Abstract
This paper concerns the traveling wave formation in macroscopic traffic flow models. The dynamics involved in this problem is described following a close analogy to compressible fluid dynamics. It is well known that vehicle clusters appear along a highway when the homogenous steady state taken as a reference is linearly unstable. The cluster properties are determined in an approximate way in terms of the parameters proper to each model and are compared between them.
Highlights
The study of density waves in traffic flow has constituted a subject of interest mainly in relation to the cluster formation
These models are based on an analogy between compressible flow in a Navier-Stokes fluid and the traffic flow, but no matter their origin the structure is similar to compressible flow equations
Our study will be focused on macroscopic models with three and two variables to be determined by the dynamics
Summary
The study of density waves in traffic flow has constituted a subject of interest mainly in relation to the cluster formation. Most macroscopic models have been studied to understand the appearance of the main traffic characteristics in closed circuits and some experiments have been done [20] All those models share some properties such as, the continuity equation and the equation of motion to describe the speed behavior and in general, the structure of balance equations. It has been shown that, under unstable conditions the models similar to it produce traveling waves with the soliton structure [25,26,27,28] With this perspective in mind, it becomes interesting to study the presence of solitons in the other macroscopic models and show that they share some characteristics even in the linearly unstable region.
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