Linearized Theory of Traffic Flow

TL;DR

This paper develops a linearized theoretical framework for macroscopic traffic flow models, providing closed-form solutions to analyze phenomena like stop-and-go waves, shock waves, and platoon splitting and merging.

Contribution

It introduces a linearized approach to traffic flow equations, enabling analytical solutions for complex traffic phenomena not previously accessible.

Findings

Analytical solutions for stop-and-go traffic waves

Modeling of shock waves at traffic lights

Description of platoon splitting and merging dynamics

Abstract

The equation of motion of a general class of macroscopic traffic flow models is linearized around a steady uniform flow. A closed-form solution of a boundary-initial value problem is obtained, and it is used to describe several phenomena. Specifically, the scenarios examined involve a smooth velocity field in stop-and-go traffic, a discontinuous velocity field with shock waves in a traffic light problem, and discontinuous displacement fields in a problem where a single platoon of vehicles splits into two, and later merges back into one.