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The purpose of this paper is to explore the impact of the mixed traffic flow, self-stabilization effect and the lane changing behavior on traffic flow stability.

An extended two-lane lattice hydrodynamic model considering mixed traffic flow and self-stabilization effect is proposed in this paper. Through linear analysis, the stability conditions of the extended model are derived. Then, the nonlinear analysis of the model is carried out by using the perturbation theory, the modified Kortweg–de Vries equation of the density of the blocking area is derived and the kink–antikink solution about the density is obtained. Furthermore, the results of theoretical analysis are verified by numerical simulation.

The results of numerical simulation show that the increase of the proportion of vehicles with larger maximum speed or larger safe headway in the mix flow are not conducive to the stability of traffic flow, while the self-stabilization effect and lane changing behavior is positive to the alleviation of traffic congestion.

This paper does not take into account the factors such as curve and slope in the actual road environment, which will have more or less influence on the stability of traffic flow, so there is still a certain gap with the real traffic environment.

The existing two-lane lattice hydrodynamic models are rarely discussed in the case of mixed traffic flow. The improved model proposed in this paper can better reflect the actual traffic, which can also provide a theoretical reference for the actual traffic governance.

The goal of this study is to explore the effect of two-sided lateral gap with uncertain velocity on the stability of traffic flow on a curved road.

In this paper, an extended car-following model considering the effect of two-sided lateral gap with uncertain velocity on a curved road is proposed. The effects of different lateral positions and radius of different sizes can be considered as control signals. The stability condition of the new model is obtained by the control theory. The numerical simulations are carried out to analyze how the control signal and lateral positions and radius of curved road affect traffic flow stability. The results show that driving between two lanes and inaccurate speed estimates both have a negative effect on traffic flow stability, and the stability also decreases with the increase in the radius of curved road.

(1) Simulation of influencing factors of vehicle lateral position indicates that if the driver drives between two lanes, it would have a negative impact on traffic flow. (2) When the speed is fixed, the traffic flow becomes more and more unstable with the increase in the radius of the curve. (3) The stability of traffic flow will be affected when the driver estimates the speed of the vehicle ahead. Therefore, whether it is manual driving or future intelligent vehicle driving, it is necessary to accurately judge the speed of the front vehicle.

There is little research on two-sided lateral gap with uncertain velocity for the stability of traffic flow on a curved road. The enhanced model constructed in this study can better reflect the real traffic, which can also give some theoretical reference for the development of connected and autonomous vehicles (CAVs).

In an intelligent transportation system (for short, ITS) environment, a vehicle’s motion is affected by the information in a large scale. The purpose of this paper is to study the integration effect of multiple vehicles’ delayed velocities on traffic flow.

This paper constructed a new car-following model to study the integration effect of multiple vehicles’ delayed velocities on traffic flow. The new model is analyzed by linear and nonlinear perturbation method theoretically and also verified by simulation.

It is found out that the integration of preceding vehicles’ delayed velocities affect the stability of traffic flow importantly, and three preceding vehicles’ delayed velocities information should be considered in real traffic.

The new car-following model by considering the integration effect of multiple vehicles’ delayed velocities is firstly proposed in this paper. The research result shows that three preceding vehicles’ delayed velocities information is the best choice to stabilizing traffic flow.

This study aims to consider the influence of density difference integral and relative flow difference on traffic flow, a novel two-lane lattice hydrodynamic model is proposed. The stability criterion for the new model is obtained through the linear analysis method.

The modified Korteweg de Vries (KdV) (mKdV) equation is derived to describe the characteristic of traffic jams near the critical point. Numerical simulations are carried out to explore how density difference integral and relative flow difference influence traffic stability. Numerical and analytical results demonstrate that traffic congestions can be effectively relieved considering density difference integral and relative flow difference.

The traffic congestions can be effectively relieved considering density difference integral and relative flow difference.

Novel two-lane lattice hydrodynamic model is presented considering density difference integral and relative flow difference. Applying the linear stability theory, the new model’s linear stability is obtained. Through nonlinear analysis, the mKdV equation is derived. Numerical results demonstrate that the traffic flow stability can be efficiently improved by the effect of density difference integral and relative flow difference.

The purpose of this paper is to explore how curved road and lane-changing rates affect the stability of traffic flow.

An extended two-lane lattice hydrodynamic model on a curved road accounting for the empirical lane-changing rate is presented. The linear analysis of the new model is discussed, the stability condition and the neutral stability condition are obtained. Also, the mKdV equation and its solution are proposed through nonlinear analysis, which discusses the stability of the extended model in the unstable region. Furthermore, the results of theoretical analysis are verified by numerical simulation.

The empirical lane-changing rate on a curved road is an important factor, which can alleviate traffic congestion.

This paper does not take into account the factors such as slope, the drivers’ characters and so on in the actual traffic, which will have more or less influence on the stability of traffic flow, so there is still a certain gap with the real traffic environment.

