Two-lane Lattice Model Research Articles

A Novel Two-Lane Lattice Model Considering the Synergistic Effects of Drivers’ Smooth Driving and Aggressive Lane-Changing Behaviors

Most existing two-lane traffic flow lattice models fail to fully consider the interactions between drivers’ aggressive lane-changing behaviors and their desire for smooth driving, as well as their combined effects on traffic dynamics. To fill this research gap, under symmetric lane-changing rules, this paper proposes a novel two-lane lattice model that incorporates these two factors as co-influencers. Based on linear and nonlinear stability analyses, we derive the linear stability conditions of the new model, along with the density wave equation and its solutions describing traffic congestion propagation near critical points. Numerical simulations validate the theoretical findings. The results indicate that in the two-lane framework, enhancing either drivers’ lane-changing aggressiveness or introducing the desire for smooth driving alone can somewhat improve traffic flow stability. However, when considering their synergistic effects, traffic flow stability is enhanced more significantly, and the traffic congestion is suppressed more effectively.

Speed limit effect during lane change in a two-lane lattice model under V2X environment

Speed limit measures are ubiquitous due to the complexity of the road environment, which can be supplied with the help of vehicle to everything (V2X) communication technology. Therefore, the influence of speed limit on traffic system will be investigated to construct a two-lane lattice model accounting for the speed limit effect during the lane change process under V2X environment. Accordingly, the stability condition and the mKdV equation are closely associated with the speed limit effect through theory analysis. Moreover, the evolution of density and hysteresis loop is simulated to demonstrate the positive role of the speed limit effect on traffic stability in the cases of strong reaction intensity and high limited speed.

Jamming transition in two-lane lattice model integrating the deception attacks on influx during the lane-changing process under vehicle to everything environment

In the information area of actual traffic, the deception attack can affect the lane-changing rate of influx during the lane-changing process on two lanes operating in a vehicle to everything environment. To counteract the deception attack, a novel lattice model integrating the driver anticipation effect (DAE) will be constructed based on the lane-changing influx rate caused by the deception attack on two lanes. The influence of the lane-changing rate of deceitful influx on traffic stability is investigated through theoretical analysis, and the corresponding modified Korteweg De Vries equation is derived. Using numerical simulation, the evolution of density waves and hysteresis loop phenomena caused by the lane-changing rate of deceitful influx are studied. Due to the rate at which deceitful influx changes lanes, the deception attack on influx will also have a significant impact on the energy consumption of the transportation system.

The influence of the optimal velocity deviation on the traffic evolution process under lane change in two-lane lattice model

In a real traffic environment, there is always a certain deviation between the real traffic information and the expected traffic information, which definitely has an important impact on traffic flow. Consequently, the optimal velocity deviation effect (OVDE) is taken into account to build a novel lattice model on two lanes. Moreover, the influence of OVDE on the linear stable condition is investigated, which shows that the OVDE plays a positive stable effect in two-lane traffic flow. Also, the OVDE can relieve more traffic congestion on two lanes via numerical simulations concerning the density and the hysteresis loop.

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.

A two-lane lattice model considering taillight effect and man–machine hybrid driving

At present, drivers can rely on road communication technology to obtain the current traffic status information, and the development of intelligent transportation makes self-driving possible. In this paper, considering the mixed traffic flow with self-driving vehicles and the taillight effect, a new macro-two-lane lattice model is established. Combined with the concept of critical density, the judgment conditions for vehicles to take braking measures are given. Based on the linear analysis, the stability conditions of the new model are obtained, and the mKdV equation describing the evolution mechanism of density waves is derived through the nonlinear stability analysis. Finally, with the help of numerical simulation, the phase diagram and kink–anti-kink waveform of neutral stability conditions are obtained, and the effects of different parameters of the model on traffic flow stability are analyzed. The results show that the braking probability, the proportion of self-driving vehicles and the critical density have significant effects on the traffic flow stability. Considering taillight effect and increasing the mixing ratio of self-driving vehicles can effectively enhance the stability of traffic flow, but a larger critical density will destroy the stability of traffic flow.

