This thesis deals with particle systems with a balancing property which have practical use in modeling vehicle headways. The full paper is available here: Full paper (2nd place at scientific conference in 2020).
- First, we summarized basic properties of balanced density functions and associated particle systems.
- We presented a unification procedure that is used for analysing traffic data and by applying this procedure to real data (recorded at a Dutch freeway) we verified, using methods of regression analysis, the balancing property of time clearances.
- Further, we rigorously defined statistical rigidity and via the central limit theorem we derived the dependency of statistical compressibility on parametres belonging tu Erlang’s density function.
- At last, we showed by graphs that the behaviour of statistical rigidity in well-known balanced particle systems is in accordance with previous derivations.
