Lattice Hydrodynamic Model Research Articles

Effect of speed deviation and anticipation effect of flux difference in the lattice hydrodynamic model

To ease traffic pressure and reduce congestion, an extended lattice hydrodynamic model by considering speed deviation and anticipation effect of flux difference is presented. The linear stability condition of this model is derived by control method. The results reveal that these two factors can enhance traffic flow stability. Through nonlinear analysis, the mKdV equation near the critical point is obtained, which describes the phase transition of traffic flow. Numerical simulations are applied to this paper to prove the result of theoretical analysis. Simulation results demonstrate that high estimate of speed and anticipation effect of flux difference play a positive role in relieving traffic jams, and the stability of traffic flow is impeded when the low estimate of speed is added.

Effect of the upstream traffic condition on traffic congestion in lattice hydrodynamic model

With the increase of vehicles, traffic congestion has become a prominent problem. Environmental pollution, energy waste and even traffic accidents are easily caused by congestion. Nowadays, with the help of V2V and V2I communications, real-time interaction of vehicle information can be achieved. Vehicles can easily get information about other vehicles. In reality, a driver looks at the following car (i.e. upstream traffic condition) as well as the preceding car while driving. However, the effect of upstream condition is rarely analyzed. In the paper, a term describing the upstream traffic condition is added in Nagatani’s model. The effect of the upstream traffic condition to linear stability is obtained by applying the perturbation method. Nonlinear stability equations, such as the mKdV equation, are also derived. Theoretical results of linear stability and nonlinear stability are shown intuitively through numerical simulations. It can be found that traffic is more stable when the upstream traffic condition is considered.

Analysis of a novel lattice hydrodynamic model considering predictive effect and flow integral

By taking the predictive effect and flow integral into consideration, we propose an improved lattice hydrodynamic model. Firstly, we apply linear stability analysis to acquire the linear stability condition, which can be used to explain the influence of predictive effect and flow integral on traffic flow stability. After that, the modified Korteweg–de Vries (mKdV) equation is derived through the nonlinear theory, which demonstrates that the solution of mKdV equation can describe traffic jams. Besides, the kink–antikink soliton wave is obtained through solving the mKdV equation, which can describe the propagation characteristics of the traffic density waves. Furthermore, we try to explore how predictive effect and flow integral influence the stability of traffic flow through numerical simulations. Finally, we find that the stability of traffic flow can be efficiently improved with the consideration of the two factors by observing and analyzing the numerical results.

Feedback control caused by honk effect incorporating the driver’s characteristics in lattice hydrodynamic model

Different drivers possess their individual driving characteristics under honk environment. To explore the honk effect incorporating the driver’s characteristics on traffic dynamic, a new control signal was offered by considering the feedback gain and the proportion coefficient of the driver’s characteristics under honk environment for lattice hydrodynamic model. Linear stability analysis was carried out via control theory. The simulation result implies that the feedback control resulted from more aggressive behaviors can play positive role on traffic stability.

Research on the stabilization effect of continuous self-delayed traffic flux in macro traffic modeling

A modified macro traffic lattice hydrodynamic model is proposed by considering the continuous self-delayed traffic flux information on traffic stability. Via linear stability theory, the influence of the continuous self-delayed traffic flux on traffic stability is derived. It reveals that the stable region in the density-sensitivity space can be enlarged by taking the continuous self-delayed traffic flux into account. Furthermore, the nonlinear feature of density wave in the unstable region is studied and it is consistent with the kink-antikink solution of the mKdV equation. Also numerical simulation is conducted to further verify the analytical results and it is shown that the continuous self-delayed traffic flux information can improve the stable level of traffic flow significantly.

Effect of density integration on the stability of a new lattice hydrodynamic model

A novel traffic lattice hydrodynamic model considering the effect of density integration is proposed and analyzed in the paper. Via linear stability theory, linear stability condition of the new model is derived, which reveals an improvement of traffic stability by considering the integration of continuous historical density information. Moreover, the nonlinear properties of the extended model are revealed through nonlinear analysis. The propagating backwards kink–antikink waves are generated by deriving the mKdV equation near the critical point and verified by numerical simulation. All the results show that the density integration effect can suppress traffic congestion efficiently in traffic lattice hydrodynamic modeling.

