A new lattice hydrodynamic model based on control method considering the flux change rate and delay feedback signal

In this paper, a new lattice hydrodynamic model is proposed by taking delay feedback and flux change rate effect into account in a single lane. The linear stability condition of the new model is derived by control theory. By using the nonlinear analysis method, the mKDV equation near the critical point is deduced to describe the traffic congestion. Numerical simulations are carried out to demonstrate the advantage of the new model in suppressing traffic jam with the consideration of flux change rate effect in delay feedback model.     

Analyses of driver’s anticipation effect in sensing relative flux in a new lattice model for two-lane traffic system

In this paper, a new lattice hydrodynamic traffic flow model is proposed by considering the driver’s anticipation effect in sensing relative flux (DAESRF) for two-lane system. The effect of anticipation parameter on the stability of traffic flow is examined through linear stability analysis and shown that the anticipation term can significantly enlarge the stability region on the phase diagram. To describe the phase transition of traffic flow, mKdV equation near the critical point is derived through nonlinear analysis. The theoretical findings have been verified using numerical simulation which confirms that traffic jam can be suppressed efficiently by considering the anticipation effect in the new lattice model for two-lane traffic.     

Flow difference effect in the lattice hydrodynamic model

In this paper, a new lattice hydrodynamic model based on Nagatani's model [Nagatani T 1998 Physica A 261 599] is presented by introducing the flow difference effect. The stability condition for the new model is obtained by using the linear stability theory. The result shows that considering the flow difference effect leads to stabilization of the system compared with the original lattice hydrodynamic model. The jamming transitions among the freely moving phase, the coexisting phase, and the uniform congested phase are studied by nonlinear analysis. The modified KdV equation near the critical point is derived to describe the traffic jam, and kink--antikink soliton solutions related to the traffic density waves are obtained. The simulation results are consistent with the theoretical analysis for the new model.     

Multiple flux difference effect in the lattice hydrodynamic model

Considering the effect of multiple flux difference, an extended lattice model is proposed to improve the stability of traffic flow. The stability condition of the new model is obtained by using linear stability theory. The theoretical analysis result shows that considering the flux difference effect ahead can stabilize traffic flow. The nonlinear analysis is also conducted by using a reductive perturbation method. The modified KdV (mKdV) equation near the critical point is derived and the kink-antikink solution is obtained from the mKdV equation. Numerical simulation results show that the multiple flux difference effect can suppress the traffic jam considerably, which is in line with the analytical result.     

Jamming transition of a two-dimensional traffic dynamics with consideration of optimal current difference

A modified two-dimensional lattice hydrodynamic traffic flow model is proposed by incorporating the optimal current difference effect of leading vehicles. Phase transitions and critical phenomenon are investigated near the critical point both analytically and numerically. Based on the configuration of vehicles, it is shown that two distinct jamming transitions occur: conventional jamming transition to the kink jam and jamming transition to the chaotic jam. It is shown that consideration of optimal current difference effect stabilizes the traffic flow and suppresses the traffic jam efficiently for all possible configurations of vehicles on a square lattice.     

Analyses of Lattice Traffic Flow Model on a Gradient Highway

The optimal current difference lattice hydrodynamic model is extended to investigate the traffic flow dynamics on a unidirectional single lane gradient highway. The effect of slope on uphill/downhill highway is examined through linear stability analysis and shown that the slope significantly affects the stability region on the phase diagram.Using nonlinear stability analysis, the Burgers, Korteweg-deVries(KdV) and modified Korteweg-deVries(mKdV) equations are derived in stable, metastable and unstable region, respectively. The effect of reaction coefficient is examined and concluded that it plays an important role in suppressing the traffic jams on a gradient highway. The theoretical findings have been verified through numerical simulation which confirm that the slope on a gradient highway significantly influence the traffic dynamics and traffic jam can be suppressed efficiently by considering the optimal current difference effect in the new lattice model.     

Analyses of Lattice Traffic Flow Model on a Gradient Highway

The optimal current difference lattice hydrodynamic model is extended to investigate the traffic flow dynamics on a unidirectional single lane gradient highway. The effect of slope on uphill/downhill highway is examined through linear stability analysis and shown that the slope significantly affects the stability region on the phase diagram. Using nonlinear stability analysis, the Burgers, Korteweg-deVries (KdV) and modified Korteweg-deVries (mKdV) equations are derived in stable, metastable and unstable region, respectively. The effect of reaction coefficient is examined and concluded that it plays an important role in suppressing the traffic jams on a gradient highway. The theoretical findings have been verified through numerical simulation which confirm that the slope on a gradient highway significantly influence the traffic dynamics and traffic jam can be suppressed efficiently by considering the optimal current difference effect in the new lattice model.     

