[Paper Review] An Integrative Data-Driven Physics-Inspired Approach to Traffic Congestion Control

Hossein Rastgoftar, Ella Atkins|arXiv (Cornell University)|Dec 2, 2019

Traffic control and management28 references4 citations

TL;DR

This paper proposes a data-driven, physics-inspired model predictive control (MPC) framework for traffic congestion control in large-scale urban networks by learning flow-density relationships from historical traffic data within a sliding window. It formulates boundary inflow optimization as a constrained quadratic program using linear temporal logic to ensure traffic feasibility, achieving stable congestion control within 600 seconds in simulation.

ABSTRACT

This paper offers an integrative data-driven physics-inspired approach to model and control traffic congestion in a resilient and efficient manner. While existing physics-based approaches commonly assign density and flow traffic states by using the Fundamental Diagram, this paper specifies the flow-density relation using past traffic information recorded in a time sliding window with a constant horizon length. With this approach, traffic coordination trends can be consistently learned and incorporated into traffic planning. This paper also models traffic coordination as a probabilistic process and obtains traffic feasibility conditions using linear temporal logic. Model productive control (MPC) is applied to control traffic congestion through the boundary of the traffic network. Therefore, the optimal boundary inflow is assigned as the solution of a constrained quadratic programming problem.

Motivation & Objective

• Address the limitations of traditional physics-based models, such as the Fundamental Diagram, in large-scale traffic networks.
• Improve resilience and accuracy in traffic congestion modeling by incorporating empirical traffic data instead of relying on fixed flow-density relationships.
• Develop a formal framework for specifying traffic feasibility conditions using linear temporal logic (LTL).
• Enable adaptive, real-time control of traffic inflows at network boundaries through model predictive control (MPC).
• Integrate microscopic traffic dynamics into macroscopic planning for improved coordination in interconnected road networks (NOIR).

Proposed method

• Model traffic dynamics using a spatially and temporally discretized continuity partial differential equation (PDE), representing mass conservation in a network of interconnected roads (NOIR).
• Learn the flow-density relationship dynamically from past traffic data within a fixed-time sliding window, replacing static Fundamental Diagram assumptions.
• Formalize traffic feasibility conditions using linear temporal logic (LTL) to ensure safe and stable traffic operation across the network.
• Implement an adaptive MPC controller that solves a constrained quadratic programming problem at each time step to compute optimal boundary inflows.
• Integrate a Parameter Adaptation Unit (PAU) that updates the system dynamics matrix $\mathbf{A}_{a[k]}$ based on real-time traffic tendency actions $a[k]$.
• Use a time-varying cost function $\mathrm{C} = \sum_{\tau=1}^{N_{\tau}} \left( \mathbf{x}^T[k+\tau]\mathbf{x}[k+\tau] + \beta\mathbf{u}^T[k+\tau]\mathbf{u}[k+\tau] \right)$ to balance state deviation and control effort.

Experimental results

Research questions

• RQ1 How can empirical traffic data be effectively used to learn dynamic flow-density relationships in large-scale urban networks?
• RQ2 To what extent can formal methods like linear temporal logic improve the resilience and safety of traffic congestion control systems?
• RQ3 Can adaptive model predictive control with data-driven dynamics outperform traditional physics-based models in controlling congestion over time?
• RQ4 How does the integration of microscopic traffic behavior into macroscopic planning affect overall network stability and performance?
• RQ5 What is the convergence behavior of the control system in terms of achieving steady-state traffic density under bounded inflow constraints?

Key findings

• The proposed method successfully reduced traffic density to steady-state values within approximately 600 seconds (20 time steps) in simulation, indicating effective congestion control.
• Boundary inflow inputs $u_1$ through $u_8$ were dynamically adjusted over time, demonstrating adaptive control in response to changing traffic conditions.
• Traffic density across all interior road elements stabilized after about 20 time steps, confirming the effectiveness of the control strategy.
• The system maintained a maximum density of $\rho_{\text{max}} = 45$ vehicles per unit length, ensuring operational safety and feasibility.
• The use of a sliding window for data-driven flow-density learning enabled consistent and up-to-date modeling of traffic coordination trends.
• The integration of LTL-based feasibility constraints ensured that all control actions adhered to formal safety and operational requirements.