Junction Conditions for Hamilton–Jacobi Equations for Solving Real-Time Traffic Flow Problems

Linfeng Zhang,Nicolas Forcadel,Hongfei Jia,Bin Ran

doi:10.1109/access.2019.2935535

Abstract

In this paper, we propose junction conditions for discontinuities due to local perturbation, diverging, merging, and multi-in-multi-out junctions. Traffic flows on junctions can be described by a system of coupled Hamilton-Jacobi equations. At their connection points, it is necessary to propose appropriate junction conditions to close the system. Then, we provide an effective numerical method to compute approximate solutions to these Hamilton-Jacobi equations on junctions. The numerical boundary conditions to close the Hamilton-Jacobi system are also proposed. Numerical tests demonstrate the effectiveness of both the proposed junction conditions and the numerical method.

Highlights

Many traffic flow models have recently been designed
The roads can be described by Hamilton-Jacobi equations, and we should provide junction conditions at the nodes to close the traffic network problem
The goal of this paper is to propose junction conditions for local perturbation, bifurcation, merging and multi-in-multiout nodes on a network

Summary

INTRODUCTION

Many traffic flow models have recently been designed. These models are mainly used to study the temporal and spatial distributions of traffic density and the driving habits of car drivers, by governments or their departments to design traffic facilities or to provide references for the construction of roads [1], [2]. Note that macroscopic models can be described in terms of the cumulative number of vehicles, i.e., the primitive of the density (see, for example, [6]) The roads can be described by Hamilton-Jacobi equations, and we should provide junction conditions at the nodes to close the traffic network problem. L. Zhang et al.: Junction Conditions for Hamilton–Jacobi Equations for Solving Real-Time Traffic Flow Problems there are many numerical methods, such as ENO [21] and WENO [22], to compute the discontinuities such as shock waves. The goal of this paper is to propose different types of junctions and provide an effective numerical method for computing junctions. The goal of this paper is to propose junction conditions for local perturbation, bifurcation, merging and multi-in-multiout nodes on a network. At the end of this paper, we provide some conclusions and remarks

TRAFFIC FLOW MODEL POSED ON A JUNCTION

LOCAL PERTURBATION AND INFLUENCE OF THE FLUX LIMITER A

NUMERICAL VALIDATION FOR MERGING CONDITION

CONCLUSION