Lattice Model Of Traffic Flow Research Articles

Stability Analysis of the New Traffic Flow Lattice Model considering Taillight Effect and Speed Deviation

A new macroscopic traffic flow lattice model is established which considered the taillight effect and velocity deviation. By combining the concept of critical density, the critical condition of taillight triggering is established. The situation of taillight appearing is fully considered, and the influence of taillight effect is analyzed. Through the stability analysis of the model, the stability conditions of the model are obtained. By nonlinear analysis, the mKdV equation is derived which can describe the evolution mechanism of the density wave. From the phase diagram, we can find that the two factors have a positive impact on the stability of traffic flow. Finally, spatiotemporal evolution of the density wave and cross-section view of the density wave are obtained by numerical simulation to verify the theoretical derivation of this paper. The simulation results show that the stability of traffic flow can be improved by considering taillight effect and speed deviation. In addition, by comparing the time-space evolution maps of different parameter values, it can be found that the stability of traffic flow considering the taillight effect and speed deviation is better than that considering one factor alone. However, the stability of traffic flow will be negatively affected by low speed estimate and high critical density.

A modified lattice model of traffic flow with the consideration of the downstream traffic condition

Traffic congestion has attracted considerable attention in modern society. Many researchers have proposed tremendous traffic flow models. These models can be divided into microscopic model, mesoscopic model and macroscopic model. With the progress of technology, it is possible to get the information of the preceding vehicles, i.e. the downstream traffic condition. Drivers can adjust their driving behaviors according to the downstream condition. This mechanism has been considered in microscopic model, and it is found that this mechanism can not only stabilize the traffic, but also bring about some new phenomena, such as synchronized traffic pattern. In the macroscopic model, what will the traffic flow be after considering the mechanism? In this paper, a term describing the downstream traffic condition is added in Nagatani’s single-lane lattice model. Through theoretical study and numerical simulation, it can be found that traffic is more stable when the downstream traffic condition is considered. Besides, the modified model can reproduce the soliton wave, kink wave properly. Moreover, the amplitude and frequency of density wave with different influence forms of the front lattices on the current lattice are almost the same as found to reflect the different influence forms do not have significant effect on the stability.

A new lattice model of traffic flow considering driver’s anticipation effect of the traffic interruption probability

In this paper, a new lattice model is proposed by considering the driver’s anticipation effect of traffic interruption probability. The stability condition of the extended model is obtained by the linear stability analysis, which shows that the driver’s anticipation effect of traffic interruption probability can enlarge the stable area of traffic flow. The kink–antikink soliton solution of the modified Korteweg–de Vries (KdV) equation is derived from nonlinear analysis, which can describe the coexisting phase. The simulation results also show that driver’s anticipation effect of the traffic interruption probability could stabilize traffic flow.

A new lattice model of traffic flow with the consideration of the drivers’ aggressive characteristics

Abstract In real traffic, aggressive driving behaviors often occurs by anticipating the front density of the next-nearest lattice site at next time step to adjust their acceleration in advance. Therefore, a new lattice model is put forward by considering the driver’s aggressive effect (DAE). The linear stability condition is derived from the linear stability theory and the modified KdV equation near the critical point is obtained through nonlinear analysis with the consideration of aggressive driving behaviors, respectively. Both the analytical results and numerical simulation indicate that the driver’s aggressive effect can increase the traffic stability. Thus driver’s aggressive effect should be considered in traffic lattice model.

Effect of optimal estimation of flux difference information on the lattice traffic flow model

Abstract In this paper, a new lattice model is proposed by considering the optimal estimation of flux difference information. The effect of this new consideration upon the stability of traffic flow is examined through linear stability analysis. Furthermore, a modified Korteweg–de Vries (mKdV) equation near the critical point is constructed and solved by means of nonlinear analysis method, and thus the propagation behavior of traffic jam can be described by the kink–antikink soliton solution of the mKdV equation. Numerical simulation is carried out under periodical condition with results in good agreement with theoretical analysis, therefore, it is verified that the new consideration can enhance the stability of traffic systems and suppress the emergence of traffic jams effectively.

A novel lattice traffic flow model on a curved road

Due to the existence of curved roads in real traffic situation, a novel lattice traffic flow model on a curved road is proposed by taking the effect of friction coefficient and radius into account. The stability condition is obtained by using linear stability theory. The result shows that the traffic flow becomes stable with the decrease of friction coefficient and radius of the curved road. Using nonlinear analysis method, the Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equation are derived to describe soliton waves and the kink–antikink waves in the meta-stable region and unstable region, respectively. Numerical simulations are carried out and the results are consistent with the theoretical results.

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.

Effects of the lattice point drivers’ heterogeneity of the disturbance risk preference on traffic flow instability

This paper defines the lattice point drivers’ heterogeneity of the disturbance risk preference and proposes a new one-dimensional traffic flow lattice model to research the effects of the lattice point drivers’ heterogeneity of the disturbance risk preference on traffic flow instability. By the analytical analysis, we obtain the traffic flow instability condition and the modified Korteweg–de Vries (mKdV) equation and the calculation formula of the unstable area density range, and the calculation method of the probability of traffic congestion caused by a small disturbance. Both the analytical and the simulation analysis show that there are important effects of the lattice point drivers’ heterogeneity of the disturbance risk preference on traffic flow instability, namely the smaller the ratio of the preceding lattice point drivers’ coefficient of the disturbance risk preference to the following lattice point drivers’ coefficient of the disturbance risk preference is, the smaller the traffic flow instability is and vice versa. It provides a viable idea to ease traffic congestion.

