A second order model of road junctions in fluid models of traffic networks

Abstract

This article deals with the modeling of junctions in a road network from a macroscopic point of view. After reviewing the Aw & Rascle second order model, a compatible junction model is proposed. The properties of this model and particularly the stability are analyzed. It turns out that this model presents physically acceptable solutions, is able to represent the capacity drop phenomenon and can be used to simulate the traffic evolution on a network.

ISS-Lyapunov functions for time-varying hyperbolic systems of balance laws

“…When the functions Λ, and F do not depend on z and t, and when Λ is invertible, the Cauchy problem (2), (3) and (4) …”

“…The study of this class of PDEs is crucial when considering a wide range physical networks having an engineering relevance. Among the potential applications we have in mind, there are for instance hydraulic networks (for irrigation or navigation), electric line networks, road traffic networks [3] or gas flow in pipeline networks [4], [5]. The importance of these applications motivates a lot of theoretical questions on hyperbolic systems which for instance pertain to optimal control and controllability as considered in [6], [7], [8].…”

Numerical Feedback Stabilization with Applications to Networks

“…Many network applications are represented by onedimensional hyperbolic systems of balance laws [4,[26][27][28][29][30]. For the analytical case it can be proven that feedback boundary values, designed under certain conditions, yield an exponential decay of a continuous Lyapunov function [3,9,31] also in the context of networks.…”

Numerical Discretization of Coupling Conditions by High-Order Schemes

“…Among the many examples where such systems arise are traffic flow [24,25,29,31], production networks [21,23,30], telecommunication networks [22], gas flow in pipe networks [3, 11-13, 15, 16] or water flow in canals [4,5,28,35]. Mathematically, flow problems on networks are boundary value problems where the boundary value is implicitly defined by a coupling condition.…”