Elucidating Super-Compressible States in Inner Structure of Vehicular Flow

Abstract

The article deals with the open questions in the theory of vehicular headway modeling. Specifically, the question of the existence of anomalous constellations in vehicular traffic micro-structure, in which the rate of fluctuations (measured by the stochastic compressibility) exceeds the fluctuation level of systems with non-interacting elements. The solution to this open problem is converted into the mathematical format working with the so-called balance particle systems, where seeking relevant relations is more straightforward and thus significantly easier. Presented research has shown that unit compressibility represents (despite popular opinion) the upper limit only for particle systems, in which there is no attractive interaction between the particles. In the article, the specific system is constructed in which the presence of an attractive force component will cause higher fluctuations than in the Poisson systems of non-interacting elements. This means that traffic constellations with higher compressibility (so-called super-compressible constellations) can be explained either by a discrepancy between the empirical traffic flow and the mathematical model used, or by the presence of attractive forces acting between individual vehicles. Using empirical vehicular data (measured on two parallel freeway lanes under reconstruction), we show that super-compressible states occur even though overtaking is prohibited. This means, therefore, that these super-compressible states arose without a doubt due to the mutual attraction of successive vehicles. In addition, the article shows that the presence of the aforementioned attractive forces appears predominantly in the fast lane, and only in situations where the traffic density is relatively low. At higher densities, the two freeway lanes are markedly synchronized, the opportunity for a sporty style of driving vanishes and the reason for changing lanes disappears. Under these circumstances, the attractive force component vanishes, which finally leads to the transition of the entire traffic system back to standard sub-compressible states.