Lattice Hydrodynamic Model Research Articles

Influence factors analysis on traffic jam for a new lattice hydrodynamic model on gyroidal road

In the paper, an extended one-dimensional lattice hydrodynamic model is proposed to investigate the related factors on a gyroidal road (i.e. a curved road with a slope). We investigate the related influences on uniform traffic jam analytically and numerically. Based on control theory, condition for no traffic jam is obtained analytically. Finally, simulations are carried out to verify the new lattice hydrodynamic model and numerical simulations are consistent with the theoretical results.Results show that the related factors including the friction coefficient, radius of curvature and slope of a gyroidal road have major effect on the stability of traffic flow respectively.

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.

A modified two-dimensional triangular lattice model under honk environment

The honk effect is not uncommon in the real traffic and may exert great influence on the stability of traffic flow. As opposed to the linear description of the traditional one-dimensional lattice hydrodynamic model, the high-dimensional lattice hydrodynamic model is a gridded analysis of the real traffic environment, which is a generalized form of the one-dimensional lattice model. Meanwhile, the high-dimensional traffic flow exposed to the open-ended environment is more likely to be affected by the honk effect. In this paper, we propose an extension of two-dimensional triangular lattice hydrodynamic model under honk environment. The stability condition is obtained via the linear stability analysis, which shows that the stability region in the phase diagram can be effectively enlarged under the honk effect. Modified Korteweg–de Vries equations are derived through the nonlinear stability analysis method. The kink–antikink solitary wave solution is obtained by solving the equation, which can be used to describe the propagation characteristics of density waves near the critical point. Finally, the simulation example verifies the correctness of the above theoretical analysis.

Analysis of an extended two-lane lattice hydrodynamic model considering mixed traffic flow and self-stabilization effect

PurposeThe purpose of this paper is to explore the impact of the mixed traffic flow, self-stabilization effect and the lane changing behavior on traffic flow stability.Design/methodology/approachAn extended two-lane lattice hydrodynamic model considering mixed traffic flow and self-stabilization effect is proposed in this paper. Through linear analysis, the stability conditions of the extended model are derived. Then, the nonlinear analysis of the model is carried out by using the perturbation theory, the modified Kortweg–de Vries equation of the density of the blocking area is derived and the kink–antikink solution about the density is obtained. Furthermore, the results of theoretical analysis are verified by numerical simulation.FindingsThe results of numerical simulation show that the increase of the proportion of vehicles with larger maximum speed or larger safe headway in the mix flow are not conducive to the stability of traffic flow, while the self-stabilization effect and lane changing behavior is positive to the alleviation of traffic congestion.Research limitations/implicationsThis paper does not take into account the factors such as curve and slope in the actual road environment, which will have more or less influence on the stability of traffic flow, so there is still a certain gap with the real traffic environment.Originality/valueThe existing two-lane lattice hydrodynamic models are rarely discussed in the case of mixed traffic flow. The improved model proposed in this paper can better reflect the actual traffic, which can also provide a theoretical reference for the actual traffic governance.

An extended lattice hydrodynamic model with time delay based on non-lane discipline

An extended lattice hydrodynamic model with time delay is proposed under non-lane discipline. We try to grasp the impacts of the non-lane discipline of the considered lattice sites. Linear stability analysis of the proposed model is executed and the stability criterion is obtained. Using the reductive perturbation method, we investigate nonlinear analysis of the proposed model and derive the mKdV equation and its solution, which could reveal the propagation of density waves. We analyze the effect of time delay, the ratio of lane deviation and the control coefficient on the stability of traffic flow via numerical experiments. We find that those indices play an important role in the stability of traffic flow. The longer the time delay, the more unstable the system becomes. Also, the ratio of lane deviation and the control coefficient is able to more quickly dissipate the traffic congestions occurring in traffic flow.

