Lattice Boltzmann model for traffic flow.

Mesoscopic models for traffic flows are usually difficult to be employed because of the appearance of integro-differential terms in the models. In this work, a lattice Boltzmann model for traffic flow is introduced on the basis of the existing kinetics models by using the Bhatnagar-Gross-Krook-type approximation interaction term in the Boltzmann equation and discretizing it in time and phase space. The so-obtained model is simple while the relevant parameters are physically meaningful. Together with its discrete feature, the model can be easily used to investigate numerically the behavior of traffic flows. In consequence, the macroscopic dynamics of the model is derived using the Taylor and Chapman-Enskog expansions. For validating the model, numerical simulations are conducted under the periodic boundary conditions. It is found that the model could reasonably reproduce the fundamental diagram. Moreover, certain interesting physical phenomena can be captured by the model, such as the metastability and stop-and-go phenomena.

Analysis of pedestrian dynamics in counter flow via an extended lattice gas model.

The modeling of human behavior is an important approach to reproduce realistic phenomena for pedestrian flow. In this paper, an extended lattice gas model is proposed to simulate pedestrian counter flow under the open boundary conditions by considering the human subconscious behavior and different maximum velocities. The simulation results show that the presented model can capture some essential features of pedestrian counter flows, such as lane formation, segregation effect, and phase separation at higher densities. In particular, an interesting feature that the faster walkers overtake the slower ones and then form a narrow-sparse walkway near the central partition line is discovered. The phase diagram comparison and analysis show that the subconscious behavior plays a key role in reducing the occurrence of jam cluster. The effects of the symmetrical and asymmetrical injection rate, different partition lines, and different combinations of maximum velocities on pedestrian flow are investigated. An important conclusion is that it is needless to separate faster and slower pedestrians in the same direction by a partition line. Furthermore, the increase of the number of faster walkers does not always benefit the counter flow in all situations. It depends on the magnitude and asymmetry of injection rate. And at larger maximum velocity, the obtained critical transition point corresponding to the maximum flow rate of the fundamental diagram is in good agreement with the empirical results.

Effects of changing orders in the update rules on traffic flow.

Based on the Nagel-Schreckenberg (NaSch) model of traffic flow, we study the effects of the orders of the evolutive rule on traffic flow. It has been found from simulation that the cellular automaton (CA) traffic model is very sensitively dependent on the orders of the evolutive rule. Changing the evolutive steps of the NaSch model will result in two modified models, called the SDNaSch model and the noise-first model, with different fundamental diagrams and jamming states. We analyze the mechanism of these two different traffic models and corresponding traffic behaviors in detail and compare the two modified model with the NaSch model. It is concluded that the order arrangement of the stochastic delay and deterministic deceleration indeed has remarkable effects on traffic flow.

Continuum traffic model with the consideration of two delay time scales.

This paper presents a continuum traffic model. The derivation of this model is based upon the assumption that the stream velocity u reaches the equilibrium velocity u(e) within the relaxation time T, while the equilibrium velocity u(e) is adjusted to be attained through the driver's reaction time t(r). It is also assumed that the former delay time scale is greater than the latter. A motion equation with nonconstant propagation velocity of a disturbance in traffic flow is derived that can reflect the anisotropy of disturbance propagation in real traffic, unlike some other higher-order continuum models. It indicates that in our model the undesirable "wrong-way travel" phenomenon and gas-like behavior have been eliminated. The formation and diffusion of traffic shock can be better simulated.