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Distributed Traffic Signal Control via Coordinated Maximum Pressure-plus-Penalty

Vinzenz Tütsch, Zhiyu He, Florian Dörfler, Kenan Zhang

TL;DR

CMPP extends Maximum Pressure (MP) by incorporating coordination among neighboring intersections through a neighborhood pressure objective and a queue-length–dependent penalty, ensuring network-wide stability via Lyapunov drift techniques. The policy is solved in a distributed fashion using two consensus mechanisms, ADMM and a Greedy heuristic, enabling online implementation in large-scale networks. Simulation on a realistic Midtown Manhattan network demonstrates that CMPP consistently reduces average travel and waiting times and controls network congestion better than FT, MP, and CA-BP, with CMPP-Greedy offering a compelling trade-off between performance and computation time. The work provides theoretical stability guarantees, practical distributed algorithms, and evidence of real-world deployability for coordinated adaptive traffic signal control.

Abstract

This paper develops an adaptive traffic control policy inspired by Maximum Pressure (MP) while imposing coordination across intersections. The proposed Coordinated Maximum Pressure-plus-Penalty (CMPP) control policy features a local objective for each intersection that consists of the total pressure within the neighborhood and a penalty accounting for the queue capacities and continuous green time for certain movements. The corresponding control task is reformulated as a distributed optimization problem and solved via two customized algorithms: one based on the alternating direction method of multipliers (ADMM) and the other follows a greedy heuristic augmented with a majority vote. CMPP not only provides a theoretical guarantee of queuing network stability but also outperforms several benchmark controllers in simulations on a large-scale real traffic network with lower average travel and waiting time per vehicle, as well as less network congestion. Furthermore, CPMM with the greedy algorithm enjoys comparable computational efficiency as fully decentralized controllers without significantly compromising the control performance, which highlights its great potential for real-world deployment.

Distributed Traffic Signal Control via Coordinated Maximum Pressure-plus-Penalty

TL;DR

CMPP extends Maximum Pressure (MP) by incorporating coordination among neighboring intersections through a neighborhood pressure objective and a queue-length–dependent penalty, ensuring network-wide stability via Lyapunov drift techniques. The policy is solved in a distributed fashion using two consensus mechanisms, ADMM and a Greedy heuristic, enabling online implementation in large-scale networks. Simulation on a realistic Midtown Manhattan network demonstrates that CMPP consistently reduces average travel and waiting times and controls network congestion better than FT, MP, and CA-BP, with CMPP-Greedy offering a compelling trade-off between performance and computation time. The work provides theoretical stability guarantees, practical distributed algorithms, and evidence of real-world deployability for coordinated adaptive traffic signal control.

Abstract

This paper develops an adaptive traffic control policy inspired by Maximum Pressure (MP) while imposing coordination across intersections. The proposed Coordinated Maximum Pressure-plus-Penalty (CMPP) control policy features a local objective for each intersection that consists of the total pressure within the neighborhood and a penalty accounting for the queue capacities and continuous green time for certain movements. The corresponding control task is reformulated as a distributed optimization problem and solved via two customized algorithms: one based on the alternating direction method of multipliers (ADMM) and the other follows a greedy heuristic augmented with a majority vote. CMPP not only provides a theoretical guarantee of queuing network stability but also outperforms several benchmark controllers in simulations on a large-scale real traffic network with lower average travel and waiting time per vehicle, as well as less network congestion. Furthermore, CPMM with the greedy algorithm enjoys comparable computational efficiency as fully decentralized controllers without significantly compromising the control performance, which highlights its great potential for real-world deployment.
Paper Structure (25 sections, 2 theorems, 32 equations, 8 figures, 1 table, 1 algorithm)

This paper contains 25 sections, 2 theorems, 32 equations, 8 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background and Motivations
  3. Contributions
  4. Problem Setting and Preliminaries
  5. Road Network, Signal Control, and Queue Dynamics
  6. Queuing Stability and Lyapunov Drift Theory
  7. Maximum Pressure Control
  8. Coordinated Maximum Pressure-plus-Penalty Control
  9. Lyapunov Minimum Drift-Plus-Penalty Control
  10. CMPP Control and Penalty Function
  11. Stability Analysis
  12. Solution Algorithm for CMPP
  13. ADMM
  14. Greedy Heuristic
  15. Simulation Experiments
  16. ...and 10 more sections

Key Result

Theorem 1

Consider the Lyapunov function $L(\mathbf{Q}(t))$ defined in eq:Lyapunov_function. Suppose the initial queues satisfy $\mathbb{E}\{L(\mathbf{Q}(0))\} < \infty$, then the queuing system is strongly stable if there exist constants $B \geq 0, V > 0, \epsilon > 0$ and $p^*$ such that $\forall t$,

Figures (8)

  • Figure 1: Eight phases in a typical intersection.
  • Figure 2: Simulated traffic network based on Midtown Manhattan.
  • Figure 3: Traffic demand over simulation horizon.
  • Figure 4: Average vehicle travel time [sec].
  • Figure 5: Example of queue spillover under MP.
  • ...and 3 more figures

Theorems & Definitions (5)

  • Definition 1: Stability of queuing process
  • Theorem 1: Lyapunov Optimization theorem
  • proof
  • Theorem 2: Stability of CMPP
  • proof