSUE-DRO) protects against calibration error and distributional misspecification by incorporating robustness over a $1$-Wasserstein ambiguity set, and when appropriate, over structured regime-dependent sets for piecewise-stationary hazards (non-stationary distribution case). Duality yields a scenario-based second-order cone program solved via Benders cuts. On a stylized grid network representing downtown Chicago, western corridor traffic increases $67.9\%$ with TSUE-SP and $100.9\%$ with TSUE-DRO relative to a baseline not impacted by the hazard. The formulations redistribute flows without large-scale rerouting, illustrating how tail weighting and distributional ambiguity fine-tune rather than subvert equilibrium choices in hazard-prone networks.