Nonlinear density wave and energy consumption investigation of traffic flow on a curved road

A new car-following model is proposed based on the full velocity difference model(FVDM) taking the influence of the friction coefficient and the road curvature into account. Through the control theory, the stability conditions are obtained,and by using nonlinear analysis, the time-dependent Ginzburg-Landau(TDGL) equation and the modified Korteweg-de Vries(mKdV) equation are derived. Furthermore, the connection between TDGL and mKdV equations is also given. The numerical simulation is consistent with the theoretical analysis. The evolution of a traffic jam and the corresponding energy consumption are explored. The numerical results show that the control scheme is effective not only to suppress the traffic jam but also to reduce the energy consumption.     

The “backward looking” effect in the lattice hydrodynamic model

The novel lattice hydrodynamic model is presented by incorporating the “backward looking” effect. The stability condition for the the model is obtained using the linear stability theory. The result shows that considering one following site in vehicle motion leads to the stabilization of the system compared with the original lattice hydrodynamic model and the cooperative driving lattice hydrodynamic model. The Korteweg-de Vries (KdV, for short) equation near the neutral stability line is derived by using the reductive perturbation method to show the traffic jam which is proved to be described by KdV soliton solution obtained from the KdV equation. The simulation result is consistent with the nonlinear analysis.     

A novel lattice model integrating the cooperative deviation of density and optimal flux under V2X environment

A novel lattice hydrodynamic model is proposed by integrating the cooperative deviation of density and optimal flux under vehicle to X (V2X) environment. According to the theoretical analysis, the stability conditions and the mKdV equations affected by the cooperative deviation of traffic information are explored. And the density wave, hysteresis loop and energy consumption of the traffic flow have been investigated via numerical simulation. The results indicate that the cooperative deviation of density and optimal flux can effectively alleviate the traffic congestion. More importantly, our new consideration can reduce fuel consumption and exhaust emission under the V2X environment.     

New Feedback Control Model in the Lattice Hydrodynamic Model Considering the Historic Optimal Velocity Difference Effect

A feedback control model of lattice hydrodynamic model is proposed by taking the information of the historic optimal velocity into account for the traffic system. The modern control theory is applied for the linear stability condition with feedback control signal. The result shows that the stability of traffic flow is closely related to the information of the historic optimal velocity. Furthermore, numerical simulations conform that the new feedback control did increase the stability of traffic flow efficiently, which is in accord with theoretical analysis.     

The Korteweg-de Vries soliton in the lattice hydrodynamic model

The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but is also closely connected with the microscopic car following model. The modified Korteweg-de Vries (mKdV) equation about the density wave in congested traffic has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail in the car following model. So we devote ourselves to obtaining the KdV equation from the lattice hydrodynamic model and obtaining the KdV soliton solution describing the traffic jam. Numerical simulation is conducted, to demonstrate the nonlinear analysis result.     

Lattice models of traffic flow considering drivers' delay in response

This paper proposes two lattice traffic models by taking into account the drivers' delay in response. The lattice versions of the hydrodynamic model are described by the differential-difference equation and difference-difference equation, respectively. The stability conditions for the two models are obtained by using the linear stability theory. The modified KdV equation near the critical point is derived to describe the traffic jam by using the reductive perturbation method, and the kink--antikink soliton solutions related to the traffic density waves are obtained. The results show that the drivers' delay in sensing headway plays an important role in jamming transition.     

The theoretical analysis of the lattice hydrodynamic models for traffic flow theory

The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but also connected with the microscopic car following model closely. The modified Korteweg-de Vries (mKdV) equation related to the density wave in a congested traffic region has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail for the car following model. We devote ourselves to obtaining the KdV equation from the original lattice hydrodynamic models and the KdV soliton solution to describe the traffic jam. Especially, we obtain the general soliton solution of the KdV equation and the mKdV equation. We review several lattice hydrodynamic models, which were proposed recently. We compare the modified models and carry out some analysis. Numerical simulations are conducted to demonstrate the nonlinear analysis results.     

