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Probe-and-Release Coordination of Platoons at Highway Bottlenecks with Unknown Parameters

Yi Gao, Xi Xiong, Karl H. Johansson, Li Jin

TL;DR

This work addresses flow-level control at highway bottlenecks with unknown and time-varying environmental parameters by integrating online parameter estimation into a probe-and-release control framework. Using a fluid queuing model with capacity drops and delay, the authors jointly estimate $\alpha$, $Q$, $R$, and $\varepsilon_{\max}$ while coordinating CAV platoons to stabilize traffic; stability is proved via a Lyapunov drift approach on an embedded Markov process. Theoretical results show bounded estimation errors and bounded traffic queues, with explicit drift bounds, and a stochastic stability condition requiring $\bar{A}+\bar{B}<\tilde{R}$. Validation in SUMO against a PPO baseline demonstrates competitive travel times with far fewer data samples (about 0.05% of PPO) and faster adaptation to environmental changes, highlighting the method’s data efficiency and practical viability for mixed-autonomy congestion management.

Abstract

This paper considers coordination of platoons of connected and autonomous vehicles (CAVs) at mixed-autonomy bottlenecks in the face of three practically important factors, viz. time-varying traffic demand, random CAV platoon sizes, and capacity breakdowns. Platoon coordination is essential to smoothen the interaction between CAV platoons and non-CAV traffic. Based on a fluid queuing model, we develop a "probe-and-release" algorithm that simultaneously estimates environmental parameters and coordinates CAV platoons for traffic stabilization. We show that this algorithm ensures bounded estimation errors and bounded traffic queues. The proof builds on a Lyapunov function that jointly penalizes estimation errors and traffic queues and a drift argument for an embedded Markov process. We validate the proposed algorithm in a standard micro-simulation environment and compare against a representative deep reinforcement learning method in terms of control performance and computational efficiency.

Probe-and-Release Coordination of Platoons at Highway Bottlenecks with Unknown Parameters

TL;DR

This work addresses flow-level control at highway bottlenecks with unknown and time-varying environmental parameters by integrating online parameter estimation into a probe-and-release control framework. Using a fluid queuing model with capacity drops and delay, the authors jointly estimate , , , and while coordinating CAV platoons to stabilize traffic; stability is proved via a Lyapunov drift approach on an embedded Markov process. Theoretical results show bounded estimation errors and bounded traffic queues, with explicit drift bounds, and a stochastic stability condition requiring . Validation in SUMO against a PPO baseline demonstrates competitive travel times with far fewer data samples (about 0.05% of PPO) and faster adaptation to environmental changes, highlighting the method’s data efficiency and practical viability for mixed-autonomy congestion management.

Abstract

This paper considers coordination of platoons of connected and autonomous vehicles (CAVs) at mixed-autonomy bottlenecks in the face of three practically important factors, viz. time-varying traffic demand, random CAV platoon sizes, and capacity breakdowns. Platoon coordination is essential to smoothen the interaction between CAV platoons and non-CAV traffic. Based on a fluid queuing model, we develop a "probe-and-release" algorithm that simultaneously estimates environmental parameters and coordinates CAV platoons for traffic stabilization. We show that this algorithm ensures bounded estimation errors and bounded traffic queues. The proof builds on a Lyapunov function that jointly penalizes estimation errors and traffic queues and a drift argument for an embedded Markov process. We validate the proposed algorithm in a standard micro-simulation environment and compare against a representative deep reinforcement learning method in terms of control performance and computational efficiency.

Paper Structure

This paper contains 27 sections, 2 theorems, 60 equations, 12 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Motivation and background
  3. Related work
  4. Our contributions
  5. Model Formulation and Algorithm Design
  6. Demand and capacity models
  7. Fluid queuing model with control
  8. Probe-and-release algorithm
  9. Probing phase
  10. Release phases
  11. Stability analysis
  12. Convergence of estimation errors
  13. Boundedness of $e_R$
  14. Boundedness of $e_{\alpha}$
  15. Convergence of $e_{F_{\mathrm{max}}}$ and $e_{\varepsilon_{\mathrm{max}}}$
  16. ...and 12 more sections

Key Result

Proposition 1

Without coordination (i.e., $b_{Bq}(t)=0$ for all $t$), the system is stable in the sense of eq_stability if and only if at least one of the following conditions is satisfied:

Figures (12)

  • Figure 1: A typical mixed traffic setting with vs. without inter-platoon coordination at the bottleneck.
  • Figure 2: The probe-and-release algorithm periodically alternates between estimation and control; a period is called a "round". Each episode in probe phases collects 2 samples in this illustration.
  • Figure 3: Highway bottleneck model; on-ramp flow is modeled as a noise to mainline flow.
  • Figure 4: Flow function $f(x_0)$. Breakdown occurs at $x_0^\mathrm{c}$. Shaded area is the noise band for actual flow $F(t)$.
  • Figure 5: Fluid queuing model with delayed entrance to traffic queue. $b_s(t)$ is the only independent control input.
  • ...and 7 more figures

Theorems & Definitions (2)

  • Proposition 1: Baseline throughput
  • Theorem 1