Abstract
Vehicular traffic can be modelled as a dynamic discrete form. As in many dynamic systems, the parameters modelling traffic can produce a number of different trajectories or orbits, and it is possible to depict different flow situations, including chaotic ones. In this paper, an approach to the wellknown density-flow fundamental diagram is suggested, using an analytical polynomial technique, in which coefficients are taken from significant values acting as the parameters of the traffic model. Depending on the values of these parameters, it can be seen how the traffic flow changes from stable endpoints to chaotic trajectories, with proper analysis in their stability features.
Highlights
Vehicular traffic studies have been carried out over the last few decades using average quantities, which can be obtained in many different and accurate ways in order to be analysed in different branches of traffic engineering [1, 2]
These quantities are related in a well-known manner through what has been called a Fundamental Diagram [3, 4], which is often presented as a plot of the traffic flow-density relation
A polynomial approximation technique has been employed [5] to fit some significant points identified as those values that are common and important in every fundamental diagram, constituting a new and proper model to describe such a relation
Summary
Vehicular traffic studies have been carried out over the last few decades using average quantities, which can be obtained in many different and accurate ways in order to be analysed in different branches of traffic engineering [1, 2] These quantities are related in a well-known manner through what has been called a Fundamental Diagram [3, 4], which is often presented as a plot of the traffic flow-density relation. A polynomial approximation technique has been employed [5] to fit some significant points identified as those values that are common and important in every fundamental diagram, constituting a new and proper model to describe such a relation This model has been modified in a discrete form, in such a way that it is possible to obtain different trajectories from an iterative scheme. The polynomial model presented here permits obtaining and illustrating all these behaviours by modifying a single parameter in it, the traffic average velocity v, showing that vehicular traffic is a dynamic nonlinear system that produces what is known as bifurcations and quasi-periodic trajectories [7]
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