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.     

Analyses of a heterogeneous lattice hydrodynamic model with low and high-sensitivity vehicles

Basic lattice model is extended to study the heterogeneous traffic by considering the optimal current difference effect on a unidirectional single lane highway. Heterogeneous traffic consisting of low- and high-sensitivity vehicles is modeled and their impact on stability of mixed traffic flow has been examined through linear stability analysis. The stability of flow is investigated in five distinct regions of the neutral stability diagram corresponding to the amount of higher sensitivity vehicles present on road. In order to investigate the propagating behavior of density waves non linear analysis is performed and near the critical point, the kink antikink soliton is obtained by driving mKdV equation. The effect of fraction parameter corresponding to high sensitivity vehicles is investigated and the results indicates that the stability rise up due to the fraction parameter. The theoretical findings are verified via direct numerical simulation.     

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.     

Analyses of driver’s anticipation effect in sensing relative flux in a new lattice model for two-lane traffic system

In this paper, a new lattice hydrodynamic traffic flow model is proposed by considering the driver’s anticipation effect in sensing relative flux (DAESRF) for two-lane system. The effect of anticipation parameter on the stability of traffic flow is examined through linear stability analysis and shown that the anticipation term can significantly enlarge the stability region on the phase diagram. To describe the phase transition of traffic flow, mKdV equation near the critical point is derived through nonlinear analysis. The theoretical findings have been verified using numerical simulation which confirms that traffic jam can be suppressed efficiently by considering the anticipation effect in the new lattice model for two-lane traffic.     

A Backward-Looking Optimal Current Lattice Model

An optimal current lattice model with backward-looking effect is proposed to describe the motion of traffic flow on a single lane highway. The behavior of the new model is investigated analytically and numerically. The stability, neutral stability, and instability conditions of the uniform flow are obtained by the use of linear stability theory. The stability of the uniform flow is strengthened effectively by the introduction of the backward-looking effect. The numerical simulations are carried out to verify the validity of the new model. The outcomes of the simulation are corresponding to the linearly analytical results. The analytical and numerical results show that the performance of the new model is better than that of the previous models.     

Jamming transition of a two-dimensional traffic dynamics with consideration of optimal current difference

A modified two-dimensional lattice hydrodynamic traffic flow model is proposed by incorporating the optimal current difference effect of leading vehicles. Phase transitions and critical phenomenon are investigated near the critical point both analytically and numerically. Based on the configuration of vehicles, it is shown that two distinct jamming transitions occur: conventional jamming transition to the kink jam and jamming transition to the chaotic jam. It is shown that consideration of optimal current difference effect stabilizes the traffic flow and suppresses the traffic jam efficiently for all possible configurations of vehicles on a square lattice.     

Stochastic Description of Traffic Flow

We propose a traffic model based on microscopic stochastic dynamics. We built a Markov chain equipped with an Arrhenius interaction law. The resulting stochastic process is comprised of both spin-flip and spin-exchange dynamics which models vehicles exiting, entering and interacting in a two-dimensional lattice environment corresponding to a multi-lane highway. The process is further equipped with a novel look-ahead type, anisotropic interaction potential which allows drivers/vehicles to ascertain local fluctuations and advance to new cells forward or sideways. The resulting vehicular traffic model is simulated via kinetic Monte Carlo and examined under both, typical and extreme traffic flow scenarios. The model is shown to correctly predict both qualitative as well as quantitative traffic observables for any highway geometry. Furthermore it also captures interesting multi-scale phenomena in traffic flows after a simulated accident which lead to oscillatory, dissipating, traffic waves with different periods per lane.     

Effect of gravitational force upon traffic flow with gradients

We study the effect of gravitational force upon traffic flow on a highway with sag, uphill, and downhill. We extend the optimal velocity model to take into account the gravitational force which acts on vehicles as an external force. We study the traffic states and jamming transitions induced by the slope of highway. We derive the fundamental diagrams (flow-density diagrams) for the traffic flow on the sag, the uphill, and downhill by using the extended optimal velocity model. We clarify where and when traffic jams occur on a highway with gradients. We show the relationship between densities before and after the jam. We derive the dependence of the fundamental diagram on the slope of gradients.     

The stabilization effect of the density difference in the modified lattice hydrodynamic model of traffic flow

A modified lattice hydrodynamic model of traffic flow is proposed by introducing the density difference between the leading and the following lattice. The stability condition of the modified model is obtained through the linear stability analysis. The results show that considering the density difference leads to the stabilization of the system. The Burgers equation and mKdV equation are derived to describe the density waves in the stable and unstable regions respectively. Numerical simulations show that considering the density difference not only could stabilize traffic flow but also makes the lattice hydrodynamic model more realistic.     

A New Lattice Model of Two-Lane Traffic Flow with the Consideration of the Honk Effect

In this paper, a new lattice model of two-lane traffic flow with the honk effect term is proposed to study the influence of the honk effect on wide moving jams under lane changing. The linear stability condition on two-lane highway is obtained by applying the linear stability theory. The modified Korteweg-de Vries (KdV) equation near the critical point is derived and the coexisting curves resulted from the modified KdV equation can be described, which shows that the critical point, the coexisting curve and the neutral stability line decrease with increasing the honk effect coefficient. A wide moving jam can be conceivably described approximately in the unstable region. Numerical simulation is performed to verify the analytic results. The results show that the honk effect could suppress effectively the congested traffic patterns about wide moving jam propagation in lattice model of two-lane traffic flow.     

