Fitting Empirical Fundamental Diagrams of Road Traffic: A Comprehensive
Review and Comparison of Models Using an Extensive Data Set
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
currently 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.