The Spatial Variability of Vehicle Densities as Determinant of Urban Network Capacity

TL;DR

This paper introduces a macroscopic fluid-dynamic simulation method for urban traffic, emphasizing the importance of vehicle density variability and its impact on network capacity and congestion dynamics.

Contribution

It presents a novel approach combining quantized vehicle flows and destination flow simulation, revealing fundamental relationships between traffic variables and variability.

Findings

Variability of vehicle densities influences congestion.

A simple analytical formula approximates network capacity.

Inhomogeneity reduces scatter in flow measurements.

Abstract

Due to the complexity of the traffic flow dynamics in urban road networks, most quantitative descriptions of city traffic so far are based on computer simulations. This contribution pursues a macroscopic (fluid-dynamic) simulation approach, which facilitates a simple simulation of congestion spreading in cities. First, we show that a quantization of the macroscopic turning flows into units of single vehicles is necessary to obtain realistic fluctuations in the traffic variables, and how this can be implemented in a fluid-dynamic model. Then, we propose a new method to simulate destination flows without the requirement of individual route assignments. Combining both methods allows us to study a variety of different simulation scenarios. These reveal fundamental relationships between the average flow, the average density, and the variability of the vehicle densities. Considering the inhomogeneity of traffic as an independent variable can eliminate the scattering of congested flow measurements. The variability also turns out to be a key variable of urban traffic performance. Our results can be explained through the number of full links of the road network, and approximated by a simple analytical formula.