Kinematic Wave Models of Network Vehicular Traffic

TL;DR

This paper develops and analyzes kinematic wave models for network vehicular traffic, introducing a multi-commodity model that is numerically convergent and applicable to complex traffic systems with inhomogeneous links and mixed vehicles.

Contribution

It introduces a multi-commodity kinematic wave model for network traffic, with new numerical methods and applications to equilibrium and periodic wave analysis.

Findings

The MCKW model is numerically convergent.

The model accurately simulates traffic flow in complex networks.

Applications include studying equilibrium states and periodic waves.

Abstract

The kinematic wave theory, originally proposed by (Lighthill and Whitham, 1955b; Richards, 1956), has been a good candidate for studying vehicular traffic. In this dissertation, we study kinematic wave models of network traffic, which are expected to be theoretically rigorous, numerically reliable, and computationally efficient. For traffic systems with inhomogeneous links, merges, diverges, or mixed-type vehicles, we study the kinematic waves in their Riemann solutions and develop numerical solution methods of the Godunov type and the supply-demand type. For a network traffic system, we propose a multi-commodity kinematic wave (MCKW) model and an implementation of it. The model observes First-In-First-Out principle in the order of a time interval and is numerically convergent. Further, we apply this simulation model to study equilibrium states and periodic waves in road networks. Finally, we summarize our work and discuss future research directions.