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.

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

A novel car-following model was proposed to describe the motion of the vehicles on a single lane gyroidal road. We explore the related effects of gyroidal road upon uniform traffic flow analytically and numerically. The analytical result shows that the related factors of gyroidal road including the friction coefficient, radius of curvature and slope have great influences on the stability of the uniform flow respectively. The modified KdV (Korteweg–de Vries) equation is derived in the unstable area and the kink solution is obtained near the critical point. A series of simulations are conducted to verify the effects upon uniform traffic flow under different road conditions. It is shown that the amplitudes of the headway oscillation wave were affected by the friction coefficient, radius of curvature and slope respectively. The numerical results are in good agreement with the analytical results.

A new car-following model considering the related factors of a gyroidal road

In this paper, we present a new lattice model which involves the effects of traffic interruption probability to describe the traffic flow on single lane freeways. The stability condition of the new model is obtained by the linear stability analysis and the modified Korteweg–de Vries (KdV) equation is derived through nonlinear analysis. Thus, the space will be divided into three regions: stable, metastable and unstable. The simulation results also show that the traffic interruption probability could stabilize traffic flow.

A new lattice model of traffic flow with the consideration of the traffic interruption probability

We investigate the slope effects upon traffic flow on a single lane gradient (uphill/downhill) highway analytically and numerically. The stability condition, neutral stability condition and instability condition are obtained by the use of linear stability theory. It is found that stability of traffic flow on the gradient varies with the slopes. The Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived to describe the triangular shock waves, soliton waves and kink–antikink waves in the stable, meta-stable and unstable region respectively. A series of simulations are carried out to reproduce the triangular shock waves, kink–antikink waves and soliton waves. Results show that amplitudes of the triangular shock waves and kink–antikink waves vary with the slopes, the soliton wave appears in an upward form when the average headway is less than the safety distance and a downward form when the average headway is more than the safety distance. Moreover both the kink–antikink waves and the solitary waves propagate backwards. The numerical simulation shows a good agreement with the analytical result.

Nonlinear analysis of traffic flow on a gradient highway

A speed feedback control mechanism was introduced into the system to improve the dynamical performance of the traffic flow. The modern control theory was used to analyze the stability of the system. It is found that the stability region varies with the feedback coefficient proportionally. In addition, the unit step responses in time domain and phase–frequency curves in frequency domain were given with different feedback coefficients in step response diagram and Bode diagram respectively. The overshoot and phase margins are inversely proportional to the speed feedback coefficients in an underdamped condition. The simulations were conducted to verify the validity of the improvement. The conclusion can be drawn that the analytical result and the simulation result are in good agreement with each other.

A speed feedback control strategy for car-following model

We use the car-following model (Phys. Rev. E 72 (2005) 066124) to further analyse the two-lane traffic waves. Our numerical results show that in the two-lane traffic, there exist triangular shock, soliton wave and kink wave which appear in the stable, mestastable and unstable regions of headway-sensitivity space, respectively. Compared with the single-lane traffic, it is found that the lateral distance has little effect on the formation of triangular shock and soliton wave although the lateral distance can enlarge the stable region and can reduce the mestastable and unstable regions.

https://iopscience.iop.org/article/10.1088/0256-307X/24/5/079/pdf

Analysis of Density Wave in Two-Lane Traffic

We use the model with the consideration of the traffic interruption probability (Physica A 387(2008)6845) to study the relationship between the traffic risk coefficient and the traffic interruption probability. The analytical and numerical results show that the traffic interruption probability will reduce the traffic risk coefficient and that the reduction is related to the density, which shows that this model can improve traffic security.

Xue Yu

Papers

Analysis of Density Wave in Two-Lane Traffic

Properties of Traffic Risk Coefficient

A new record species of hyalopsora in china