Traffic flow can be understood as a realization of a broad class of one dimensional physical systems, where a hard core repulsive interaction competes with a longer ranged attraction between the particles. It can be shown rigorously that the statistical properties of such systems in thermal equilibrium are well described by a family of distributions that stems from the random matrix theory. Analyzing the traffic data from different sources, we show that traffic on real roads belongs to that class of random matrix distributions. Also, various traffic simulation models show a similar behavior. It is demonstrated in such a way that the headway distribution of a highway traffic, that serves usually as a paradigm of systems driven far from equilibrium, is reasonably well described by a distribution originating from equilibrium statistical physics.