# Elucidating Super-Compressible States in Inner Structure of Vehicular Flow
## 9 Discussion and Conclusions  
The article discusses atypical states in the micro-structure of the vehicular traffic system that seem to disrupt ingrained ideas about one-dimensional systems with maximum fluctuation rates. These states, which were found in empirical traffic data recorded at lower traffic densities, exceed the fluctuation rate of the Poisson systems, in which the freedom of particle movement is not restricted in any way, and which were intuitively suspected to be the upper limit for the fluctuation rate. The experimentally detected anomalies were transformed by mathematical reformatting into the language of so-called balance particle systems. Within the framework of the relevant theory, the detected properties are much better quantified and the reasons for their occurrence are also more straightforwardly determined. In this way, it has been found that anomalous traffic states represent (from a mathematical point of view) so-called super-compressible states whose statistical compressibility (i.e., the slope of statistical rigidity) exceeds the unit value. By combining the physical background of the problem and the mathematical apparatus of balanced particle systems, it has been proven that super-compressible states in a closed system can occur only if an attractive force component acts between the particles of the system. And since freeway flow analysis cannot rule out that the detected anomaly is caused by a large percentage of vehicles changing lanes during overtaking maneuvers, a traffic experiment was performed in which overtaking maneuvers were completely forbidden. For this purpose, the section of the freeway where the reconstruction work was taking place was chosen. The physical barrier between the narrowed lanes then served as an ideal overtaking blocker. The analysis of the measured data then convincingly revealed that super-compressible states occur even when the traffic streams are fully isolated. To conclude, this study demonstrated that the repulsive force effect (which is a typical leading factor in all traffic models) is accompanied by a weaker inter-vehicular attraction, which has its origin in the competitive nature of sporty drivers. According to the results of this study, such an attractive force depends on the reciprocal value of the clearance, while the repulsive force depends on the reciprocal value of the square of the clearance. From a comparison of the mathematical nature of both dependencies, it is clear that for short clearances the repulsive impulses preventing collisions prevail, while for large clearances,  
Figure 12: Statistical distribution of vehicular speeds in individual traffic lanes. The velocities have been analyzed for traffic densities between 18 and 23 vehicles per kilometer. the dominant component is the attractive force corresponding to the effort to catch up with the preceding vehicle. However, it is important to note that this mixed nature of interactions can only be fully manifested for lower traffic density. Once the density reaches a threshold value (about 25 vehicles per kilometer), then the attractive component disappears and the flow in both streams becomes significantly synchronized. To summarize, the added value of this article is the detection and explanation of anomalous traffic states that are quite common in all multi-lane traffic systems. As far as the authors of this article are aware, these states have never been relevantly investigated before. The presented research is based on relatively strong theoretical foundations, as it is based on a time-tested traffic model, which enables an analytical solution of the respective stationary states. In addition, the research is supported by a robust mathematical theory. As a current weak point of the research, we understand the limitation of the interpretation of the results to homogeneous traffic systems, i.e., systems composed only of passenger vehicles. The extension of the research to heterogeneous systems will be a logical continuation of the recent research. Methodology, M.K.