Analysis of a Novel Two-Lane Hydrodynamic Lattice Model Accounting for Driver’s Aggressive Effect and Flow Difference Integral

In the actual traffic environment, the driver’s aggressive driving behaviors are closely related to the traffic conditions at the next-nearest grid point at next time step. The driver adjusts the acceleration of the driving vehicle by predicting the density of the front grid points. Considering the driver’s aggressive effect and the relative flow difference integral, a novel two-lane lattice hydrodynamic model is presented in this paper. The linear stability method is used to analyze the current stability of the new model, and the neutral stability curve is obtained. The nonlinear analysis of the new model is carried out by using the theory of perturbations, and the mKdV equation describing the density of the blocked area is derived. The theoretical analysis results are verified by numerical simulation. From the analysis results, it can be seen that the driver’s aggressive effect and the relative flow difference integral can improve the stability of traffic flow comprehensively.

A New Two-Lane Lattice Hydrodynamic Model considering the Traffic Interruption Probability under Honk Environment

By accounting for the traffic interruption probability on two-lane highway under honk environment, an extended lattice hydrodynamic model is presented in the paper. In view of the novel model, a series of researches are carried out. The neutral stability condition and the stable condition can be derived through linear analysis. Then, the mKdV equation near the critical point can be obtained by applying nonlinear analysis, which describes the traffic jams according to the kink-antikink density waves. In addition, numerical simulation is performed, which confirms that traffic interruption probability on two-lane highway under honk environment can develop traffic jams by the change of density waves. Also, the phenomenon is consistent with the results of previous theoretical analysis. It shows that accounting for the traffic interruption probability on two-lane highway under honk environment can stabilize the traffic flow efficiently.

Analysis of a novel two-lane lattice model with consideration of density integral and relative flow information

PurposeThis study aims to consider the influence of density difference integral and relative flow difference on traffic flow, a novel two-lane lattice hydrodynamic model is proposed. The stability criterion for the new model is obtained through the linear analysis method.Design/methodology/approachThe modified Korteweg de Vries (KdV) (mKdV) equation is derived to describe the characteristic of traffic jams near the critical point. Numerical simulations are carried out to explore how density difference integral and relative flow difference influence traffic stability. Numerical and analytical results demonstrate that traffic congestions can be effectively relieved considering density difference integral and relative flow difference.FindingsThe traffic congestions can be effectively relieved considering density difference integral and relative flow difference.Originality/valueNovel two-lane lattice hydrodynamic model is presented considering density difference integral and relative flow difference. Applying the linear stability theory, the new model’s linear stability is obtained. Through nonlinear analysis, the mKdV equation is derived. Numerical results demonstrate that the traffic flow stability can be efficiently improved by the effect of density difference integral and relative flow difference.

Effect of Changing Path on Pedestrian Traffic under the Cumulative Effect of Delay Time

In this paper, a lattice hydrodynamic model of two-dimensional bidirectional pedestrian traffic is proposed with consideration of altering path under the cumulative effect of delay time. The stability condition is acquired by linear analysis, and the mKdV equation to describe congestion evolution is derived by reductive perturbation technique. According to the result from the stability analysis, the stability region of pedestrian flow can be divided into stable region, unstable region, and metastable region. On the basis of stable condition, the unstable region is narrowed with the increase of delay time td and the path changing rate γ. It indicates that changing path can effectively improve the stability of the pedestrian flow under the cumulative effect of delay time td. For numerical simulation and analysis of density wave, it is found that the increase of path changing rate γ and the cumulative effect of delay time td are conducive to alleviate pedestrian congestion.

A new two-lane lattice hydrodynamic model with the introduction of driver’s predictive effect

This paper devises a new two-lane lattice hydrodynamic model (TLHM) to explore driver’s predictive effect (DPE) on traffic oscillation. First, a linear approach is conducted to analytically predict the DPE on traffic performance. Theoretical analysis shows that with the help of DPE, the traffic flow stability will be gradually enhanced. Then, nonlinear analysis is implemented to explore the characteristics of traffic oscillation when sensitivity coefficient is near the critical point. The modified KdV equation derived from the new model and its analytical solution related kink–antikink density waves are obtained. Finally, numerical experiments show that the DPE can effectively dampen the growth of oscillation, which is well consistent with the theoretical analysis of the new model.