The curved road and empirical lane-changing rate are researched simultaneously in a two-lane lattice hydrodynamic models in this paper. The improved model can better reflect the actual traffic, which can also provide a theoretical reference for the actual traffic governance.

The performance of the classical car-following system is easily affected by external disturbances. To enhance the performance of the classical car-following model under sudden external disturbances, a novel car-following model is established to smooth traffic flow.

This paper proposed a Proportion Integration Differentiation (PID) control strategy based on classical control theory and developed a novel car-following model. The linear system theory and Laplace transform are used to derive a closed-loop transfer function. Then, the stability condition is obtained by using the Routh stability criterion and the small gain theorem. Finally, the validity and feasibility of the PID control strategy is proved by numerical simulations.

The analytic results and the numerical simulation results show that both the integration part and the differential part have the positive effect to suppress traffic oscillation efficiently; the collaboration of these two parts has more power to improve the stability of traffic flow. It means that the proposed model integrated with the PID control strategy has the ability of anti-interference and smooth traffic compared with the classical car-following model.

This paper introduces the PID control strategy into the classical car-following system, which enhances the stability of the system and also provides an efficient method for optimizing the traffic flow system.

In the era of connected and autonomous vehicles, a large amount of surrounding vehicular information can be acquired by the focal vehicle in real time using vehicle-to-vehicle communication technology, such as the core variable of electronic throttle opening angle. Meanwhile, the traffic jerk, such as the non-compliance of drivers and pedestrians, worsens the chaos of the surrounding traffic environment. To reflect the future traffic environment, the authors simultaneously incorporate the electronic throttle (ET) and traffic jerk into the traditional continuum model. The authors derive the stability criterion of the enhanced continuum model via the perturbation method.

To facilitate insight into the propagation and evolution mechanism of traffic jam near the stability condition, the authors use the nonlinear stability analysis method to derive the KdV-Burgers equation of proposed continuum model.

The new item of ET opening angle and traffic jerk have a positive impact on suppressing traffic congestion and improving road robustness.

The research on autonomous continuum models is rare. This model can better reflect the actual traffic, which can also provide a theoretical reference for the future traffic governance.

The purpose of this study is to explore the influence of the electronic throttle (ET) dynamics and the average speed of multiple preceding vehicles on the stability of traffic flow.

An extended car-following model integrating the ET dynamics and the average speed of multiple preceding vehicles is presented in this paper. The novel model’s stability conditions are obtained by using the thought of control theory, and the modified Korteweg–de Vries equation is inferred in terms of the nonlinear analysis method. In addition, some simulation experiments are implemented to explore the properties of traffic flow, and the results of these experiments confirm the correctness of theoretical analysis.

In view of the results of theoretical analysis and numerical simulation, traffic flow will become more stable when the average speed and ET dynamics of multiple preceding vehicles are considered, and the stability of traffic flow will also be enhanced by increasing the number of preceding vehicles considered.

This study leaves the factors such as the mixed traffic flow, the multilane and so on out of account in real road environment, which more or less influences the traffic flow’s stability, so the real traffic environment is not fully reflected.

There is little research integrating ET dynamics and the average velocity of multiple preceding vehicles to study the properties of traffic flow. The enhanced model constructed in this study can better reflect the real traffic, which can also give some theoretical reference for the development of connected and autonomous vehicles.

This paper aims to put forward an extended lattice hydrodynamic model, explore its effects on alleviating traffic congestion and provide theoretical basis for traffic management departments and traffic engineering implementation departments.

The control method is applied to study the stability of the new model. Through nonlinear analysis, the mKdV equation representing kink-antikink soliton is acquired.

The predictive effect and the control signal can enhance the traffic flow stability and reduce the energy consumption.

The predictive effect and feedback control are first considered in lattice hydrodynamic model simultaneously. Numerical simulations demonstrate that these two factors can enhance the traffic flow stability.

This paper aims to present a cooperative adaptive cruise control, called stable smart driving model (SSDM), for connected and autonomous vehicles (CAVs) in mixed traffic streams with human-driven vehicles.

Considering the linear stability, SSDM is able to provide smooth deceleration and acceleration in the vehicle platoons with or without cut-in. Besides, the calibrated Virginia tech microscopic energy and emission model is applied in this study to investigate the impact of CAVs on the fuel consumption of the vehicle platoon and traffic flows. Under the cut-in condition, the SSDM outperforms ecological SDM and SDM in terms of stability considering different desired time headways. Moreover, single-lane vehicle dynamics are simulated for human-driven vehicles and CAVs.

The result shows that CAVs can reduce platoon-level fuel consumption. SSDM can save the platoon-level fuel consumption up to 15%, outperforming other existing control strategies. Considering the single-lane highway with merging, the higher market penetration of SSDM-equipped CAVs leads to less fuel consumption.

The proposed rule-based control method considered linear stability to generate smoother deceleration and acceleration curves. The research results can help to develop environmental-friendly control strategies and lay the foundation for the new methods.