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 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 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.     

Phase transitions in the two-lane density difference lattice hydrodynamic model of traffic flow

In this paper, we derive the KdV equation from the two-lane lattice hydrodynamic traffic model considering density difference effect. The soliton solution is obtained from the KdV equation. Under periodical boundary, the KdV soliton of traffic flow is demonstrated by numerical simulation. The numerical simulation result is consistent with the nonlinear analytical result. Under open system, the density fluctuation of the downstream last one lattice is designed to explore the empirical congested traffic states. A phase diagram is presented which includes free traffic, moving localized cluster, triggered stop-and-go traffic, oscillating congested traffic, and homogeneous congested traffic. Finally, the spatiotemporal evolution of all the traffic states described in phase diagram are reproduced. Results suggest that the two-lane density difference hydrodynamic traffic model is suitable to describe the actual traffic.     

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 delayed feedback control method for the two-lane traffic flow

This study extended a delayed feedback control method for the two-lane car-following model. In order to suppress the traffic jams more actually in the two-lane vehicle groups with lane-changing behavior, we introduced the delayed time of receiving the longitudinal and lateral interaction information in the controller into the feedback signals for the control scheme. The stability conditions for different cases were derived, respectively, according to the delayed time by the theory analysis. And the delayed time in the controller was found to instigate the traffic oscillations when the feedback gains were designed improper, which showed that the longer delayed time induces worse traffic jams. The numerical simulation results were found consistent with the theoretical findings as well. Finally, we further presented a comparative study of the proposed control method by a comparison with one existing controller which did not consider the delayed time. And it showed that the delayed time in the controller also affects the traffic flow and performance of control method.     

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.      

KINEMATIC WAVE PROPERTIES OF ANISOTROPIC DYNAMICS MODEL FOR TRAFFIC FLOW

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Impact of lattice’s self-anticipative density on traffic stability of lattice model on two lanes

Nonlinear Dynamics - The self-anticipative density (SAD) term is embedded to traffic modeling for two-lane freeway in this paper. In view of linear stability analysis, SAD effect on two lanes is...     

Dynamics in phase transitions of TASEP coupled with multi-lane SEPs

In this paper, we study a traffic model constituted by totally asymmetric simple exclusion process (TASEP) and two-lane simple exclusion processes (SEP). Then we generalize it to study TASEP coupled with multiple SEP lanes. Numerical results by the mean-field approximation have been presented to show the dynamics of TASEP competing with multi-lane SEPs. Complemented by simulation results, numerical results show that phase diagrams and current diagrams qualitatively vary with current splitting parameter \({\theta _i}\), hopping rate \({D_i}\) (\({D'_i}\)) and the global density \(n_{\mathrm{p}}\).     

A Model for the Formation and Evolution of Traffic Jams

In this paper, we establish and analyze a traffic flow model which describes the formation and dynamics of traffic jams. It consists of a pressureless gas dynamics system under a maximal constraint on the density and is derived through a singular limit of the Aw-Rascle model. From this analysis, we deduce the particular dynamical behavior of clusters (or traffic jams), defined as intervals where the density limit is reached. An existence result for a generic class of initial data is proved by means of an approximation of the solution by a sequence of clusters. Finally, numerical simulations are produced.     

TWO-DIMENSIONAL CELLULAR AUTOMATON TRAFFIC MODELWITH RANDOMLY SWITCHING TRAFFIC LIGHTS

I.IntroductionWiththedevelopmentofsocietyandeconomyinmetropolises,thecontradictionbet\"eentheincreaseoftrat'ficflowandtheexistingconditionoftrafticftlcilitiesbecolllesmorealldmore'serious,resultinginaprincipalI'actorofconstrainingthedevelopmentofmetropolititneconomy.Therefore,inrecentdecadesthetrat'l'ictlowproblemhasdrawntheattelltiollofInanyspecialistsinvariousfieldsincludingphysics,mechanicsalldmathelllatics.Alargenumberoftraftic1llodelshavebeenpropes.Inthispaper,thecellularautomaton(CA)tr…     