A new lattice hydrodynamic model for bidirectional pedestrian flow with consideration of pedestrians’ honk effect

Understanding the pedestrian behavior contributes to traffic simulation and facility design/redesign. In practice, the interactions between individual pedestrians can lead to virtual honk effect, such as urging surrounding pedestrians to walk faster in a crowded environment. To better reflect the reality, this paper proposes a new lattice hydrodynamic model for bidirectional pedestrian flow with consideration of pedestrians’ honk effect. To this end, the concept of critical density is introduced to define the occurrence of pedestrians’ honk event. In the linear stability analysis, the stability condition of the new bidirectional pedestrian flow model is given based on the perturbation method, and the neutral stability curve is also obtained. Based on this, it is found that the honk effect has a significant impact on the stability of pedestrian flow. In the nonlinear stability analysis, the modified Korteweg–de Vries (mKdV) equation of the model is obtained based on the reductive perturbation method. By solving the mKdV equation, the kink-antikink soliton wave is obtained to describe the propagation mechanism and rules of pedestrian congestion near the neutral stability curve. The simulation example shows that the pedestrians’ honk effect can mitigate the pedestrians crowding efficiently and improve the stability of the bidirectional pedestrian flow.

Analysis of the predictive effect and feedback control in an extended lattice hydrodynamic model

PurposeThis paper aims to put forward an extended lattice hydrodynamic model, explore its effects on alleviating traffic congestion and provide theoretical basis for traffic management departments and traffic engineering implementation departments.Design/methodology/approachThe control method is applied to study the stability of the new model. Through nonlinear analysis, the mKdV equation representing kink-antikink soliton is acquired.FindingsThe predictive effect and the control signal can enhance the traffic flow stability and reduce the energy consumption.Originality/valueThe predictive effect and feedback control are first considered in lattice hydrodynamic model simultaneously. Numerical simulations demonstrate that these two factors can enhance the traffic flow stability.

Lattice hydrodynamic modeling with continuous self-delayed traffic flux integral and vehicle overtaking effect

This paper presents a new lattice hydrodynamic model with vehicle overtaking and the continuous self-delayed traffic flux integral. The linear stability condition of the model is derived through the linear stability analysis, which shows that the stable region can be enlarged by increasing the step of delay time. The modified Korteweg–de Vries (mKdV) equation is formulated through nonlinear analysis to describe the propagating behavior of traffic density wave near the critical point. The kink–anti-kink solution under different passing constants is also obtained. Results show that when the passing constant is lower than a threshold (Case I) that is associated with the delay time step, uniform flow and kink jam phase exhibits, and jamming transition occurs between the uniform flow and kink jam. When the passing constant exceeds the threshold (Case II), jamming transitions occur from uniform traffic flow to kink-Bando traffic wave through chaotic phase with decreasing sensitivity. Simulation examples verify that when the delay time increases from 0 to 0.6, the fluctuation amplitude of the traffic density is reduced from 0.07 to 0 even with exogenous initial disturbance, whereas under Case II, chaotic traffic flow appears when the density ranges from 0.18 to 0.31 and the delay time is 0.6.

The stabilization effect of self-delayed flux integral for two-lane lattice hydrodynamic model

In this paper, a novel lattice model is presented by considering the self-delayed flux integral (SDFI) effect on two lanes. The linear stability condition related to SDFI effect is deduced via theoretic analysis for two-lane freeway. Simulation is executed to explore the SDFI effect on the amplitude of density wave in two-lane system. Based on simulation, the information of continuous self-delayed flux contributes to the stability of traffic flow on two lanes significantly.

