A new lattice model of the traffic flow with the consideration of the driver anticipation effect in a two-lane system

In this paper, a new lattice model of the traffic flow is proposed with the consideration of the driver anticipation effect for a two-lane system. The linear stability condition is derived by employing linear stability analysis. The analytical result shows that the driver anticipation effect can improve the stability of the traffic flow in a two-lane system. The mKdV equation near the critical point is obtained to describe the propagating behavior of a traffic density wave with the perturbation method. The simulation results are also in good agreement with the analytical results, which show that the traffic jam can be suppressed efficiently when the driver anticipation effect is considered in a two-lane system.     

TDGL and mKdV equations for an extended car-following model

In this paper, we construct an improved car-following model by accounting for the effect of the optimal velocity difference and a two-velocity difference. The effect of this model is examined through the linear stability analysis. The TDGL equation and the mKdV equation are derived from nonlinear analysis. Then, the energy consumption and the stability in car-following models considering the optimal velocity difference and a two-velocity difference are discussed. Moreover, numerical simulation shows that the new model can improve the stability of traffic flow, which is consistent with the theoretical analysis.     

Stabilization effect of multiple density difference in the lattice hydrodynamic model

In this paper, an extended lattice model is proposed by introducing the multiple density difference effect (MDDE). Stability condition of the new model is obtained through linear stability theory, which shows that considering the MDDE ahead can stabilize traffic flow effectively. The mKdV equation is derived to explore the density waves in the stable and unstable regions, respectively. The kink-antikink solution is obtained from the mKdV equation. Numerical simulation results show that multiple density difference effect (MDDE) can suppress traffic jam considerably, which is in line with the analytical results.     

Lattice hydrodynamic model for traffic flow on curved road with passing

In order to investigate the effect of passing upon traffic flow on curved road, in this paper, an extended one-dimensional lattice hydrodynamic model for traffic flow on curved road with passing is proposed. The stability condition is obtained by the use of linear stability analysis. The result of stability analysis shows that passing behavior plays an important role in influencing the stability of traffic flow as well as radian of curved road. The nonlinear wave equations including Burgers, Korteweg-de Vries and modified Korteweg-de Vries equations are derived to describe the nonlinear traffic behavior in different regions, respectively. The analytical results show that reducing the coefficient of passing may enhance the stability of traffic flow. Jamming transition occurs between uniform flow and kink jam when the coefficient of passing is less than the critical value. When the coefficient of passing is larger than the critical value, jamming transition occurs from uniform flow to irregular wave through chaotic phase with decreasing sensitivity parameter. In addition, compared with other segments of curved road, traffic flow with passing easily becomes unstable and complicated at the entrance and exit of curved road, especially at the entrance of curved road. The numerical simulations are given to illustrate and clarify the analytical results.     

Generalized macroscopic traffic model with time delay

The effect of delay or reaction time on traffic flow dynamics has been investigated widely in the literature using microscopic traffic models. Recent studies using second-order Payne-type models have shown analytically that, on a macroscopic scale, time delay does not contribute to whether traffic instabilities occur. This paper will attempt to show that it all depends on the (macroscopic) model used for the analysis that delay does have effect on traffic instabilities or not. To this end, we will formulate a generalized (linear) stability condition for a second-order macroscopic model with delay and investigate analytically the effect of such delay on traffic instabilities in some specific macroscopic models. It is found that the choice of the equilibrium speed function in a (second order) macroscopic model will determine how delay affects such (linear) stability condition     

An improved lattice hydrodynamic model considering the “backward looking” effect and the traffic interruption probability

By incorporating the “backward looking” effect and traffic interruption probability, we put forward an improved lattice model. Applying linear stability analysis, linear stability criterion is derived. The mKdV equation is deduced through nonlinear theory, which demonstrates that the solution of mKdV equation can describe traffic congestion. Furthermore, numerical simulation shows that the two factors can enhance traffic flow stability in the driving process.     

Feedback control for the lattice hydrodynamics model with drivers’ reaction time

In this paper, a new lattice hydrodynamic model (LH model) of traffic flow under consideration of reaction time of drivers and a corresponding feedback control scheme are proposed. Based on the model, stability analysis is conducted through linear stability analysis of transfer function. The obtained phase diagram indicates that the reaction time of driver can affect the instability region of traffic flow. Under the action of a feedback control, the unstable region is shrunken to reach suppressing jams. The numerical simulations are performed to validate the effect of reaction time of driver in the new LH model. The study results confirm that the reaction time of driver significantly affects the unstability of traffic system, and the feedback control can suppress traffic jams. Furthermore, it is found that the traffic system from the chaotic traffic state to periodic steady one is successfully realizing the control of traffic system.     

