Generic second-order macroscopic traffic node model for general multi-input multi-output road junctions via a dynamic system approach

TL;DR

This paper introduces a novel second-order macroscopic traffic node model for complex multi-road junctions, leveraging a dynamic system approach to better capture diverse vehicle behaviors and improve traffic flow modeling.

Contribution

It extends the generic class of node models to second-order traffic dynamics and provides a simple solution algorithm based on dynamic systems theory.

Findings

Enables modeling of behaviorally complex traffic flows.

Provides a solution for arbitrary multi-input/output junctions.

Improves understanding of second-order traffic node dynamics.

Abstract

This paper addresses an open problem in traffic modeling: the second-order macroscopic node problem. A second-order macroscopic traffic model, in contrast to a first-order model, allows for variation of driving behavior across subpopulations of vehicles in the flow. The second-order models are thus more descriptive (e.g., they have been used to model variable mixtures of behaviorally-different traffic, like car/truck traffic, autonomous/human-driven traffic, etc.), but are much more complex. The second-order node problem is a particularly complex problem, as it requires the resolution of discontinuities in traffic density and mixture characteristics, and solving of throughflows for arbitrary numbers of input and output roads to a node (in other words, this is an arbitrary-dimensional Riemann problem with two conserved quantities). In this paper, we extend the well-known "Generic Class of Node Model" constraints to the second order and present a simple solution algorithm to the second-order node problem. Our solution makes use of a recently-introduced dynamic system characterization of the first-order node model problem, which gives insight and intuition as to the continuous-time dynamics implicit in node models. We further argue that the common "supply and demand" construction of node models that decouples them from link models is not suitable to the second-order node problem. Our second-order node model and solution method have immediate applications in allowing modeling of behaviorally-complex traffic flows of contemporary interest (like partially-autonomous-vehicle flows) in arbitrary road networks.