Traffic Flow Models and Their Numerical Solutions

TL;DR

This thesis develops advanced numerical methods for traffic flow models, including Riemann problems and Godunov methods, and analyzes inhomogeneous road models with a novel two-level simulation framework.

Contribution

It introduces higher order traffic flow models and a two-level simulation framework using Godunov-type methods with supply-demand approach.

Findings

Rigorous analysis of inhomogeneous road traffic models

Development of a two-level network simulation framework

Implementation of supply-demand method as an alternative Riemann solver

Abstract

In this thesis, Riemann problems and Godunov methods are developed for higher order traffic flow models. A rigorous analysis of the first order traffic flow model of inhomogeneous road is presented. A two-level simulation framework of network vehicular traffic is proposed as a Godunov-type finite difference system with the supply-demand method as an alternative of Riemann solver.