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 model by considering predictive effect in traffic flow

In this paper, a new hydrodynamic lattice model is proposed by considering the predictive effect in traffic flow and the optimal current difference effect (OCDE) on two-lane unidirectional traffic system. The model is further analyzed theoretically by the means of stability analysis. The influence of the predictive effect with the consideration of OCDE is analyzed on traffic stream stability through linear stability analysis in a two-lane system when lane changing is allowed. The mKdV equation is derived by using nonlinear stability analysis and the density wave in terms of the kink–antikink wave is obtained around the critical point. It is observed that the predictive effect plays an important role to enhance the stability of traffic flow in a two-lane system. Numerical simulation verifies the theoretical predictions which confirms that the traffic jam can be suppressed more effectively by taking predictive effect in a traffic system when lane changing is permitted.

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.

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

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 uncovered from the linear stability condition, which reveals that SAD effect in two-lane system stabilizes traffic flow. Moreover, numerical simulation verifies that SAD effect can increase the traffic stability and depress the traffic jam efficiently in new two-lane lattice model.

A new lattice model accounting for multiple optimal current differences’ anticipation effect in two-lane system

This paper extends a two-lane lattice hydrodynamic traffic flow model to take into account the driver’s anticipation effect in sensing the multiple optimal current differences. Based on the proposed model, we derive analytically the effect of driver’s anticipation of multiple optimal current differences on the instability of traffic dynamics. The phase diagrams have been plotted and discussed that the stability region enhances with anticipation effect in sensing multiple optimal current differences. Through simulation, it is found that the oscillation of density wave around critical density decreases with an increase in lattice number and anticipation time for transient and steady state. The simulation results are in good agreement with the theoretical analysis, which show that considering the driver’s anticipation of multiple optimal current differences in two-lane lattice model stabilizes the traffic flow and suppresses the traffic jam efficiently.

Analysis of a novel two-lane lattice model on a gradient road with the consideration of relative current

In this paper, a novel hydrodynamic lattice model is proposed by considering of relative current for two-lane gradient road system. The stability condition is obtained by using linear stability theory and shown that the stability of traffic flow varies with three parameters, that is, the slope, the sensitivity of response to the relative current and the rate of lane changing. The stable region increases with the increasing of one of them when another two parameters are constant. By using nonlinear analysis, the Burgers, Korteweg–de Vries, and modified Korteweg–de Vries equations are derived to describe the phase transition of traffic flow. Their solutions present the density wave as the triangular shock wave, soliton wave, and kink–antikink wave in the stable, metastable, and unstable region, respectively, which can explain the phase transitions from free traffic to stop-and-go traffic, and finally to congested traffic. To verify the theoretical results, a series of numerical simulations are carried out. The numerical results are consistent with the analytical results. To check the novel model, calibration are taken based on the empirical traffic flow data. The theoretical results and numerical results show that the traffic flow on the gradient road becomes more stable and the traffic congestion can be efficiently suppressed by considering the relative current and lane changing, and the empirical analysis shows that the novel lattice model is reasonable.

Analysis of a new two-lane lattice hydrodynamic model with consideration of the global average flux

A new two-lane traffic lattice hydrodynamic model is proposed with the consideration of the global average-and-optimal flux difference effect based on the local relative flux two-lane lattice model. First, the influence of the global average-and-optimal flux difference on the stability of traffic flow is investigated through linear stability theory. The results reveal that the unstable region will be shrunk by taking the global average-and-optimal flux difference effect into account. Additionally, by using the reductive perturbation method, the mKdV equation near the critical point is derived and traffic jam transition can be described by its kink–antikink soliton solution. The good agreement between the numerical simulations and the analytical results shows that traffic congestion can be suppressed efficiently by considering the global average-and-optimal flux difference and the local relative flux effects in two-lane traffic system and the local relative flux is more important than the global average-and-optimal flux difference in stabilizing traffic flow.