Correlation analysis of synchronization flow at a traffic bottleneck

In this paper, we study the correlation characteristics of synchronization flow in a two-lane model with the partial reduced lane based on the Kerner–Klenov–Wolf cellular automation model using the detrended fluctuation analysis (DFA). The local fundamental diagram and cross-correlation near the entry of the partial reduced lane have been analyzed in the periodic boundary condition. The typical two-dimensional scatter diagram in the local fundamental diagram and the noncorrelation of the cross-correlation between the local density and flow reveal characteristics of synchronization flow near the entry of the reduced lane. By the DFA, the synchronized flow at a traffic bottleneck exhibits the characteristics of long-range correlation. The results of investigation indicate that the injection rate, removal rate, and the location of the partial reduced lane have an obvious influence on the change of the scale exponent in the open boundary condition. Moreover, the length of the partial reduced lane has impact on the change of the scale exponent in the periodic boundary condition.     

考虑道路信息和转向灯的可换道BML模型

车辆换道是司机为获得更好行驶条件而采用的常见措施, 而转向灯对车辆换道行为有重要的指导作用. 本文在BML (Biham-Middleton-Levine)模型的基础上加以改进, 提出了综合考虑道路信息和前车转向灯影响的可换道BML模型. 当车辆无法前行时, 如满足换道条件, 则将道路信息(车道密度及平均速度)和转向灯影响量化为车辆换道概率, 确定车辆是否可以换道. 通过数值模拟, 研究了周期边界条件下车辆换道行为对有、无交通灯控制的两种BML模型发生相变的临界密度以及系统通行能力的影响. 模拟结果表明对于无交通灯BML模型, 引入换道规则可以明显提高系统发生相变的临界密度, 在较小尺度下该临界密度接近有交通灯BML模型, 换道效果明显, 并发现了一种新的局部拥堵和自由流的共存相, 讨论了该共存相的生成和演化机制. 在较高密度下局部阻塞将演化为全局拥堵; 对于有交通灯BML模型, 引入换道规则对系统发生相变的临界密度没有明显的影响, 但相变的过渡区域更窄. 这表明有交通灯时, 换道虽然可以改变局部交通特征, 但难以显著影响交通系统的全局特征.      

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.      

Effect of driver behaviours on the formation and dissipation of traffic flow instabilities

This paper extends a non-local second order continuum traffic model to take into account the timid or aggressive driver behaviours. Based on the proposed model, we derive analytically the effect of timid or aggressive driver behaviours on the instability of traffic dynamics. Simulation results are presented to show how the timid or aggressive driver behaviours influence the formation and dissipation of stop-and-go waves. It is found theoretically and numerically that aggressive drivers tend to stabilize traffic flow whereas timid drivers tend to destabilize traffic flow.     

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.     

Chaotic behavior of logistic map in superior orbit and an improved chaos-based traffic control model

With a vital role of discrete chaos, standard logistic map has found a celebrated place in the dynamics of chaos theory and in various applications of science, such as a discrete traffic flow model, image encryption in cryptography, secure communication, and weather forecasting. Traditionally, this discrete chaos is controlled by one parameter \(\lambda \) using Picard orbit, a one-step feedback procedure. This article presents a one-step forward, applying Mann orbit (superior orbit) the chaotic properties such as period-doubling, period-3 window, and Lyapunov exponent of the standard logistic map is investigated. The results are illustrated analytically and experimentally followed by concluding remarks and a few counter examples. Due to the extra degree of freedom in parameter \(\lambda \), the map provides improved chaotic properties that increases the performance of dynamical phenomena. Moreover, this study describes an improved chaos-based discrete traffic control model. Surprisingly, added new parameter \(\alpha \) in Mann orbit works as control variable that increases the stability performance of the traffic model.     

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.     

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