The impact of the individual difference on traffic flow under honk environment in lattice hydrodynamic model

A feedback control method is utilized with the consideration of the individual difference of drivers’ characteristics under honk environment on single lane. The linear stability analysis is implemented with feedback term in virtue of modern control method. Numerical simulations also show that the individual difference of drivers’ characteristics plays a different role on the stability of traffic flow.

Analysis of predictive effect on lattice hydrodynamic traffic flow model

This paper proposes a new lattice hydrodynamic traffic flow model which works by incorporating the predictive effect of expected traffic variation tendencies. We use a linear method to analyze the influence of predictive effect on traffic stream stability. The derived analytical critical stable lines indicate that the expected behavior of the vehicle ahead can enhance traffic stability. Then we adapt the reductive perturbation method to deduce the modified Korteweg–de Vries (mKdV) equation. Also, kink–antikink solutions capable of describing traffic jams are derived. The numerical results show that the predictive effect has the capability to improve traffic stability.

Analysis of a novel lattice hydrodynamic model considering density integral and “backward looking” effect

By introducing the “backward looking” influence and the integration form of the density difference between the front and rear vehicles, an improved lattice hydrodynamic model is proposed. The linear stability condition is derived by linear stability analysis. The results of the linear stability analysis demonstrate that the influence of “backward looking” and density difference between the front and rear vehicles play a positive part in improving the steadiness of the traffic flow system. The nonlinear analysis testifies that the mKdV equation can describe the propagation feature of density wave. The results of numerical simulation show that the steadiness of traffic flow can be amenable to improvement effectively by considering these two factors. Comprehensive analysis demonstrates that the effect of the “backward looking” and density difference is propitious to improve traffic stability and suppress traffic congestion.

A new lattice hydrodynamic model accounting for the traffic interruption probability on a gradient highway

In this paper, a novel lattice hydrodynamic model is presented by accounting for the traffic interruption probability on a gradient highway. The stability condition can be obtained by the use of linear analysis. Linear analysis demonstrates that the traffic interruption probability and the slope will affect the stability region. Through nonlinear analysis, the mKdV equation is derived to describe the phase transition of traffic flow. Furthermore, the numerical simulation is carried out, and the results are consistent with the analytical results. Numerical results demonstrate that the traffic flow can be efficiently improved by accounting for the traffic interruption probability on a gradient highway.

Two-lane lattice hydrodynamic model considering the empirical lane-changing rate

As a common behavior, lane changing has a significant influence on traffic flow. Lane changing is heavily dependent on the surrounding environment, so having a constant lane-changing rate in a traffic flow model would be unreasonable. Through an analysis of three empirical lane-changing datasets, we find that the lane-changing rate depends on traffic density. The structure of the lane-changing rate is similar to an optimization velocity function. We propose a new two-lane lattice model by modifying the lane-changing rate in the conservation equation. The linear stability of the new model and the effects of the parameters in the lane-changing rate on linear stability are analyzed through theory and simulation. Moreover, the new model and Nagatani's two-lane model are compared with actual observation results, which shows that the new model can better reproduce the observation results.

Analysis of the historical time integral form of relative flux and feedback control in an extended lattice hydrodynamic model

An extended lattice hydrodynamic model is presented by considering the historical relative flux in integral form and flux change rate. The flux change rate can be regarded as the control signal. Control method is applied to the linear stability analysis and the stability condition of the model is obtained. In addition, energy consumption is also explored. To prove the theoretical findings, numerical simulations are carried out in this paper. Simulation results show that the historical relative flux can worsen the traffic flow stability and increase the energy consumption. The control signal plays a significant role in stabilizing the traffic flow and leading to a lower energy consumption. The simulation results are found consistent with the theoretical results.

An extended macroscopic model for traffic flow on curved road and its numerical simulation

In this paper, we propose a full angular velocity difference model by introducing the angular velocity and displacement on curved road. The relation of transformation of microscopic model in form of angular variables into macroscopic one is deduced. Consequently, a corresponding continuum traffic flow model on curved road is derived. The critical condition for the steady traffic flow is obtained. Meanwhile, the stability condition of this continuum traffic model is compared with one of the microscopic model and lattice hydrodynamic traffic model on curved road. By nonlinear analysis, the KdV–Burgers equation which describes the density wave near the neutral stability line is derived. Furthermore, the numerical simulations are carried out to verify the validity of this macroscopic traffic. Results indicate the radius of curved road have a great impact on the formation of traffic jams. Local clustering effects in the state of instability of traffic flow give rise to the stop&go traffic jams. Numerical simulation also indicates the unstable region is shrunken under the increasing strength of the angular velocity difference.

