An extended macroscopic model for traffic flow on curved road and its numerical simulation

Nonlinear Dynamics - In this paper, we propose a full angular velocity difference model by introducing the angular velocity and displacement on curved road. The relation of transformation of...     

Tunnel effects on ring road traffic flow based on an urgent-gentle class traffic model

To explore tunnel effects on ring road traffic flow, a macroscopic urgent-gentle class traffic model is put forward. The model identifies vehicles with urgent and gentle classes, chooses the tunnel speed limit as free flow speed to express the fundamental diagram in the tunnel, and adopts algebraic expressions to describe traffic pressure and sound speed. With two speed trajectories at the Kobotoke tunnel in Japan,the model is validated, with good agreement with observed data. Numerical results indicate that in the case of having no ramp effects, tunnel mean travel time is almost constant dependent on tunnel length.When initial density normalized by jam density is above a threshold of about 0.21, a traffic shock wave originates at the tunnel entrance and propagates backward. Such a threshold drops slightly as a result of on-ramp merging effect, the mean travel time drops as off-ramp diversion effect intensifies gradually.These findings deepen the understanding of tunnel effects on traffic flow in reality.     

Phase transitions in the two-lane density difference lattice hydrodynamic model of traffic flow

In this paper, we derive the KdV equation from the two-lane lattice hydrodynamic traffic model considering density difference effect. The soliton solution is obtained from the KdV equation. Under periodical boundary, the KdV soliton of traffic flow is demonstrated by numerical simulation. The numerical simulation result is consistent with the nonlinear analytical result. Under open system, the density fluctuation of the downstream last one lattice is designed to explore the empirical congested traffic states. A phase diagram is presented which includes free traffic, moving localized cluster, triggered stop-and-go traffic, oscillating congested traffic, and homogeneous congested traffic. Finally, the spatiotemporal evolution of all the traffic states described in phase diagram are reproduced. Results suggest that the two-lane density difference hydrodynamic traffic model is suitable to describe the actual traffic.     

A new lattice hydrodynamic model for two-lane traffic with the consideration of density difference effect

A new lattice hydrodynamic model for two-lane traffic flow is proposed by introducing the density difference effect (DDE). Using linear stability theory, stability condition of the presented model is obtained. Jamming transitions among the freely moving phase, the coexisting phase, and the uniform congested phase are investigated by employing nonlinear analysis. The modified KdV (mKdV) equation near the critical point is derived and the kink-antikink soliton solutions are obtained. Numerical simulations are presented to verify analytical results, showing that DDE can improve the stability of traffic flow effectively.     

Coevolution dynamics model of road surface and urban traffic structure

In this paper, a new dynamics model based on the logistic equation is proposed to capture the dynamic characteristics in the coevolution process between road surface and urban traffic structure. The stability analysis shows that ignoring the coevolution relation will lead to the disequilibrium development and cause the chaotic state of the urban transportation system eventually. To avoid the unsteadily development, a chaos control method is established. Results indicate that the suggested control model is effective in the coevolution management and control.     

KINEMATIC WAVE PROPERTIES OF ANISOTROPIC DYNAMICS MODEL FOR TRAFFIC FLOW

ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙｔｈｅａｕｔｈｏｒｓｐｒｅｓｅｎｔｅｄａｎｅｗｄｙｎａｍｉｃｓｍｏｄｅｌｆｏｒｔｒａｆｆｉｃｆｌｏｗ[1].Ｔｈｅｍｏｄｅｌｃｏｍｐｒｉｓｅｓａｃｏｎｔｉｎｕｕｍｅｑｕａｔｉｏｎａｎｄａｄｙｎａｍｉｃｓｅｑｕａｔｉｏｎ ｋ/ ｔ+ (ｋｕ) / ｘ=0 ,( 1 ) ｕ ｔ+ｕ ｕ ｘ=ｕｅ(ｋ) -ｕＴ +ａ ｕ ｘ,( 2 )ｗｈｅｒｅｋｉｓｔｒａｆｆｉｃｄｅｎｓｉｔｙ ;ｕｉｓｍｅａｎｓｐｅｅｄ ;ｘ ,ｔａｒｅｓｐａｃｅａｎｄｔｉｍｅｃｏｏｒｄｉｎａｔｅｓｒｅｓｐｅｃｔｉｖｅｌｙ .Ｔｉｓｒｅｌ…     

Solitary wave solutions to higher-order traffic flow model with large diffusion

This paper uses the Taylor expansion to seek an approximate Korteweg- de Vries equation （KdV） solution to a higher-order traffic flow model with sufficiently large diffusion. It demonstrates the validity of the approximate KdV solution considering all the related parameters to ensure the physical boundedness and the stability of the solution. Moreover, when the viscosity coefficient depends on the density and velocity of the flow, the wave speed of the KdV solution is naturally related to either the first or the second characteristic field. The finite element method is extended to solve the model and examine the stability and accuracy of the approximate KdV solution.     

A continuum traffic flow model with the consideration of coupling effect for two-lane freeways

A new higher-order continuum model is proposed by considering the coupling and lane changing effects of the vehicles on two adjacent lanes. A stability analysis of the proposed model provides the conditions that ensure its linear stability. Issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are also investigated with numerical experiments. The simulation results show that the proposed model is capable of providing explanations to some particular traffic phenomena commonly observable in real traffic flows.     

Phase-plane analysis of conserved higher-order traffic flow model

The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system. The analysis identifies the types and stabilities of the equilibrium solutions, and the overall distribution structure of the nearby solutions is drawn in the phase plane for the further analysis and comparison. The analytical and numerical results are in agreement, and may help to explain the simulated phenomena, such as the stop-and-go wave and oscillation near a bottleneck. The findings demonstrate the model ability to describe the complexity of congested traffic.     

An extended continuum model incorporating the electronic throttle dynamics for traffic flow

This study develops a novel continuum model with consideration of the effect of electronic throttle (ET) dynamics to capture the behaviour of vehicles in traffic flow. In particular, the continuum model is proposed by incorporating the opening angle of ET based on the throttle-based full velocity difference model. Theoretical analyses including stability, negative velocity and shock wave are performed systematically. Numerical experiments and comparisons are conducted to verify the performance of the proposed continuum model. Results show that the steady-state performance of the proposed model is improved with respect to the stability. In addition, the proposed model is effective to rapidly dissipate the effect of external perturbation. Also, the phenomenon of negative velocity can be avoided by the proposed model.