Risk Control of Traffic Flow Through Chance Constraints and Large Deviation Approximation

TL;DR

This paper introduces a novel traffic management control framework that uses large deviation theory to efficiently enforce rare safety constraints, improving computational scalability and precision in probabilistic safety regulation.

Contribution

The paper develops a large deviation theory-based approximation for chance-constrained traffic control, enabling scalable and precise safety management under stochastic disturbances.

Findings

Achieves near-target probability control in traffic safety.

Maintains constant computational complexity regardless of risk level.

Outperforms traditional sampling-based methods in efficiency and accuracy.

Abstract

Existing macroscopic traffic control methods often struggle to strictly regulate rare, safety-critical extreme events under stochastic disturbances. In this paper, we develop a rare chance-constrained optimal control framework for autonomous traffic management. To efficiently enforce these probabilistic safety specifications, we exploit a large deviation theory (LDT) based approximation method, which converts the original highly non-convex, sampling-heavy optimization problem into a tractable deterministic nonlinear programming problem. In addition, the proposed LDT-based reformulation exhibits superior computational scalability, as it maintains a constant computational burden regardless of the target violation probability level, effectively bypassing the extreme scaling bottlenecks of traditional sampling-based methods. The effectiveness of the proposed framework in achieving precise near-target probability control and superior computational efficiency over risk-averse baselines is illustrated through extensive numerical simulations across diverse traffic risk measures.