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In this paper, a modified continuum model considering the vehicle’s taillight effect is presented. The high order fluid dynamics model of taillight effect is derived by means of the transformation from micro to macro. Combined with the continuous conservation equation of traffic flow, the linear and nonlinear analysis of the new macroscopic hydrodynamic model is carried out. The linear analysis proves that the model has the characteristics of heterogeneity and the stability condition of traffic flow is obtained. KdV–Burgers equations describing the qualitative characteristics of density waves are obtained by nonlinear analysis, and the corresponding density wave solutions are obtained. Numerical simulation results show that the unstable state region of the macro model with taillight effect is shrinking. In addition, the energy consumption of the model is simulated numerically, and the results show that the energy consumption of the vehicle is reduced by considering the taillight effect. Therefore, we believe that the taillight effect is beneficial to traffic flow stability and reduce energy consumption.

Considering the anticipation and traffic jerk simultaneously, a new macro model of traffic flow is put forwarded in this paper. By means of linear stability theory, the new model's linear stability with the effect of traffic jerk and anticipation term is obtained. Through nonlinear analysis, the KdV–Burgers equation is derived to describe the propagating behavior of traffic density wave near the neutral stability line. Numerical simulation is carried out to study the influence about the traffic jerk and anticipation effect. The evolution of traffic jam and corresponding energy consumption are then explored and compared each other. The outputs of these findings demonstrate the extended model can suppress traffic jam and reduce energy consumption in real traffic condition.

In this paper, an extended continuum model of traffic flow is proposed with the consideration of optimal velocity changes with memory. The new model’s stability condition and KdV–Burgers equation considering the optimal velocities change with memory are deduced through linear stability theory and nonlinear analysis, respectively. Numerical simulation is carried out to study the extended continuum model, which explores how optimal velocity changes with memory affected velocity, density and energy consumption. Numerical results show that when considering the effects of optimal velocity changes with memory, the traffic jams can be suppressed efficiently. Both the memory step and sensitivity parameters of optimal velocity changes with memory will enhance the stability of traffic flow efficiently. Furthermore, numerical results demonstrates that the effect of optimal velocity changes with memory can avoid the disadvantage of historical information, which increases the stability of traffic flow on road, and so it improve the traffic flow stability and minimize cars’ energy consumptions.

In the paper, an improved car-following model based on the full velocity difference model considering the influence of optimal velocity for leading vehicle on a single-lane road is proposed. The linear stability condition of the model is obtained by applying the linear stability theory. Through nonlinear analysis, the time-dependent Ginzburg–Landau (TDGL) equation and the modified Korteweg–de Vries (mKdV) equation are derived to describe the traffic flow near the critical point. In addition, the connection between the TDGL and the mKdV equations is also given. Good agreement between the simulation and the theoretical results shows that the improved model can be enhanced the stability of traffic flow.

Based on the full velocity difference car-following model, an improved car-following model is put forward by considering the driver’s desired inter-vehicle distance. The stability conditions are obtained by applying the control method. The results of theoretical analysis are used to demonstrate the advantages of our model. Numerical simulations are used to show that traffic congestion can be improved as the desired inter-vehicle distance is considered in the full velocity difference car-following model.

The present paper deals with the numerical solution of a two-dimensional linear hyperbolic equation by using the element-free Galerkin (EFG) method which is based on the moving least-square approximation for the test and trial functions. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Compared with numerical methods based on mesh, the EFG method for hyperbolic problems needs only the scattered nodes instead of meshing the domain of the problem. It neither requires any element connectivity nor suffers much degradation in accuracy when nodal arrangements are very irregular. The effectiveness of the EFG method for two-dimensional hyperbolic problems is investigated by two numerical examples in this paper.

In this paper the new continuum traffic flow model proposed by Jiang et al is developed based on an improved car-following model, in which the speed gradient term replaces the density gradient term in the equation of motion. It overcomes the wrong-way travel which exists in many high-order continuum models. Based on the continuum version of car-following model, the condition for stable traffic flow is derived. Nonlinear analysis shows that the density fluctuation in traffic flow induces a variety of density waves. Near the onset of instability, a small disturbance could lead to solitons determined by the Korteweg–de-Vries (KdV) equation, and the soliton solution is derived.

A modified cellular automaton model for traffic flow on highway is proposed with a novel concept about the variable security gap. The concept is first introduced into the original Nagel–Schreckenberg model, which is called the non-sensitive driving cellular automaton model. And then it is incorporated with a sensitive driving NaSch model, in which the randomization brake is arranged before the deterministic deceleration. A parameter related to the variable security gap is determined through simulation. Comparison of the simulation results indicates that the variable security gap has different influence on the two models. The fundamental diagram obtained by simulation with the modified sensitive driving NaSch model shows that the maximum flow are in good agreement with the observed data, indicating that the presented model is more reasonable and realistic.