Analyses of the driver’s anticipation effect in a new lattice hydrodynamic traffic flow model with passing

In this paper, we studied the effect of driver’s anticipation with passing in a new lattice model. The effect of driver’s anticipation is examined through linear stability analysis and shown that the anticipation term can significantly enlarge the stability region on the phase diagram. Using nonlinear stability analysis, we obtained the range of passing constant for which kink soliton solution of mKdV equation exist. For smaller values of passing constant, uniform flow and kink jam phase are present on the phase diagram and jamming transition occurs between them. When passing constant is greater than the critical value depending on the anticipation coefficient, jamming transitions occur from uniform traffic flow to kink-bando traffic wave through chaotic phase with decreasing sensitivity. The theoretical findings are verified using numerical simulation which confirm that traffic jam can be suppressed efficiently by considering the anticipation effect in the new lattice model.     

Lattice hydrodynamic traffic flow model with explicit drivers’ physical delay

An extended lattice hydrodynamic model is presented by considering the effect of drivers’ delay in sensing relative flux. The linear stability criterion of the new model is obtained by employing the linear stability theory. By means of nonlinear analysis method, the modified Korteweg–deVries (mKdV) equation near the critical point is constructed and solved. The propagation behavior of traffic jam can thus be described by the kink–antikink soliton solution for the mKdV equation. The good agreement between the simulation results and the analytical results show that the drivers’ delay in sensing relative flux effect plays an important role in traffic jamming transition.     

The self-stabilization effect of lattice’s historical flow in a new lattice hydrodynamic model

In order to reveal the self-stabilization effect of the lattice’s historical information on traffic flow, a new lattice hydrodynamic model with consideration of the considered lattice’s historical flow is proposed. The impact of the lattice’s historical flow on traffic stability is uncovered through theoretical analyses and numerical simulation. Through theoretical analyses, the linear stability condition of the new model is obtained, and the nonlinear mKdV equation is derived to describe traffic jamming transition of the new model near the critical point. From numerical simulation, the theoretical analyses are verified and it is shown that the traffic stability can be enhanced by considering the current lattice’s self-information of its historical flow.     

The theoretical analysis of the anticipation lattice models for traffic flow

Based on the anticipation lattice hydrodynamic models, which are described by the partial differential equations, the continuum version of the model is investigated through a reductive perturbation method. The linear stability theory is used to discuss the stability of the continuum model. The Korteweg–de Vries (for short, KdV) equation near the neutral stability line and the modified Korteweg–de Vries (for short, mKdV) equation near the critical point are obtained by using the nonlinear analysis method. And the corresponding solutions for the traffic density waves are derived, respectively. The results display that the anticipation factor has an important influence on traffic flow. From the simulation, it is shown that the traffic jam is suppressed efficiently with taking into account the anticipation effect, and the analytical result is consonant with the simulation one.     

A new car-following model with consideration of anticipation driving behavior

A new anticipation driving car-following (AD-CF) model is presented based on the effect of traffic anticipation in the real world. The model??s linear stability condition was obtained by applying the linear stability theory. Additionally, a modified Korteweg?Cde Vries (mKdV) equation was derived via nonlinear analysis to describe the propagating behavior of traffic density wave near the critical point. Good agreement between the simulation and the analytical results shows that the stability of traffic flow can be enhanced when the driver??s anticipation effects are considered.     

A driver’s memory lattice model of traffic flow and its numerical simulation

A new lattice model of traffic flow based on Nagatani’s model is proposed by taking the effect of driver’s memory into account. The linear stability condition of the extended model is obtained by using the linear stability theory. The analytical results show that the stabile area of the new model is larger than that of the original lattice hydrodynamic model by adjusting the driver’s memory intensity parameter p of the past information in the system. The modified KdV equation near the critical point is derived to describe the traffic jam by nonlinear analysis, and the phase space could be divided into three regions: the stability region, the metastable region, and the unstable region, respectively. Numerical simulation also shows that our model can stabilize the traffic flow by considering the information of driver’s memory.     

A new lattice hydrodynamic model with the consideration of flux change rate effect

A new lattice hydrodynamic traffic flow model is proposed by considering the preceding lattice site’s flux change rate effect. Using linear stability theory, stability condition of the presented model is obtained. It is shown that the stability region significantly enlarges as the flux change rate effect increases. To describe the propagation behavior of a density wave near the critical point, nonlinear analysis is conducted and mKdV equation representing kink-antikink soliton is derived. To verify the theoretical findings, numerical simulation is conducted which confirms that preceding lattice site’s flux change rate can improve the stability of traffic flow effectively.     

