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

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/humandriven 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 arbitrarydimensional Riemann problem with two conserved quantities). We propose a solution to this problem by making 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 first-order node models. We use this intuition to extend the dynamic system node model to the second-order setting. We also 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. This node model has immediate applications in allowing modeling of behaviorally-complex traffic flows of contemporary interest (like partially-autonomous-vehicle flows) in arbitrary road networks.