Structure of road networks and the shape of the macroscopic fundamental diagram

TL;DR

This paper develops scaling laws linking the macroscopic fundamental diagram's key traffic quantities to road network structure, explaining empirical observations across multiple cities and enhancing understanding of urban traffic dynamics.

Contribution

It introduces a theoretical framework using numerical modeling and dimensional analysis to relate MFD properties to network structure, a novel approach in traffic flow analysis.

Findings

Scaling laws for maximum flow and optimal density are derived.

The framework explains empirical scaling observed in various cities.

Impact of buses on network capacity is quantitatively analyzed.

Abstract

The macroscopic fundamental diagram (MFD) is a large scale description of the traffic in a urban area and relates the average car flow to the average car density. This MFD has been observed empirically in several cities but how its properties are related to the structure of the road network has remained unclear so far. The MFD displays in general a maximum flow $q^*$ for an optimal car density $k^*$ which are crucial quantities for practical applications. Here, using numerical modeling and dimensional arguments, we propose scaling laws for these quantities $q^*$ and $k^*$ in terms of the road density, the intersection density, the average car size and the maximum velocity. This framework is able to explain the scaling observed empirically for several cities in the world, such as the scaling of $k^*$ with the road density, the relation between $q^*$ and $k^*$ and the impact of buses on the overall capacity $q^*$. This work opens the way to a better understanding of the traffic on a road network at a large urban scale.