A new lattice hydrodynamic model for two-lane traffic with the consideration of density difference effect

A new lattice hydrodynamic model for two-lane traffic flow is proposed by introducing the density difference effect (DDE). Using linear stability theory, stability condition of the presented model is obtained. Jamming transitions among the freely moving phase, the coexisting phase, and the uniform congested phase are investigated by employing nonlinear analysis. The modified KdV (mKdV) equation near the critical point is derived and the kink-antikink soliton solutions are obtained. Numerical simulations are presented to verify analytical results, showing that DDE can improve the stability of traffic flow effectively.     

The velocity difference control signal for two-lane car-following model

Based on single-lane traffic model, a two-lane traffic model is presented considering the velocity difference control signal. The stability condition of the model is obtained by the control theory. The delayed feedback control signal is added to the two-lane model, and the corresponding stability condition is derived again. The numerical simulations show that as the stability conditions are satisfied, the small disturbance will not amplify with and without control signal. In the meantime, the stability is strengthened as the control signal is considered. So the control signal would suppress the traffic disturbance successfully.     

A car-following model with the anticipation effect of potential lane changing

In this paper, a new car-following model is presented, taking into account the anticipation of potential lane changing by the leading vehicle. The stability condition of the model is obtained by using the linear stability theory. The modified Korteweg-de Vries （KdV） equation is constructed and solved, and three types of traffic flow in the headway-sensitivity space, namely stable, metastable and unstable ones, are classified. Both the analytical and simu- lation results show that anxiety about lane changing does indeed have an influence on driving behavior and that a consideration of lane changing probability in the car-following model could stabilize traffic flows. The quantitative relationship between stability improvement and lane changing probability is also investigated.     

An extended two-lane traffic flow lattice model with driver’s delay time

In this paper, a new two-lane lattice model is presented by considering the effect of drivers’ delay in sensing relative flux. By means of the linear stability analysis, the effect of drivers’ delay time on the stability of two-lane traffic flow is examined and shown that with the drivers’ delay time increasing, the unstable areas expand accordingly on the phase diagram, which is also confirmed by direct computer simulations. Through nonlinear analysis method, the modified Korteweg–deVries equation near the critical point is obtained and solved to describe the traffic- jamming transitions in a two-lane system.     

An extended continuum model incorporating the electronic throttle dynamics for traffic flow

This study develops a novel continuum model with consideration of the effect of electronic throttle (ET) dynamics to capture the behaviour of vehicles in traffic flow. In particular, the continuum model is proposed by incorporating the opening angle of ET based on the throttle-based full velocity difference model. Theoretical analyses including stability, negative velocity and shock wave are performed systematically. Numerical experiments and comparisons are conducted to verify the performance of the proposed continuum model. Results show that the steady-state performance of the proposed model is improved with respect to the stability. In addition, the proposed model is effective to rapidly dissipate the effect of external perturbation. Also, the phenomenon of negative velocity can be avoided by the proposed model.     

宏观交通流模型的余维2分岔分析

交通流特性是混合交通流建模的一个重要因素. 交通流模型中的分岔现象是导致复杂交通现象的因素之一. 交通流的分岔, 涉及复杂的动力学特征且研究较少. 因此, 提出了一个最优速度模型来研究驾驶员记忆对驾驶行为的影响. 基于带有记忆的最优速度连续交通流模型, 利用非线性动力学, 分析和预测了复杂交通现象. 推导了鞍结 (LP) 分岔存在条件, 并通过数值计算得到了余维1 Hopf (H) 分岔、LP分岔和同宿轨 (HC) 分岔以及余维2广义Hopf (GH) 分岔、尖点 (CP) 分岔和Bogdanov-Takens (BT) 分岔等多种分岔结构. 根据双参数分岔区域的特点, 研究了记忆参数对单参数分岔结构的影响, 分析了不同分岔结构对交通流的影响, 并用相平面描述了平衡点附近轨迹的变化特征. 选择Hopf分岔和鞍结分岔作为密度演化的起点, 描述了均匀流、稳定和不稳定的拥挤流以及走走停停现象. 结果表明, 驾驶员记忆对交通流的稳定性有重要影响; 动力学行为很好地解释了交通拥堵现象; 考虑余维2分岔的影响, 能更好地理解交通拥堵产生的根源, 并为制定有效抑制拥堵的方法提供一定的理论依据.