The stabilization effect of the density difference in the modified lattice hydrodynamic model of traffic flow

A modified lattice hydrodynamic model of traffic flow is proposed by introducing the density difference between the leading and the following lattice. The stability condition of the modified model is obtained through the linear stability analysis. The results show that considering the density difference leads to the stabilization of the system. The Burgers equation and mKdV equation are derived to describe the density waves in the stable and unstable regions respectively. Numerical simulations show that considering the density difference not only could stabilize traffic flow but also makes the lattice hydrodynamic model more realistic.     

A study of wide moving jams in a new lattice model of traffic flow with the consideration of the driver anticipation effect and numerical simulation

In this paper, a new lattice model of traffic flow is proposed to investigate wide moving jams in traffic flow with the consideration of the driver anticipation information about two preceding sites. The linear stability condition is obtained by using linear stability analysis. The mKdV equation is derived through nonlinear analysis, which can be conceivably taken as an approximation to a wide moving jam. Numerical simulation also confirms that the congested traffic patterns about wide moving jam propagation in accordance with empirical results can be suppressed efficiently by taking the driver anticipation effect of two preceding sites into account in a new lattice model.     

Decentralized delayed-feedback control of an optimal velocity traffic model

The jam phenomenon in traffic flow wastes not only considerable traffic-transportation time but also great amounts of fuel due to many accelerate-decelerate actions. From traffic-economic and traffic-pollution viewpoints, the suppression of traffic jam is an important issue we have to solve. The present paper shows that -norm, which has been used in the field of control theory, can reveal the traffic jam phenomenon in an optimal velocity traffic model under an open boundary condition. Furthermore, we suppress the traffic jam in the model by the decentralized delayed-feedback control method. Some numerical simulations are shown to verify our theoretical results. Received 27 October 1999     

A New Lattice Model of Two-Lane Traffic Flow with the Consideration of the Honk Effect

In this paper, a new lattice model of two-lane traffic flow with the honk effect term is proposed to study the influence of the honk effect on wide moving jams under lane changing. The linear stability condition on two-lane highway is obtained by applying the linear stability theory. The modified Korteweg-de Vries (KdV) equation near the critical point is derived and the coexisting curves resulted from the modified KdV equation can be described, which shows that the critical point, the coexisting curve and the neutral stability line decrease with increasing the honk effect coefficient. A wide moving jam can be conceivably described approximately in the unstable region. Numerical simulation is performed to verify the analytic results. The results show that the honk effect could suppress effectively the congested traffic patterns about wide moving jam propagation in lattice model of two-lane traffic flow.     

A two-dimensional lattice hydrodynamic model considering shared lane marking

Lane markings are painted on the ground to permit movement turns along traffic lanes at signalized junctions. Drivers have to follow the guidance to turn different directions to enter different downstream lanes. A new two-dimensional lattice hydrodynamic model is proposed to model the effects of a shared lane marking. The control method is used to analyze the model and new stability conditions are derived. A shared lane marking can divert traffic with different directions to enter different downstream lanes. Under different turning proportion, intensities of traffic at downstream vary. Results show that the traffic diversion could influence the flow stability. Shared lane marking is able to divert traffic flows to different downstream lanes. A feedback control signal is added in the proposed model. Revised stability conditions are obtained using the proposed control method. Numerical simulations present the results for the stability under different traffic conditions.     

考虑最邻近前车综合信息的反馈控制跟驰模型

拥堵控制中, 通过车辆运行状态感知与控制的交互融合, 实现对车辆有效控制的过程, 具有信息物理融合系统的典型特征. 本文基于Konishi等的研究工作, 从交通信息系统与交通物理系统融合的角度, 进一步考虑优化速度差和安全间距对车流的影响, 在耦合映射跟驰模型中, 提出了一种考虑最邻近前车综合信息的交通拥堵反馈控制方案. 运用反馈控制理论, 给出了头车速度发生变化时交通流保持稳定的条件, 并与前人工作进行了比较. 理论分析与数值模拟结果一致表明, 耦合映射跟驰模型在本文提出的控制方案下能更有效地抑制交通拥堵. 关键词： 交通流 交通拥堵控制 耦合映射跟驰模型 信息物理融合系统