An Extended Mean-Field Lattice Hydrodynamic Model With Consideration of the Average Effect of Multi-Lattice Interaction

In this paper, an extended mean-field lattice hydrodynamic model is proposed which considers the average effect of multi-lattices interaction. By stability analysis, the linear stability criterion of the proposed model is given. Through nonlinear analysis, we derive the mKdV equation to investigate the traffic jams described by traffic density wave. Then, the numerical simulations are carried out. The simulation results show that that the average effect of multi-lattices interaction plays the great important part in curbing traffic congestion. Increasing the impact of the mean-field multi-lattices interaction can curb the congestion effectively and make the traffic system more stable.

A Lattice Hydrodynamic Model of Bidirectional Pedestrian Traffic Considering the Cumulative Effect of Delay Time

A Lattice Hydrodynamic Model of Bidirectional Pedestrian Traffic Considering the Cumulative Effect of Delay Time

Analysis of a Novel Two-Lane Lattice Hydrodynamic Model Considering the Empirical Lane Changing Rate and the Self-Stabilization Effect

Considering the impact of the empirical lane changing rate and self-stabilization effect on traffic flow stability synthetically, an extended two-lane lattice hydrodynamic model was proposed in this paper. In the first place, the stability condition is acquired through applying liner stability analysis method and it reveals that both the empirical lane changing rate and self-stabilization effect can enhance the stability of traffic flow to some extent. Next, in order to analyze the transmission mechanism of traffic congestion, the modified Korteweg-de Vries (mKdV) equation is deduced by using nonlinear theory near the critical point. At the same time, the kink-antikink solitary wave solution is obtained to describe the propagation behavior of traffic density wave by solving the mKdV equation. Subsequently, the numerical simulations are carried out and the results coincide well with the theoretical analysis, which indicate the empirical lane changing rate and the self-stabilization effect can improve the traffic stability.

Feedback control pattern for a new lattice hydrodynamic model accounting for historic evolution information

ABSTRACT A feedback control pattern is considered in traffic system with the consideration of the historic evolution information about considered site based on the lattice hydrodynamic model of traffic flow. The linear stability conditions with and without control are obtained by applying linear stability analysis with the control method. It is found that the stability of traffic flow is closely related to the historic evolution information about the considered site. Numerical simulations are carried out to prove that both new consideration and feedback control can improve the stability of traffic flow efficiently. The theoretical findings are in accordance with numerical simulation.

New Feedback Control Model in the Lattice Hydrodynamic Model Considering the Historic Optimal Velocity Difference Effect**Supported by the National Natural Science Foundation of China under Grant No. 61673168

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.

Dynamic congested traffic states of lattice hydrodynamic model with an on-ramp and its immediate upstream off-ramp

This paper investigates the features of congested traffic flow near the combination of off-ramp and on-ramp. Firstly, the stochastic off-ramp and on-ramp are designed. Then, a two-lane lattice hydrodynamic traffic flow model coupled with a combination bottleneck is proposed to reproduce the empirical phenomena. In the simulation, the asymmetric-lane change rules were adopted, and many congested traffic flow patterns were observed near the combination bottlenecks, such as homogeneous synchronized traffic (HST), moving localized cluster (MLC), triggered stop-and-go traffic (TSG), oscillating congested traffic (OCT), pinned localized cluster (PLC), and homogeneous congested traffic (HCT). The obtained simulation results suggest that the proposed model is good and can produce the observed congestion spatiotemporal traffic patterns well.

The impact of self-stabilization on traffic stability considering the current lattice’s historic flux for two-lane freeway

Self-stabilization effect reflects the adaptive change of the current lattice in traffic flow. To improve traffic flow, a new self-stabilization term in this paper is inserted into lattice hydrodynamic model for two-lane freeway. It is shown that the self-stabilization effect can increase traffic stability on two lanes whether lane changing occurs or not according to linear stability analysis. In view of numerical simulation, the self-stabilization effect enhances the stability of the traffic flow in the modified lattice hydrodynamic model for two-lane freeway.