Traffic Flow

By: Anders Rømer Gylling, Azeez Deji Salami, Daniel Jacob Grover, Mehmet Temizsoy, og Michael Skytte Petersen Supervisor: Jesper Schmidt Hansen

Modeling of Traffic Flow Subject module project – 5th semester – fall 2014

Roskilde University

Abstract

In modern times, traffic flow is one of the main societal and economical inconveniences related to transportation. Better understanding of traffic flow is needed to reduce congestion and prevent it from happening. Being able to manage traffic flow phenomena requires knowledge of its intricate and seemingly enigmatic workings through modeling its behavior. Many mathematical methods have been developed to model the behavior of traffic systems, both analytically and numerically. This report endeavors to address the effects of a having a velocity that is dependent on vehicle density on the road. Numerical simulation is an important means for modeling the operations of dynamic traffic flow. This paper presents a macroscopic model simulation to capture the dynamics of global traffic systems through application of the advection equation. The Upwind Scheme is the choice of method used for numerical discretization to solve the advection equation. The way in which three different velocity functions are illustrative of real-world traffic flow is the main topic of discussion. Additionally, the report discusses certain issues which arose in the use of the Upwind Scheme and influenced the realism of the results. These are numerical diffusion and inability to handle negative density values. Our results demonstrated the basic characteristics of traffic flow while presenting models for traffic flow which show some ability to accurately portray a real-world highway.