Risk-Averse Stochastic User Equilibrium on Uncertain Transportation Networks

TL;DR

This paper introduces a risk-averse stochastic user equilibrium framework for transportation networks under hazard-induced uncertainty, incorporating tail-risk management and distributional robustness.

Contribution

It develops a convex truncated stochastic user equilibrium model that accounts for tail risks and ambiguity, with two solution approaches: risk-aware stochastic programming and distributionally robust optimization.

Findings

Traffic increases significantly under hazard scenarios with risk-aware models.

Flow redistribution occurs without large rerouting, showing fine-tuning of equilibrium.

The models effectively manage tail risks and calibration errors in hazard-prone 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.