A novel lattice hydrodynamic model accounting for individual difference of honk effect for two-lane highway under V2X environment

In this work, the individual difference of the honk effect is explored on two lanes via traffic modeling of the lattice model under Vehicle to X (V2X) environment. We study the impact of individual difference corresponding to honk cases on traffic stability through linear stability analysis for a two-lane highway. Furthermore, the mKdV equation under the lane changing phenomena is conducted via nonlinear analysis. Simulation cases for the early time and longtime impact reveal that individual difference of driving characteristics has a distinct impact on two lanes under the whistling environment.

The impact of equilibrium optimal flux deviation on traffic dynamics in lattice hydrodynamic model under V2X environment

In this work, the equilibrium optimal flux deviation is explored as a control signal under V2X environment via traffic modeling of the lattice hydrodynamic model. According to the control theory, the sufficient stable condition can be deduced. In addition, numerical simulation is implemented for the early time impact, the steady-state effect, and the hysteresis phenomenon of traffic flow with the increase of the feedback gain response to the equilibrium optimal flux deviation. The result demonstrates that the equilibrium optimal flux deviation effect has significantly positive influence on the stability of the traffic flow.

Impact of Strong Wind and Optimal Estimation of Flux Difference Integral in a Lattice Hydrodynamic Model

A modified lattice hydrodynamic model is proposed, in which the impact of strong wind and the optimal estimation of flux difference integral are simultaneously analyzed. Based on the control theory, the stability condition is acquired through linear analysis. The modified Korteweg-de Vries (mKdV) equation is derived via nonlinear analysis, in order to express a description of the evolution of density waves. Then, numerical simulation is conducted. From the simulation results, strong wind can largely influence the traffic flow stability. The stronger the wind becomes, the more stable the traffic flow is, to some extent. Similarly, the optimal estimation of flux difference integral also contributes to stabilizing traffic flow. The simulation results show no difference compared with the theoretical findings. In conclusion, the new model is able to make the traffic flow more stable.

An Improved Lattice Hydrodynamic Model by considering the Effect of “Backward-Looking” and Anticipation Behavior

In order to prevent the occurrence of traffic accidents, drivers always focus on the running conditions of the preceding and rear vehicles to change their driving behavior. By taking into the “backward-looking” effect and the driver’s anticipation effect of flux difference consideration at the same time, a novel two-lane lattice hydrodynamic model is proposed to reveal driving characteristics. The corresponding stability conditions are derived through a linear stability analysis. Then, the nonlinear theory is also applied to derive the mKdV equation describing traffic congestion near the critical point. Linear and nonlinear analyses of the proposed model show that how the “backward-looking” effect and the driver’s anticipation behavior comprehensively affect the traffic flow stability. The results show that the positive constant γ , the driver’s anticipation time τ , and the sensitivity coefficient p play significant roles in the improvement of traffic flow stability and the alleviation of the traffic congestion. Furthermore, the effectiveness of linear stability analysis and nonlinear analysis results is demonstrated by numerical simulations.

Lyapunov stability analysis for a discrete-time lattice hydrodynamic model with steady flow control

This paper put forward a new discrete-time lattice hydrodynamic model with a steady flow control strategy. The controlled discrete-time lattice hydrodynamic model is theoretically studied by the discrete-time Lyapunov stability theory, and a sufficient stable condition to suppress traffic congestion is given in the form of linear matrix inequality. Also, the traffic flow evolution rules under different conditions of control gain are exhibited through numerical simulation, and the stabilization effect of the steady flow control strategy on traffic flow is verified intuitively.

Analysis of a Novel Two-Dimensional Lattice Hydrodynamic Model Considering Predictive Effect

In actual driving, the driver can estimate the traffic condition ahead at the next moment in terms of the current traffic information, which describes the driver’s predictive effect. Due to this factor, a novel two-dimensional lattice hydrodynamic model considering a driver’s predictive effect is proposed in this paper. The stability condition of the novel model is obtained by performing the linear stability analysis method, and the phase diagram between the driver’s sensitivity coefficient and traffic density is drawn. The nonlinear analysis of the model is conducted and the kink-antikink of modified Korteweg-de Vries (mKdV) equation is derived, which describes the propagation characteristics of the traffic density flow waves near the critical point. The numerical simulation is executed to explore how the driver’s predictive effect affects the traffic flow stability. Numerical results coincide well with theoretical analysis results, which indicates that the predictive effect of drivers can effectively avoid traffic congestion and the fraction of eastbound cars can also improve the stability of traffic flow to a certain extent.

A novel two-lane lattice hydrodynamic model on a gradient road considering heterogeneous traffic flow

In the actual traffic, there are not only cars, but also buses, trucks and other vehicles. These vehicles with different maximum speeds or security headway or both are interspersed irregularly to form a heterogeneous traffic flow. In addition, most of the maximum speed of modern cars is hardly affected by gradients due to the fact that the car engine and brakes are rarely operated at their max while the maximum speed of trucks is affected. Considering that the performance of various types of vehicles is multifarious and the vehicles sometimes drive on the road with slopes, a novel two-lane lattice hydrodynamic model on a gradient road considering heterogeneous traffic flow is proposed in this paper. In order to verify the rationality of the model, the linear stability analysis is carried out first, that is, the linear stability conditions are derived from the linear stability theory and the stability curve is drawn accordingly. The results of the above analysis prove that the three factors studied in this paper, namely, time lane change, slope and mixing of different types of vehicles, all have a significant influence on the stability of traffic flow. The modified Korteweg–de Vries (mKdV) equation is deduced by the nonlinear analysis method, which can describe the propagation characteristics of the traffic density waves near the critical point. Last but not least, the numerical simulation for new model is conducted and the numerical simulation results obtained are in good agreement with theoretical ones. In summary, increasing the lane changing rate or the slope on the uphill can improve the traffic flow stability. What is more, increasing the slope can lower the traffic flow stability on the downhill. Finally, in the heterogeneous traffic flow of different types of vehicles, the vehicles with larger security headway will make traffic flow difficult to stabilize, as do the vehicles with larger maximum speed.