Effect of driver’s anticipation in a new two-lane lattice model with the consideration of optimal current difference

In this paper, a new lattice hydrodynamic traffic flow model is proposed by considering the driver’s anticipation effect (DAE) in sensing optimal current difference (OCD) for two-lane system. The effect of anticipation parameter on the stability of traffic flow is examined through linear stability analysis and shown that it can significantly enlarge the stability region on the phase diagram. Nonlinear analysis is conducted, and mKdV equation is derived to describe propagation behavior of a density wave near the critical point. The driver’s physical delay in sensing optimal current difference effect is also investigated and found that it has different effect on two-lane traffic based on whether lane changing is allowed or not. Simulation results are found in good agreement with the theoretical findings, which confirms that traffic jam can be suppressed efficiently by considering the DAEOCD effect in a two-lane traffic system.

Analysis of average density difference effect in a new two-lane lattice model

A new lattice model is proposed by taking the average density difference effect into account for two-lane traffic system according to Transportation Cyber-physical Systems. The influence of average density difference effect on the stability of traffic flow is investigated through linear stability theory and nonlinear reductive perturbation method. The linear analysis results reveal that the unstable region would be reduced by considering the average density difference effect. The nonlinear kink–antikink soliton solution derived from the mKdV equation is analyzed to describe the properties of traffic jamming transition near the critical point. Numerical simulations confirm the analytical results showing that traffic jam can be suppressed efficiently by considering the average density difference effect for two-lane traffic system.

An extended lattice model for two-lane traffic flow with consideration of the slope effect

An extended two-lane lattice model of traffic flow with consideration of the slope effect is proposed. The slope effect is reflected in both the maximal velocity and the relative current. The stability condition of the model is derived by applying the linear stability method. By using the nonlinear analysis method, we obtain the Korteweg–de Vries (KdV) equation near the neutral stability line and the modified Korteweg–de Vries (mKdV) equation near the critical point. The analytical and numerical results demonstrate that the stability of traffic flow is enhanced on the uphill but is weakened on the downhill when the slope angle increases.

Study on the effects of driver’s lane-changing aggressiveness on traffic stability from an extended two-lane lattice model

In this paper, the effects of driver’s lane-changing aggressiveness on the stability of traffic flow of two-lane are studied by using a generalized lattice hydrodynamic model with consideration of lane-changing aggressiveness of each individual. The effect of lane-changing aggressiveness parameter on traffic stability is derived through employing linear stability analysis with finding that the driver’s lane-changing aggressiveness has an important impact on the stability of the traffic flow in a two-lane system. To describe the phase transition, the mKdV equation near the critical point is derived by using the reductive perturbation method, with obtaining the dependence of the propagation kink solution for traffic jams on the lane-changing aggressiveness. It can be concluded from the phase diagram of stability criterion that the higher lane-changing aggressiveness leads to a more stable traffic flow. In addition, the stabilizing effect of the optimal current difference weakens gradually with the increasing of the lane-changing aggressiveness adjusting coefficient, even vanishes when the value of lane-changing aggressiveness adjusting coefficient is greater than a critical value. Theoretical conclusions are also confirmed by the numerical simulations.

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.

Analysis of a modified two-lane lattice model by considering the density difference effect

In this paper, a modified lattice hydrodynamic model of traffic flow is proposed by considering the density difference between leading and following lattice for two-lane system. The effect of density difference on the stability of traffic flow is examined through linear stability analysis and shown that the density difference term can significantly enlarge the stability region on the phase diagram. To describe the phase transition of traffic flow, the Burgers equation and mKdV equation near the critical point are derived through nonlinear analysis. To verify the theoretical findings, numerical simulation is conducted which confirms that traffic jam can be suppressed efficiently by considering the density difference effect in the modified lattice model for two-lane traffic.

A NEW LATTICE MODEL OF TWO-LANE TRAFFIC FLOW WITH THE CONSIDERATION OF MULTI-ANTICIPATION EFFECT

In this paper, a new two-lane lattice model of traffic flow is proposed with the consideration of multi-anticipation effect. The linear stability condition of two-lane traffic is derived with the multi-anticipation effect term by linear stability analysis, which shows that the stable region enlarges with the number of multi-anticipation sites increasing. Nonlinear analysis near the critical point is carried out to obtain kink–antikink soliton solution of the mKdV equation with the multi-anticipation effect term. Numerical simulation also shows that the multi-anticipation effect can suppress the traffic jam efficiently with lane changing in two-lane system.