Inner structure of vehicular ensembles and random matrix theory

• New class of random matrices (DUE) is proposed and analyzed in detail.
• Approximation formula for level spacing distribution in DUE ensembles is analytically derived.
• Connection between DUE and vehicular systems (analogical to a well-known link between GUE and Mexico buses) is presented.
• It is shown that LS distribution of DUE matrices is the same as clearance distribution measured on expressways.

We introduce a special class of random matrices (DUE) whose spectral statistics corresponds to statistics of microscopical quantities detected in vehicular flows. Comparing the level spacing distribution (for ordered eigenvalues in unfolded spectra of DUE matrices) with the time-clearance distribution extracted from various areas of the flux-density diagram (evaluated from original traffic data measured on Czech expressways with high occupancies) we demonstrate that the set of classical systems showing an universality associated with Random Matrix Ensembles can be extended by traffic systems.