Centralized adaptive traffic control strategy design across multiple intersections based on vehicle path flows: An approximated Lagrangian decomposition approach

TL;DR

This paper introduces a centralized, adaptive traffic control strategy for multiple intersections using an approximated Lagrangian decomposition approach, aiming to optimize travel times and reduce congestion.

Contribution

It presents a novel centralized traffic control model based on dynamic path flows and an innovative approximated Lagrangian decomposition framework for efficient optimization.

Findings

The approach effectively minimizes total travel time.

It prevents short-term traffic congestions.

Demonstrated robustness and scalability in real-world scenarios.

Abstract

In this paper, we first present a centralized traffic control model based on the emerging dynamic path flows. This new model in essence views the whole target network as one integral piece in which traffic propagates based on traffic flow dynamics, vehicle paths, and traffic control. In light of this centralized traffic control concept, most requirements for the existing traffic control coordination will be dropped in the optimal traffic control operations, such as the common cycle length or offsets. Instead, the optimal traffic control strategy across intersections will be highly adaptive over time to minimize the total travel time and it can also prevent any short-term traffic congestions according to the space-time characteristics of vehicle path flows. A mixed integer linear programming (MILP) formulation is then presented to model the propagations of path flows given a centralized traffic control strategy. Secondly, a new approximated Lagrangian decomposition framework is presented. Solving the proposed MILP model with the traditional Lagrangian decomposition approach faces the leveraging challenge between the problem tractability after decomposition and computing complexity. To address this issue, we propose an approximate Lagrangian decomposition framework in which the target problem is reformulated into an approximated problem by constructing its complicating attributes into the objective function instead of in constraints to reduce the computing complexity. The computing efficiency loss of the objective function can be mitigated via multiple advanced computing techniques. With the proposed approximated approach, the upper bound and tight lower bound can be obtained via two customized dynamic network loading models. In the end, one demonstrative and one real-world example are illustrated to show the validness, robustness, and scalability of the new approach.