Derivation of a Fundamental Diagram for Urban Traffic Flow

TL;DR

This paper develops a theoretical model for urban traffic flow that explains the fundamental relationships between key variables like density, speed, and travel time, providing a systematic understanding of empirical observations.

Contribution

It introduces a novel theoretical approach to derive fundamental traffic flow relationships from intersection models, advancing beyond empirical fit curves.

Findings

Derived fundamental diagrams from the model

Expressed travel time as a function of utilization

Linked average vehicle speed to traffic variables

Abstract

Despite the importance of urban traffic flows, there are only a few theoretical approaches to determine fundamental relationships between macroscopic traffic variables such as the traffic density, the utilization, the average velocity, and the travel time. In the past, empirical measurements have primarily been described by fit curves. Here, we derive expected fundamental relationships from a model of traffic flows at intersections, which suggest that the recently measured fundamental diagrams for urban flows can be systematically understood. In particular, this allows one to derive the average travel time and the average vehicle speed as a function of the utilization and/or the average number of delayed vehicles.