Probabilistic physical characteristics of phase transitions at highway bottlenecks: incommensurability of three-phase and two-phase traffic-flow theories

Model of driver overacceleration causing breakdown in vehicular traffic

We introduce a mathematical approach for the description of driver overacceleration in a microscopic traffic flow model. The model, in which no driver overreaction occurs, explains the empirical nucleation nature of traffic breakdown.

Investigating safety impact of sun glare in urban tunnels based on cellular automata approach

This study applies a simulation-based traffic conflict technique to evaluate the hypothesis that sun glare under upper vents exerts negative impacts on traffic safety in urban tunnels. A modified cellular automata (CA) model is applied to simulate the deceleration behavior due to sun glare (DBSG) in real traffic. And the model is calibrated and validated against the empirical data. Conflict occurrences are generated through simulating vehicular interactions based on this model. Simulation experiments are conducted with different density and illuminance to evaluate the safety impacts of sun glare. Comparison of simulated conflict occurrences shows that rear-end conflicts occur more frequently as illuminance and density get higher. And the impacts of sun glare are more obvious on weak conflicts in moderate-density flow and more severe conflicts in high-density flows, respectively. To alleviate the negative impacts of sun glare, a sunshade system is designed based on the quantitative results.

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.

Jamming transitions induced by an attraction in pedestrian flow

We numerically study jamming transitions in pedestrian flow interacting with an attraction, mostly based on the social force model for pedestrians who can join the attraction. We formulate the joining probability as a function of social influence from others, reflecting that individual choice behavior is likely influenced by others. By controlling pedestrian influx and the social influence parameter, we identify various pedestrian flow patterns. For the bidirectional flow scenario, we observe a transition from the free flow phase to the freezing phase, in which oppositely walking pedestrians reach a complete stop and block each other. On the other hand, a different transition behavior appears in the unidirectional flow scenario, i.e., from the free flow phase to the localized jam phase and then to the extended jam phase. It is also observed that the extended jam phase can end up in freezing phenomena with a certain probability when pedestrian flux is high with strong social influence. This study highlights that attractive interactions between pedestrians and an attraction can trigger jamming transitions by increasing the number of conflicts among pedestrians near the attraction. In order to avoid excessive pedestrian jams, we suggest suppressing the number of conflicts under a certain level by moderating pedestrian influx especially when the social influence is strong.

Cluster statistics and quasisoliton dynamics in microscopic optimal-velocity models

Using the non-linear optimal velocity models as an example, we show that there exists an emergent intrinsic scale that characterizes the interaction strength between multiple clusters appearing in the solutions of such models. The interaction characterizes the dynamics of the localized quasisoliton structures given by the time derivative of the headways, and the intrinsic scale is analogous to the "charge" of the quasisolitons, leading to non-trivial cluster statistics from the random perturbations to the initial steady states of uniform headways. The cluster statistics depend both on the quasisoliton charge and the density of the traffic. The intrinsic scale is also related to an emergent quantity that gives the extremum headways in the cluster formation, as well as the coexistence curve separating the absolute stable phase from the metastable phase. The relationship is qualitatively universal for general optimal velocity models.

Finite-size effects in the Nagel-Schreckenberg traffic model

We examine the Nagel-Schreckenberg traffic model for a variety of maximum speeds. We show that the low-density limit can be described as a dilute gas of vehicles with a repulsive core. At the transition to jamming, we observe finite-size effects in a variety of quantities describing the flow and the density correlations, but only if the maximum speed V_{max} is larger than a certain value. A finite-size scaling analysis of several order parameters shows universal behavior, with scaling exponents that depend on V_{max}. The jamming transition at large V_{max} can be viewed as the nucleation of jams in a background of freely flowing vehicles. For small V_{max} no such clean separation into jammed and free vehicles is possible.

Microscopic theory of traffic-flow instability governing traffic breakdown at highway bottlenecks: Growing wave of increase in speed in synchronized flow

We have revealed a growing local speed wave of increase in speed that can randomly occur in synchronized flow (S) at a highway bottleneck. The development of such a traffic flow instability leads to free flow (F) at the bottleneck; therefore, we call this instability an S→F instability. Whereas the S→F instability leads to a local increase in speed (growing acceleration wave), in contrast, the classical traffic flow instability introduced in the 1950s-1960s and incorporated later in a huge number of traffic flow models leads to a growing wave of a local decrease in speed (growing deceleration wave). We have found that the S→F instability can occur only if there is a finite time delay in driver overacceleration. The initial speed disturbance of increase in speed (called "speed peak") that initiates the S→F instability occurs usually at the downstream front of synchronized flow at the bottleneck. There can be many speed peaks with random amplitudes that occur randomly over time. It has been found that the S→F instability exhibits a nucleation nature: Only when a speed peak amplitude is large enough can the S→F instability occur; in contrast, speed peaks of smaller amplitudes cause dissolving speed waves of a local increase in speed (dissolving acceleration waves) in synchronized flow. We have found that the S→F instability governs traffic breakdown-a phase transition from free flow to synchronized flow (F→S transition) at the bottleneck: The nucleation nature of the S→F instability explains the metastability of free flow with respect to an F→S transition at the bottleneck.