Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Rui Xu, Shanyin Tong, Xuan Di

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.

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

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.

Paper Structure

This paper contains 15 sections, 11 equations, 3 figures, 4 tables.

Table of Contents

  1. INTRODUCTION
  2. Related Work
  3. Methodology
  4. PDE-constrained stochastic optimal control
  5. Traffic risk measure
  6. Maximum density
  7. Maximum coefficient of variation of speed (CVS)
  8. Maximum flux
  9. Traffic risk control through rare chance constraints
  10. LDT reformulation of chance-constrained optimization
  11. Numerical Experiments
  12. Risk control on maximum density
  13. Risk control on maximum variation of speed
  14. Risk control on maximum flux
  15. Conclusions

Figures (3)

  • Figure D1: Probability density function of the maximum density under the stochastic source term for the optimal controls obtained by four different strategies respectively: baseline, nonseparable, LDT-CC, and CVaR. The vertical dashed line marks the density threshold $z=0.65$.
  • Figure D2: Macroscopic density/velocity snapshots for the maximum density case with $\alpha=0.2\%$ under the MPP $s(x,t;\theta^\ast)$. At $t=4.5\,\mathrm{s}$, the CVaR solution exhibits a sharp velocity field, whereas LDT-CC remains smoother and more stable.
  • Figure D3: Probability density function of the maximum CVS under the stochastic source term for the optimal controls obtained by four different strategies respectively. The broken x-axis is used to accommodate different scales of risk: the left panel highlights the low-risk profiles of CVaR and LDT-CC, while the right panel captures the high-risk distribution of the baseline.