Statistical Physics of Synchronized Traffic Flow: Spatiotemporal Competition between S$\to$F and S$\to$J Instabilities

Abstract

We have revealed statistical physics of synchronized traffic flow that is governed by a spatiotemporal competition between S$\to$F and S$\to$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 $P_{\mathrm{S}}$, or an S$\to$F transition occurs with probability $P_{\mathrm{SF}}$, or else an S$\to$J transition occurs with probability $P_{\mathrm{SJ}}$. Space-gap dependencies of the probabilities $P_{\mathrm{S}}$, $P_{\mathrm{SF}}$, and $P_{\mathrm{SJ}}$ have been found. 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$\to$F and S$\to$J instabilities occur at random road locations of the homogeneous road, due to a permanent non-homogeneity introduced by the bottleneck, nuclei for initial S$\to$F and S$\to$J instabilities appear mostly at the bottleneck.

23 pages, 24 figures

References in corpus (3)

• Microscopic driving theory with oscillatory congested states: model and empirical verification
• Traffic Network Optimum Principle - Minimum Probability of Congestion Occurrence
• Realizing Wardrop Equilbria with Real-Time Traffic Information

Cited by in corpus (1)

• Effect of Autonomous Driving on Traffic Breakdown in Mixed Traffic Flow: A Critical Mini-Review