Kerner BS. Statistical physics of synchronized traffic flow: Spatiotemporal competition between S→F and S→J instabilities.
Phys Rev E 2019;
100:012303. [PMID:
31499898 DOI:
10.1103/physreve.100.012303]
[Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2019] [Indexed: 06/10/2023]
Abstract
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.
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