A dynamic system characterization of road network node models

TL;DR

This paper introduces a hybrid dynamic system that models traffic flow at road junctions, providing an intuitive physical understanding and a basis for controlling complex network congestion phenomena.

Contribution

It presents a simple, physically interpretable dynamic system for solving node models in traffic networks, unifying and deriving existing models.

Findings

The dynamic system accurately reproduces solutions of popular node models.

It offers an intuitive physical interpretation of traffic flow at junctions.

Provides a foundation for controlling and analyzing network congestion.

Abstract

The propagation of traffic congestion along roads is a commonplace nonlinear phenomenon. When many roads are connected in a network, congestion can spill from one road to others as drivers queue to enter a congested road, creating further nonlinearities in the network dynamics. This paper considers the node model problem, which refers to methods for solving for cross-flows when roads meet at a junction. We present a simple hybrid dynamic system that, given a macroscopic snapshot of the roads entering and exiting a node, intuitively models the node's throughflows over time. This dynamic system produces solutions to the node model problem that are equal to those produced by many popular node models without intuitive physical meanings. We also show how the earlier node models can be rederived as executions of our dynamic system. The intuitive physical description supplied by our system provides a base for control of the road junction system dynamics, as well as the emergent network dynamics.