Multiple flux difference effect in the lattice hydrodynamic model

Considering the effect of multiple flux difference, an extended lattice model is proposed to improve the stability of traffic flow. The stability condition of the new model is obtained by using linear stability theory. The theoretical analysis result shows that considering the flux difference effect ahead can stabilize traffic flow. The nonlinear analysis is also conducted by using a reductive perturbation method. The modified KdV (mKdV) equation near the critical point is derived and the kink-antikink solution is obtained from the mKdV equation. Numerical simulation results show that the multiple flux difference effect can suppress the traffic jam considerably, which is in line with the analytical result.     

A new lattice model of traffic flow with the anticipation effect of potential lane changing

A new lattice model of traffic flow is presented by taking into account the anticipation of potential lane changing on front site on single lane. The stability condition of the extended model is obtained by using the linear stability theory. The modified KdV equation near the critical point is constructed and solved through nonlinear analysis. And the phase space of traffic flow in the density-sensitivity space could be divided into three regions: stable, metastable and unstable ones, respectively. Numerical simulation also shows that the consideration of lane changing probability in lattice model can stabilize traffic flow, which implies that the new consideration has an important effect on traffic flow in lattice models.     

Phase transition on speed limit traffic with slope

Through introducing a generalized optimal speed function to consider spatial position, slope grade and variable safe headway, the effect of slope in a single-lane highway on the traffic flow is investigated with the extended optimal speed model. The theoretical analysis and simulation results show that the flux of the whole road with the upgrade （or downgrade） increases linearly with density, saturates at a critical density, then maintains this saturated value in a certain density range and finally decreases with density. The value of saturated flux is equal to the maximum flux of the upgrade （or downgrade） without considering the slight influence of the driver＇s sensitivity. And the fundamental diagrams also depend on sensitivity, slope grade and slope length. The spatiotemporal pattern gives the segregation of different traffic phases caused by the rarefaction wave and the shock wave under a certain initial vehicle number. A comparison between the upgrade and the downgrade indicates that the value of saturated flux of the downgrade is larger than that of the upgrade under the same condition. This result is in accordance with the real traffic.     

Flow difference effect in the lattice hydrodynamic model

In this paper, a new lattice hydrodynamic model based on Nagatani's model [Nagatani T 1998 Physica A 261 599] is presented by introducing the flow difference effect. The stability condition for the new model is obtained by using the linear stability theory. The result shows that considering the flow difference effect leads to stabilization of the system compared with the original lattice hydrodynamic model. The jamming transitions among the freely moving phase, the coexisting phase, and the uniform congested phase are studied by nonlinear analysis. The modified KdV equation near the critical point is derived to describe the traffic jam, and kink--antikink soliton solutions related to the traffic density waves are obtained. The simulation results are consistent with the theoretical analysis for the new model.     

Dynamic characteristics and simulation of traffic flow with slope

This paper proposes a new traffic model to describe traffic flow with slope under consideration of the gravity effect. Based on the model, stability analysis is conducted and a numerical simulation is performed to explore the characteristics of the traffic flow with slope. The result shows that the perturbation of the system is an inherent one, which is induced by the slope. In addition, the hysteresis loop is represented through plotting the figure of velocity against headway and highly depends on the slope angle. The kinematic wave at high density is also obtained through reproducing the phenomenon of stop-and-go traffic, which is significant to explore the phase transition of traffic flow and the evolution of traffic congestion.     

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.     

New Feedback Control Model in the Lattice Hydrodynamic Model Considering the Historic Optimal Velocity Difference Effect

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.     

A new control method based on the lattice hydrodynamic model considering the double flux difference

A new feedback control method is derived based on the lattice hydrodynamic model in a single lane. A signal based on the double flux difference is designed in the lattice hydrodynamic model to suppress the traffic jam. The stability of the model is analyzed by using the new control method. The advantage of the new model with and without the effect of double flux difference is explored by the numerical simulation. The numerical simulations demonstrate that the traffic jam can be alleviated by the control signal.     

The stability analysis of the full velocity and acceleration velocity model

The stability analysis is one of the important problems in the traffic flow theory, since the congestion phenomena can be regarded as the instability and the phase transition of a dynamical system. Theoretically, we analyze the stable conditions of the full velocity and acceleration difference model (FVADM), which is proposed by introducing the acceleration difference term based on the previous car-following models (the optimal velocity model and the full velocity difference model, OVM and FVDM). By numerical simulations, it is found that when the traffic flow is unstable, the traffic jam in the FVADM is weaker than that in the FVDM. Also it is observed that the spreading speed of the jam is slower in the FVADM than that in the FVDM and the fluctuations of vehicles in the FVADM are smaller than those in the FVDM. Therefore, the acceleration difference term has strong effects on traffic dynamics and plays an important role in stabilizing the traffic flow.     

Optimal velocity difference model for a car-following theory

In this Letter, we present a new optimal velocity difference model for a car-following theory based on the full velocity difference model. The linear stability condition of the new model is obtained by using the linear stability theory. The unrealistically high deceleration does not appear in OVDM. Numerical simulation of traffic dynamics shows that the new model can avoid the disadvantage of negative velocity occurred at small sensitivity coefficient λ in full velocity difference model by adjusting the coefficient of the optimal velocity difference, which shows that collision can disappear in the improved model.