Jamming transitions and the effect of interruption probability in a lattice traffic flow model with passing

A new lattice hydrodynamic model is proposed by considering the interruption probability effect on traffic flow with passing and analyzed both theoretically and numerically. From linear and non-linear stability analysis, the effect of interruption probability on the phase diagram is investigated and the condition of existence for kink–antikink soliton solution of mKdV equation is derived. The stable region is enhanced with interruption probability and the jamming transition occurs from uniform flow to kink flow through chaotic flow for higher and intermediate values of non-interruption effect of passing. It is also observed that there exists conventional jamming transition between uniform flow and kink flow for lower values of non-interruption effect of passing. Numerical simulations are carried out and found in accordance with the theoretical findings which confirm that the effect of interruption probability plays an important role in stabilizing traffic flow when passing is allowed.

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.

Multiple optimal current difference effect in the lattice traffic flow model

Kerner and Konhäuser study moving jam dynamics first discovered in 1993 in Ref. 1. In light of their previous work, a new lattice hydrodynamic model is presented with consideration of the effect of multiple optimal current difference. To investigate the influences of new consideration on traffic jams, the linear stability analysis of the new model is conducted by employing the linear stability theory. Theoretical analysis result shows that the new consideration can stabilize traffic flow. By means of nonlinear analysis method, a modified Korteweg–deVries (mKdV) equation near the critical point is constructed and solved. The propagation behavior of traffic jam can thus be described by the kink–antikink soliton solution for the mKdV equation. Numerical simulation result shows that the effect of the multiple optimal current differences can suppress the emergence of traffic jams and the result is in good agreement with the analytical results.

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.

Nonlinear Analysis of a New Extended Lattice Model With Consideration of Multi-Anticipation and Driver Reaction Delays

A new extended lattice model of traffic flow is presented by taking into account both multianticipative behavior and the reaction-time delay of drivers. The linear stability theory and the nonlinear analysis method are applied to the model. The linear stability condition is obtained. The Korteweg–de Vries (KdV) equation near the neutral stability line and the modified Korteweg–de Vries (mKdV) equation near the critical point are derived. The numerical results show that the stability of traffic flow will be enhanced by multianticipative consideration and will be weakened with the increase of the reaction-time delay. The unfavorable effect induced by driver reaction delays can be partly compensated by considering multianticipative behavior.

Modeling and Simulation of a Traffic Flow Model Considering the Influence of Traffic Interruption

In this paper, we present a new lattice model of traffic flow by considering the effects of traffic interruption probability. The stability condition of the proposed model is obtained by employing the linear stability theory. The results show that the stability of traffic flow is improved by considering the influence of traffic interruption. Applying the method of nonlinear analysis, the modified Korteweg-de Vries (mKdV) equation is derived to describe the traffic behavior near the critical point. The kink- antikink soliton and the solution of the mKdV equation are obtained to describe the traffic jams. The good agreement between theoretical analysis and numerical simulation indicates that our new consideration can stabilize the traffic flow effectively.

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.

A new lattice model of traffic flow with the consideration of individual difference of anticipation driving behavior

In this paper, we propose a new lattice model of traffic flow with the consideration of individual difference of anticipation driving behavior. The linear stability condition and the mKdV equation are derived from linear stability analysis and nonlinear analysis, respectively. Furthermore, numerical simulation shows that the anticipation driving behavior can increase the cell number of low density, which means that more cars can run freely and traffic congestion can be suppressed efficiently by taking the anticipation driving behavior into account in lattice model. Moreover, with the coefficient of the anticipation driving behavior increasing, the low density region turns wide corresponding to individual difference of anticipation driving behavior.

A new lattice model of two-lane traffic flow with the consideration of optimal current difference

In this paper, a new lattice model of traffic flow is proposed with the consideration of the optimal current difference for two-lane system. The linear stability condition is derived through linear stability analysis, which shows that the optimal current difference term can improve the stability of traffic flow. The mKdV equation is obtained through nonlinear analysis. Thus the space of traffic flow is divided into three regions: the stable region, the metastable region and the unstable region respectively. Moreover, numerical simulation confirms that the traffic jam can be suppressed efficiently by considering the optimal current difference effect in extended lattice model of two-lane traffic flow.

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.

Multiple Lattices Model of Traffic Flow with Relative Current

A new lattice model of traffic flow is proposed by considering the information of front multiple sites with relative current. The linear stability condition is obtained by using the linear stability theory. Numerical simulation shows that the proposed model is consistent with the theoretical analysis.

The Modeling and Simulation of a New Cooperative Driving Lattice Model of Traffic Flow with the consideration of Forecasting Effect

The Modeling and Simulation of a New Cooperative Driving Lattice Model of Traffic Flow with the consideration of Forecasting Effect