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Platoon Forming Algorithms for Intelligent Street Intersections

R. W. Timmerman, M. A. A. Boon

TL;DR

This work addresses improving intersection throughput for autonomous vehicles by forming speed-enabled platoons through PFAs that schedule crossing times and regulate approaching trajectories. It couples PFAs with speed-profile algorithms, presenting both optimization-based and closed-form solutions to generate safe, efficient trajectories while maintaining a regular, cycling service structure. The study develops mean-delay and fairness approximations via a polling-model framework, demonstrates substantial capacity gains over traditional traffic signals in SUMO simulations, and discusses trade-offs and extensions for practical deployment. The results highlight a promising path to significantly reduce urban congestion with autonomous-enabled intersection control, while underscoring the need to balance delay and fairness and to consider network-wide implications.

Abstract

We study intersection access control for autonomous vehicles. Platoon forming algorithms, which aim to organize individual vehicles in platoons, are very promising. To create those platoons, we slow down vehicles before the actual arrival at the intersection in such a way that each vehicle can traverse the intersection at high speed. This increases the capacity of the intersection significantly, offering huge potential savings with respect to travel time compared to nowadays traffic. We propose several new platoon forming algorithms and provide an approximate mean delay analysis for our algorithms. A comparison between the current day practice at intersections (through a case study in SUMO) and our proposed algorithms is provided. Simulation results for fairness are obtained as well, showing that platoon forming algorithms with a low mean delay sometimes are relatively unfair, indicating a potential need for balancing mean delay and fairness.

Platoon Forming Algorithms for Intelligent Street Intersections

TL;DR

This work addresses improving intersection throughput for autonomous vehicles by forming speed-enabled platoons through PFAs that schedule crossing times and regulate approaching trajectories. It couples PFAs with speed-profile algorithms, presenting both optimization-based and closed-form solutions to generate safe, efficient trajectories while maintaining a regular, cycling service structure. The study develops mean-delay and fairness approximations via a polling-model framework, demonstrates substantial capacity gains over traditional traffic signals in SUMO simulations, and discusses trade-offs and extensions for practical deployment. The results highlight a promising path to significantly reduce urban congestion with autonomous-enabled intersection control, while underscoring the need to balance delay and fairness and to consider network-wide implications.

Abstract

We study intersection access control for autonomous vehicles. Platoon forming algorithms, which aim to organize individual vehicles in platoons, are very promising. To create those platoons, we slow down vehicles before the actual arrival at the intersection in such a way that each vehicle can traverse the intersection at high speed. This increases the capacity of the intersection significantly, offering huge potential savings with respect to travel time compared to nowadays traffic. We propose several new platoon forming algorithms and provide an approximate mean delay analysis for our algorithms. A comparison between the current day practice at intersections (through a case study in SUMO) and our proposed algorithms is provided. Simulation results for fairness are obtained as well, showing that platoon forming algorithms with a low mean delay sometimes are relatively unfair, indicating a potential need for balancing mean delay and fairness.

Paper Structure

This paper contains 12 sections, 4 theorems, 8 equations, 6 figures, 5 algorithms.

Table of Contents

  1. Introduction
  2. Model Formulation
  3. Platoon Forming Algorithms
  4. Speed Profile Algorithms
  5. Optimization based Speed Profile Algorithms
  6. Closed-form Speed Profile Algorithms
  7. Performance Analysis
  8. Polling Model
  9. Mean Delay
  10. Fairness
  11. Comparison traditional Traffic Light and PFAs
  12. Conclusion and Discussion

Key Result

Lemma 3.2

The MotionSynthesize procedure and Algorithm alg:aanrijdenAna are equivalent in the sense that both minimize the distance between vehicle and intersection across the time period $t_0$ to $t_f$.

Figures (6)

  • Figure 1: A schematic representation of the model discussed in this paper. The platoon forming algorithms in this paper determine how the platoons are constructed. In the next step, a speed profiling algorithm determines how each individual vehicle approaches the intersection. Fig (a) and (b) correspond, respectively, to the situation in (c) at times $t=4$ and $t=8$ seconds.
  • Figure 3: Algorithm \ref{['alg:aanrijdenAna']} (solid lines) and Algorithm \ref{['alg:aanrijdenEigenAna']} (dashed lines) for several vehicles with $t$ (s) on the horizontal axis and $|x(t)|$ (m) on the vertical axis for several vehicles.
  • Figure 4: Visualization of the link between the traffic model with PFAs and polling models. The black line represents a self-driving vehicle, and the red dotted line represents the corresponding 'vehicle' in the vertical queueing model.
  • Figure 5: Mean delay experienced by an arbitrary car for the symmetric case (top) and asymmetric case (bottom). The solid lines represent simulation results and the dashed lines approximations.
  • Figure 6: Fairness experienced by an arbitrary car for the symmetric case (top) and asymmetric case (bottom).
  • ...and 1 more figures

Theorems & Definitions (8)

  • Definition 3.1: miculescu2014pollingmiculescu2016polling
  • Lemma 3.2
  • Remark 1
  • Lemma 3.3
  • Remark 2
  • Lemma 4.1
  • Theorem 4.2
  • Remark 3