Abstract
Understanding the inter-relationships between traffic flow, density, and speed through the study of the fundamental diagram of road traffic is critical for traffic modelling and management. Consequently, over the last 85 years, a wealth of models have been developed for its functional form. However, there has been no clear answer as to which model is the most appropriate for observed (i.e. empirical) fundamental diagrams and under which conditions. A lack of data has been partly to blame. Motivated by shortcomings in previous reviews, we first present a comprehensive literature review on modelling the functional form of empirical fundamental diagrams. We then perform fits of 50 previously proposed models to a high quality sample of 10 150 empirical fundamental diagrams pertaining to 25 cities. Comparing the fits using information criteria, we find that the non-parametric Sun model greatly outperforms all of the other models. The Sun model maintains its winning position regardless of road type and congestion level. Our study, the first of its kind when considering the number of models tested and the amount of data used, finally provides a definitive answer to the question “Which model for the functional form of an empirical fundamental diagram is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">currently</i> the best?”. The word “currently” in this question is key, because previously proposed models adopt an inappropriate Gaussian noise model with constant variance. We advocate that future research should shift focus to exploring more sophisticated noise models. This will lead to an improved understanding of empirical fundamental diagrams and their underlying functional forms.
Highlights
Understanding the inter-relationships between traffic flow, density, and speed through the study of the fundamental diagram of road traffic is critical for traffic modelling and management
On visual inspection of the flow-occupancy empirical fundamental diagram (EFD) for the remaining Loop detectors (LDs), we observe that a non-negligible number of EFDs exhibit features that will either require special modelling, or that are indicative of a malfunctioning LD
Before we delve into the review, it is important to emphasise that any model for an EFD consists of two main components; namely, a model component that specifies the functional form of the fundamental diagram (FD) relationship, and a model component that specifies the noise properties
Summary
HE macroscopic description of traffic flow along a road requires the definition of quantities characterising the average properties of the vehicular traffic at a specific location x and time t; namely, traffic density k(x, t) as the number of vehicles per unit length at time t (veh km−1 ), traffic flow q(x, t) as the number of vehicles passing location x per unit. While there is value in understanding the theoretical FD relationship for uninterrupted flow facilities, we believe that it is of great benefit to be able to correctly model the observed FD for any road This relates more to the practicalities of traffic management and real-time control both at the individual link and urban network levels It is blatantly clear that the question as to which model(s) for the functional form of the FD are the most appropriate for EFDs, including how this may depend on road topology, is still unresolved This is the issue that we aim to tackle with this work, and the path to an answer lies in testing the performance of as many as possible of the existing models on a very large and varied data set.
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