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.     

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.     

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 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.     

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.     

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.     

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.     

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.     

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.     

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.     

基于元胞自动机模型的C型交织区交通流特性

根据C型双侧交织区的车辆换道特征建立相应的换道规则,采用多车道元胞自动机模型研究交织区系统的交通流特性. 通过数值模拟得到了不同交织区长度下的相图,表明当主路和匝道交通流均为自由流时,交织区长度对系统影响不大,但当主路或匝道拥挤时,交织区长度的增加可以明显改善入口匝道的交通流状况. 进一步讨论了主路畅通而交织流量较大情形下主路上的车辆密度、速度和换道频率分布,发现换道集中在合流区和分流区附近,并造成相应路段上的局部拥堵.      

Chaotic behavior of modified stretch-twist-fold (STF) flow with fractal property

This study proposes a new lattice hydrodynamic model considering the effects of bilateral gaps on a road without lane discipline. In particular, a lattice hydrodynamic model is proposed to capture the impacts from the lateral gaps of the right-side and left-side sites of the considered lattice sites. Linear stability analysis of the proposed model is performed using the perturbation method to obtain the stability condition. Nonlinear analysis of the proposed model is performed using the reductive perturbation method to derive the modified Korteweg–de Vries (mKdV) equation to characterize the density wave propagation. Results from numerical experiments illustrate that the smoothness and stability of the proposed model are improved compared with the model that considers the effect of unilateral gap. Also, the proposed model is able to more quickly dissipate the effect of perturbation occurring in the vehicular traffic flow.     

Solitary wave solution to Aw-Rascle viscous model of traffic flow

A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries (KdV) equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution.     

非港湾式公交车站停靠特性的研究

基于Nagel-Schreckenberg交通流模型(简称NaSch模型),通过引入换道规则,建立包含非港湾式公交车站在内的双车道混合车辆元胞自动机交通流模型.计算机数值模拟表明,在周期边界条件下非港湾式公交车站路段的交通流存在一定的特性,在中等密度区域的拥挤流, 车辆的平均速度与车流密度存在一次幂律关系.      

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.     

A mesoscopic approach on stability and phase transition between different traffic flow states

It is understood that congestion in traffic can be interpreted in terms of the instability of the equation of dynamic motion. The evolution of a traffic system from an unstable or metastable state to a globally stable state bears a strong resemblance to the phase transition in thermodynamics. In this work, we explore the underlying physics of the traffic system, by examining closely the physical properties and mathematical constraints of the phase transitions therein. By using a mesoscopic approach, one entitles the catastrophe model the same physical content as in the Landau's theory, and uncovers its close connections to the instability of the equation of motion and to the transition between different traffic states. In addition to the one-dimensional configuration space, we generalize our discussions to the higher-dimensional case, where the observed temporal oscillation in traffic flow data is attributed to the curl of a vector field. We exhibit that our model can reproduce the main features of the observed fundamental diagram including the inverse-λ shape and the wide scattering of congested traffic data. When properly parameterized, the main feature of the data can be reproduced reasonably well either in terms of the oscillating congested traffic or in terms of the synchronized flow.     

Nonlinear surface waves on a ferromagnetic fluid of variable depth

A nonlinear ray method is used to study surface waves on a ferromagnetic fluid of variable depth subject to a horizontal magnetic field, and an equation of the KdV type with variable coefficients is derived. An approximate solution of the equation representing a three-dimensional soliton with varying amplitude and phase is constructed and numerical results are presented.     

A new lattice hydrodynamic model for bidirectional pedestrian flow considering the visual field effect

In this paper, a new lattice hydrodynamic model for bidirectional pedestrian flow is proposed by considering the pedestrian’s visual field effect. The stability condition of this model is obtained by the linear stability analysis. The mKdV equation near the critical point is derived to describe the density wave of pedestrian jam by applying the reductive perturbation method. The phase diagram indicates that the phase transition occurs among the freely moving phase, the coexisting phase, and the uniformly congested phase below the critical point \(a_c\) . Furthermore, the analytical results show that the visual field effect plays an important role in jamming transition. To take into account the visual information about the motion of more pedestrian in front can improve efficiently the stability of pedestrian system. In addition, the numerical simulations are in accordance with the theoretical analysis.     

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.     

Generation and evolution of oblique solitary waves in supercritical flows

It is considered that a thin strut sits in a supercritical shallow water flow sheet over a homogeneous or very mildly varying topography. This stationary 3-D problem can be reduced from a Boussinesq-type equation into a KdV equation with a forcing term due to uneven topography, in which the transverse coordinate Y plays a same role as the time in original KdV equation. As the first example a multi-soliton wave pattern is shown by means of N-soliton solution. The second example deals with the generation of solitary wave-train by a wedge-shaped strut on an even bottom. Whitham's average method is applied to show that the shock wave jump at the wedge vertex develops to a cnoidal wave train and eventually to a solitary wavetrain. The third example is the evolution of a single oblique soliton over a periodically varying topography. The adiabatic perturbation result due to Karpman & Maslov (1978) is applied. Two coupled ordinary differential equations with periodic disturbance are obtained for the soliton amplitude and phase. Numerical solutions of these equations show chaotic patterns of this perturbed soliton.