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Intervention Strategies for Fairness and Efficiency at Autonomous Single-Intersection Traffic Flows

Salman Ghori, Ania Adil, Melkior Ornik, Eric Feron

TL;DR

This work tackles centralized coordination of autonomous agents at a signal-less, orthogonal intersection by introducing a fairness-aware MILP that coordinates trajectories within a circular control zone. Safety, efficiency, and fairness are jointly optimized, with fairness quantified via reversal-based metrics and embedded as a constraint in the MILP; a receding-horizon MPC framework guides ongoing decisions. Key findings show there exists an optimal control-zone radius that improves performance, while fairness constraints reduce reversals and improve equity at the expense of increased delay and energy, illustrating a clear efficiency–fairness trade-off. The results inform the design of robust, fairness-aware intersection management for autonomous fleets and have potential extensions to logistics, airspace, and multi-intersection networks.

Abstract

Intersections present significant challenges in traffic management, where ensuring safety and efficiency is essential for effective flow. However, these goals are often achieved at the expense of fairness, which is critical for trustworthiness and long-term sustainability. This paper investigates how the timing of centralized intervention affects the management of autonomous agents at a signal-less, orthogonal intersection, while satisfying safety constraints, evaluating efficiency, and ensuring fairness. A mixed-integer linear programming (MILP) approach is used to optimize agent coordination within a circular control zone centered at the intersection. We introduce the concept of fairness, measured via pairwise reversal counts, and incorporate fairness constraints into the MILP framework. We then study the relationship between fairness and system efficiency and its impact on platoon formation. Finally, simulation studies analyze the effectiveness of early versus late intervention strategies and fairness-aware control, focusing on safe, efficient, and robust management of agents within the control zone.

Intervention Strategies for Fairness and Efficiency at Autonomous Single-Intersection Traffic Flows

TL;DR

This work tackles centralized coordination of autonomous agents at a signal-less, orthogonal intersection by introducing a fairness-aware MILP that coordinates trajectories within a circular control zone. Safety, efficiency, and fairness are jointly optimized, with fairness quantified via reversal-based metrics and embedded as a constraint in the MILP; a receding-horizon MPC framework guides ongoing decisions. Key findings show there exists an optimal control-zone radius that improves performance, while fairness constraints reduce reversals and improve equity at the expense of increased delay and energy, illustrating a clear efficiency–fairness trade-off. The results inform the design of robust, fairness-aware intersection management for autonomous fleets and have potential extensions to logistics, airspace, and multi-intersection networks.

Abstract

Intersections present significant challenges in traffic management, where ensuring safety and efficiency is essential for effective flow. However, these goals are often achieved at the expense of fairness, which is critical for trustworthiness and long-term sustainability. This paper investigates how the timing of centralized intervention affects the management of autonomous agents at a signal-less, orthogonal intersection, while satisfying safety constraints, evaluating efficiency, and ensuring fairness. A mixed-integer linear programming (MILP) approach is used to optimize agent coordination within a circular control zone centered at the intersection. We introduce the concept of fairness, measured via pairwise reversal counts, and incorporate fairness constraints into the MILP framework. We then study the relationship between fairness and system efficiency and its impact on platoon formation. Finally, simulation studies analyze the effectiveness of early versus late intervention strategies and fairness-aware control, focusing on safe, efficient, and robust management of agents within the control zone.

Paper Structure

This paper contains 17 sections, 1 theorem, 35 equations, 13 figures, 9 tables.

Table of Contents

  1. Introduction
  2. Problem Description
  3. MODEL FORMULATION
  4. Fairness Measure
  5. Order shift (Table \ref{['tab:crossing_orders_example']})
  6. Reversal Indicator
  7. Zero‑sum block
  8. Why Reversal Happens.
  9. Simulation Framework
  10. Results
  11. System Performance without Fairness Constraints
  12. System Performance with Fairness Constraints
  13. MILP Optimality
  14. Reversals, Platooning, and System efficiency
  15. Effect of Control Zone Radius on Velocity Profiles and System Behavior
  16. ...and 2 more sections

Key Result

Proposition 1

Let $d_{\mathrm{stop}}$ be the worst-case braking distance, $d_{\mathrm{sep}}$ the minimum cross-flow separation distance, and $\delta_{\mathrm{platoon}}$ the length of the longest continuous platoon for a given traffic density, $\Lambda$, which has an inter-agent distance as $d_{\mathrm{safe}}$. Th where $n_{\mathrm{platoon}}=\max\{n_1,n_2\}$. $n_1$ and $n_2$ represent platoon sizes in each flow,

Figures (13)

  • Figure 1: Illustration of the control zone circle (radius $R$) in an intersection scenario. The QR code links to a video demonstrating the control zone implementation.
  • Figure 2: Illustration of shifts or swapping in intersection crossing order.
  • Figure 3: Total delay of all the agents evaluated over the entire control zone path length ($2R$) around the intersection for different traffic densities for the system without fairness constraint vs varying control zone radius.
  • Figure 4: Total energy of all the agents evaluated over the entire control zone path length ($2R$) around the intersection for different traffic densities for the system without fairness constraint vs varying control zone radius.
  • Figure 5: Total delay of all the agents evaluated over the entire control zone path length ($2R$) around the intersection for different traffic densities for the system with fairness constraint vs varying control zone radius.
  • ...and 8 more figures

Theorems & Definitions (5)

  • Proposition 1
  • proof
  • Remark 1
  • Remark 2
  • Remark 3