Two-lane Lattice Hydrodynamic Model Research Articles

Analyses of a two-lane lattice hydrodynamic model incorporating predictive effect and self-delayed flux integral

To explore the mechanism among disturbance, spatiotemporal evolution characteristics and stability for traffic flow, this paper presents an improved lattice hydrodynamic model with lane change into consideration and investigates the influence of three influencing factors, namely, lane change effect, predictive effect, and self-delayed flux integral effect on traffic flow. Moreover, theoretical analyses containing linear and nonlinear analysis are further developed. By linear stability analysis, we obtain the model’s neutral stability curve. Moreover, the Burgers equation and modified Korteweg–de Vries equation are derived in nonlinear stability analysis section. The phase transition of traffic flow and its propagation behavior of congestion near the critical point are described. In addition, under the influence of disturbance, the spatiotemporal evolution characteristics of density wave and energy consumption are intuitively shown by numerical simulations. The results reveal that appropriate lane change behavior, predictive effect and self-delayed flux integral effect are conducive to improve traffic stability and reduce energy consumption.

Incorporating the traffic interruption probability effect during evolution process in two-lane lattice hydrodynamic model

By incorporating the interruption probability effect, this paper provides a novel lattice hydrodynamic model for two lanes. The two-lane stability is investigated from linear stable analysis, which implies that the interruption probability effect can extend the stable region in the two-lane system. Moreover, the density waves and the hysteresis loops shrink from simulation tests as the intensity of the interruption probability effect increases, which indicates that the interruption probability effect strengthens the two-lane stability. More importantly, the fuel consumption and emissions fall down clearly with the interruption probability effect increasing on two lanes according to simulation tests.

A New Two-Lane Lattice Model with the Consideration of the Driver’s Self-Anticipation Current Difference Effect

To prevent traffic congestion, drivers always adjust the driving behavior with their driving information. By considering the self-anticipation effect and the optimal current difference effect on traffic flow stability, a novel two-lane lattice hydrodynamic model is proposed. Compared with Peng’s model, the linear stability analysis results reveal that the self-anticipation term can effectively enlarge the stable region on the phase diagram. Then, a reductive perturbation method is used to derive the mKdV equation describing traffic congestion near the critical point. Nonlinear analyses show that the traffic congestions can be effectively suppressed by taking the coefficient of lane-changing behaviors γ and the anticipation time τ into account. These results further indicate that the driver’s self-anticipation current difference effect can efficiently alleviate traffic jams. Furthermore, the numerical simulations with periodic boundary conditions also confirm the effectiveness of theoretical results.

An Improved Lattice Hydrodynamic Model by considering the Effect of “Backward-Looking” and Anticipation Behavior

In order to prevent the occurrence of traffic accidents, drivers always focus on the running conditions of the preceding and rear vehicles to change their driving behavior. By taking into the “backward-looking” effect and the driver’s anticipation effect of flux difference consideration at the same time, a novel two-lane lattice hydrodynamic model is proposed to reveal driving characteristics. The corresponding stability conditions are derived through a linear stability analysis. Then, the nonlinear theory is also applied to derive the mKdV equation describing traffic congestion near the critical point. Linear and nonlinear analyses of the proposed model show that how the “backward-looking” effect and the driver’s anticipation behavior comprehensively affect the traffic flow stability. The results show that the positive constant γ , the driver’s anticipation time τ , and the sensitivity coefficient p play significant roles in the improvement of traffic flow stability and the alleviation of the traffic congestion. Furthermore, the effectiveness of linear stability analysis and nonlinear analysis results is demonstrated by numerical simulations.

A novel two-lane lattice hydrodynamic model on a gradient road considering heterogeneous traffic flow

In the actual traffic, there are not only cars, but also buses, trucks and other vehicles. These vehicles with different maximum speeds or security headway or both are interspersed irregularly to form a heterogeneous traffic flow. In addition, most of the maximum speed of modern cars is hardly affected by gradients due to the fact that the car engine and brakes are rarely operated at their max while the maximum speed of trucks is affected. Considering that the performance of various types of vehicles is multifarious and the vehicles sometimes drive on the road with slopes, a novel two-lane lattice hydrodynamic model on a gradient road considering heterogeneous traffic flow is proposed in this paper. In order to verify the rationality of the model, the linear stability analysis is carried out first, that is, the linear stability conditions are derived from the linear stability theory and the stability curve is drawn accordingly. The results of the above analysis prove that the three factors studied in this paper, namely, time lane change, slope and mixing of different types of vehicles, all have a significant influence on the stability of traffic flow. The modified Korteweg–de Vries (mKdV) equation is deduced by the nonlinear analysis method, which can describe the propagation characteristics of the traffic density waves near the critical point. Last but not least, the numerical simulation for new model is conducted and the numerical simulation results obtained are in good agreement with theoretical ones. In summary, increasing the lane changing rate or the slope on the uphill can improve the traffic flow stability. What is more, increasing the slope can lower the traffic flow stability on the downhill. Finally, in the heterogeneous traffic flow of different types of vehicles, the vehicles with larger security headway will make traffic flow difficult to stabilize, as do the vehicles with larger maximum speed.

A new two-lane lattice hydrodynamic model on a curved road accounting for the empirical lane-changing rate

Purpose The purpose of this paper is to explore how curved road and lane-changing rates affect the stability of traffic flow. Design/methodology/approach An extended two-lane lattice hydrodynamic model on a curved road accounting for the empirical lane-changing rate is presented. The linear analysis of the new model is discussed, the stability condition and the neutral stability condition are obtained. Also, the mKdV equation and its solution are proposed through nonlinear analysis, which discusses the stability of the extended model in the unstable region. Furthermore, the results of theoretical analysis are verified by numerical simulation. Findings The empirical lane-changing rate on a curved road is an important factor, which can alleviate traffic congestion. Research limitations/implications This paper does not take into account the factors such as slope, the drivers’ characters and so on in the actual traffic, 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/value The curved road and empirical lane-changing rate are researched simultaneously in a two-lane lattice hydrodynamic models in this paper. The improved model can better reflect the actual traffic, which can also provide a theoretical reference for the actual traffic governance.

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.

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.

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.

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.

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.

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 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.

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.

A two-lane lattice hydrodynamic model with heterogeneous lane changing rates

Capturing lane changing behavior is crucial when developing a traffic flow modeling and optimization algorithm. This paper presents a two-lane lattice hydrodynamic model with consideration of heterogeneous lane changing rates over space. We further derive its linear stability condition for this extended lattice model with heterogeneous lane changing rates. Numerical experiments are carried out to investigate the effect of different values and percentages of lane changing rates on the system stability. This study contributes to the modeling and analytical techniques involving use of inter-vehicle communications.

Stability analysis of two-lane lattice hydrodynamic model considering lane-changing and memorial effects

In this paper, a new lattice two-lane hydrodynamic model is proposed by considering the lane changing and the optimal current change with memory effect. The linear stability condition of the model is obtained through the linear stability analysis, which depends on both the lane-changing rate and the memory step. A modified Korteweg–de Vries (mKdV) equation is derived through nonlinear analysis to describe the propagating behavior of traffic density wave near the critical point. To verify the analytical findings, numerical simulation was carried out, which confirms that the optimal current change with memory of drivers and the memory step contribute to the stabilization of traffic flow, and that traffic congestion can be suppressed efficiently by taking the lane-changing behavior into account in the lattice model.