Lattice hydrodynamic model-based feedback control method with traffic interruption probability

Connected vehicles are expected to become commercially available by the next decade, while traffic interruption is not uncommon in the real traffic environment. In this paper, we propose a feedback control method for lattice hydrodynamic model considering the traffic interruption probability effect. The stability criterion of the new model is explored through linear stability analysis of transfer function. When the stability conditions are not satisfied, a delay feedback controller is used to control the discharging flow to suppress traffic congestion. The impact of gain coefficient and delay time on the performance is discussed. We verify the effectiveness of the devised delay feedback controller by simulations. Results show that the traffic interruption probability effect has a considerable impact on the stability of traffic flow, while the controller is effective in suppressing traffic congestion.

Memory’s effect on bidirectional pedestrian flow based on lattice hydrodynamic model

In this paper, an extended lattice hydrodynamic model for bidirectional pedestrian flow is proposed to analyze the effect of pedestrian’s memory during a period of time on the pedestrian flow. The effect of pedestrian’s memory during a period of time is investigated by using analytical and numerical methods. The linear stability analysis indicates that the time length of pedestrian’s memory has an important effect on the stability of pedestrian flow. With increasing of the time length of pedestrian’s memory, pedestrian flow will become unstable and pedestrian congestion appear. By the use of nonlinear analysis method, three typical nonlinear wave equations including Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (MKdV) equations are derived to describe the evolutions of pedestrian flow with a small amplitude disturbance in the stable, meta-stable and unstable regions, respectively. The theoretical results show that jams may be aggravated by considering the effect of pedestrian’s memory with a time length. Numerical simulations are carried out in order to clarify the theoretical results.

Study on the continuous delayed optimal flow on traffic stability in a new macro traffic model

The influence of the continuous delayed optimal flow on traffic stability is studied based on a new traffic lattice hydrodynamic model in this paper. Linear analysis derives the model’s linear stable condition and it shows that the stability of traffic flow is enhanced by considering the continuous delayed optimal flow. Also the feature of the unstable traffic flow is uncovered by the solution of the mKdV equation with nonlinear analysis. Finally, numerical simulation is carried out to intuitively show the stabilization effect of the continuous delayed optimal flow on traffic flow and the continuous delayed optimal flow should be considered in traffic theory.

An extended two-lane lattice hydrodynamic model for traffic flow on curved road with passing

An extended two-lane lattice hydrodynamic model is proposed for the purpose of studying the effects of lane changing behavior and passing behavior on curved road. The main work of this paper is as follows. Firstly, the stability condition is acquired through the use of linear stability analysis and it reveals that passing effect as well as the angle of the curve road can affect the stability of traffic flow to some extent. Meanwhile, the stability of traffic flow varies greatly under different lane changing coefficients. The modified Korteweg–de Vries (mKdV) equation is deduced to describe the characteristic of traffic jams near the critical point. Furthermore, the numerical simulations are performed and the results coincide well with the theoretical analysis. In conclusion, the angle of curved road and lane changing behavior have a positive impact on traffic flow stability, while passing effect, on the contrary, will aggravate traffic congestion.

Nonlinear analysis of a new two-lane lattice hydrodynamic model accounting for “backward looking” effect and relative flow information

In this paper, a new two-lane lattice hydrodynamic model is presented by accounting for the “backward looking” effect and the relative flow information. Linear analysis is applied to deduce the linear stability condition. With this method, we can demonstrate that “backward looking” and relative flow information have great positive significance in improving traffic flow stability. Nonlinear analysis is performed to derive the mKdV equation, which can represent transmission characteristic of density waves. The results achieved by the numerical simulation are consistent with theoretical analytical results. Numerical results indicate that both “backward looking” effect and relative flow information are helpful to heighten the traffic flow stability efficiently in two-lane traffic model.

The impact of the density difference memory integral on traffic stability in two-lane lattice hydrodynamic model

The density difference memory integral (DDMI) term can be applied to describe traffic density information of the driver’s historical memory during a continuous period of time. In this paper, a new lattice model is provided with the consideration of the DDMI effect for two-lane freeway. The linear stability condition of two lanes has been derived by considering the DDMI effect through linear stability theory, which shows that the DDMI effect can improve traffic stability under lane changing. According to the observation of simulation, the DDMI effect conduces to the stability of traffic flow for two-lane freeway.