Statistical physics of synchronized traffic flow: Spatiotemporal competition between S → F and S → J instabilities

We have revealed statistical physics of synchronized traffic flow that is governed by a spatiotemporal competition between S -> F and S -> J instabilities (where F, S, and J denote, respectively, the free flow, synchronized flow, and wide moving jam traffic phases). A probabilistic analysis of synchronized flow based on simulations of a cellular automaton model in the framework of three-phase traffic theory is made. This probabilistic analysis shows that there is a finite range of the initial space gap between vehicles in synchronized flow within which during a chosen time for traffic observation either synchronized flow persists with probability P-S, or an S -> F transition occurs with probability P-SF, or else an S -> J transition occurs with probability P-SJ. Space-gap dependencies of the probabilities P-S, P-SF, and P-SJ have been found. It has been also found that (i) an initial S -> F instability can lead to sequences of S -> F -> S -> J transitions; (ii) an initial S -> J instability can lead to sequences of S -> J -> S -> F transitions. Each of the phase transitions in the sequences S -> F -> S -> J transitions and S -> J -> S -> F transitions exhibits the nucleation nature; these sequences of phase transitions determine spatiotemporal features of traffic patterns resulting from the competition between S -> F and S -> J instabilities. The statistical features of synchronized flow found for a homogeneous road remain qualitatively for a road with a bottleneck. However, rather than nuclei for S -> F and S -> J instabilities occurring at random road locations of the homogeneous road, due to a permanent nonhomogeneity introduced by the bottleneck, nuclei for initial S -> F and S -> J instabilities appear mostly at the bottleneck.