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Distributed MPC-based Coordination of Traffic Perimeter and Signal Control: A Lexicographic Optimization Approach

Viet Hoang Pham, Hyo-Sung Ahn

TL;DR

This work tackles urban congestion by integrating traffic perimeter control with internal signal optimization through a lexicographic MPC framework. It models the UTN with a store-and-forward CTM-based prediction and employs a two-stage objective: first maximize inflows at the perimeter under safety constraints, then optimize internal signal timings to improve conditions without sacrificing perimeter capacity. A fully distributed solution based on ADMM decomposes the problem into subnetworks, enabling parallel computation and local communication with neighbors. Simulations in VISSIM and MATLAB demonstrate that the proposed lexicographic MPC strategy enhances network throughput and mitigates congestion under varied demand, while remaining computationally tractable for real-time operation. The approach offers a scalable, principled method to jointly manage boundary inflows and element-level traffic signals in large urban networks.

Abstract

This paper introduces a comprehensive strategy that integrates traffic perimeter control with traffic signal control to alleviate congestion in an urban traffic network (UTN). The strategy is formulated as a lexicographic multi-objective optimization problem, starting with the regulation of traffic inflows at boundary junctions to maximize the capacity while ensuring a smooth operation of the UTN. Following this, the signal timings at internal junctions are collaboratively optimized to enhance overall traffic conditions under the regulated inflows. The use of a model predictive control (MPC) approach ensures that the control solution adheres to safety and capacity constraints within the network. To address the computational complexity of the problem, the UTN is divided into subnetworks, each managed by a local agent. A distributed solution method based on the alternating direction method of multipliers (ADMM) algorithm is employed, allowing each agent to determine its optimal control decisions using local information from its subnetwork and neighboring agents. Numerical simulations using VISSIM and MATLAB demonstrate the effectiveness of the proposed traffic control strategy.

Distributed MPC-based Coordination of Traffic Perimeter and Signal Control: A Lexicographic Optimization Approach

TL;DR

This work tackles urban congestion by integrating traffic perimeter control with internal signal optimization through a lexicographic MPC framework. It models the UTN with a store-and-forward CTM-based prediction and employs a two-stage objective: first maximize inflows at the perimeter under safety constraints, then optimize internal signal timings to improve conditions without sacrificing perimeter capacity. A fully distributed solution based on ADMM decomposes the problem into subnetworks, enabling parallel computation and local communication with neighbors. Simulations in VISSIM and MATLAB demonstrate that the proposed lexicographic MPC strategy enhances network throughput and mitigates congestion under varied demand, while remaining computationally tractable for real-time operation. The approach offers a scalable, principled method to jointly manage boundary inflows and element-level traffic signals in large urban networks.

Abstract

This paper introduces a comprehensive strategy that integrates traffic perimeter control with traffic signal control to alleviate congestion in an urban traffic network (UTN). The strategy is formulated as a lexicographic multi-objective optimization problem, starting with the regulation of traffic inflows at boundary junctions to maximize the capacity while ensuring a smooth operation of the UTN. Following this, the signal timings at internal junctions are collaboratively optimized to enhance overall traffic conditions under the regulated inflows. The use of a model predictive control (MPC) approach ensures that the control solution adheres to safety and capacity constraints within the network. To address the computational complexity of the problem, the UTN is divided into subnetworks, each managed by a local agent. A distributed solution method based on the alternating direction method of multipliers (ADMM) algorithm is employed, allowing each agent to determine its optimal control decisions using local information from its subnetwork and neighboring agents. Numerical simulations using VISSIM and MATLAB demonstrate the effectiveness of the proposed traffic control strategy.

Paper Structure

This paper contains 26 sections, 2 theorems, 54 equations, 14 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Traffic Model for MPC approach
  3. Graph Representation
  4. Prediction model
  5. Vehicle conservation equations
  6. Traffic signal in internal junctions
  7. Traffic flows
  8. MPC traffic control via perimeter and signal control coordination
  9. Introduction to MPC-based traffic control
  10. Lexicographic multi-objective MPC problem
  11. Distributed control problem
  12. Proposed strategy
  13. Distributed solution method for solving $\textbf{(PC)}$
  14. Distributed solution method for solving $\textbf{(TSC)}$
  15. Strategy for Optimal Traffic Control
  16. ...and 11 more sections

Key Result

Lemma 1

Let $\tilde{\textbf{x}}^{opt} = \textrm{col}\{\tilde{\textbf{x}}_i^{opt}: 1 \le i \le N\}$ be the optimal solution of the problem eq_TSC_tosolve. Then the vector $\hat{\textbf{x}}^{opt} = \textrm{col}\{\textbf{D}_i\tilde{\textbf{x}}_i^{opt}: 1 \le i \le N\}$, where $\textbf{D}_i = [\textbf{I}, \text

Figures (14)

  • Figure 1: Traffic flows in a road link $z \in \mathcal{L}$ for two cases: (top) $\sigma(z) = B_v \in \mathcal{J}^B$; (bottom) $\sigma(z) = J_v \in \mathcal{J}^I$ and $\mathcal{N}_z^+ = \{w_1, w_2, w_3\}$. The blue arrows correspond to downstream traffic flows, the green arrows are exogenous traffic flows of the road link $z$, and the red arrows are the exogenous traffic inflows from the boundary junction.
  • Figure 2: Illustration of multiobjective optimization.
  • Figure 3: Diagram for proposed control strategy.
  • Figure 4: The tested UTN built in VISSIM.
  • Figure 5: Simulation results in under-saturated scenario.
  • ...and 9 more figures

Theorems & Definitions (4)

  • Remark 1
  • Lemma 1
  • proof
  • Theorem 1