Lattice Hydrodynamic Traffic Model Research Articles

Psychological Driver Sensitivity in Lattice Hydrodynamic Traffic Model under Passing Behaviour

Objectives: In order to control and manage the traffic flow in contexts of congestion, real-time highway traffic flow models play a significant role in intelligent transportation system. The objective of our investigation is to examine the effect of psychological driver sensitivity (PDS) when coupled with passing behaviour. Methods: In this study, we developed the lattice hydrodynamic (LH) model which is a good and simple representation for solving traffic problems. Its variants have been valuable tools in traffic research and also contributed to our understanding of traffic phenomena and the development of traffic management strategies. The effect of the proposed LH model with the factor PDS and passing is examined through linear stability analysis. Employing nonlinear stability analysis, we are able to establish the permissible range of PDS values in conjunction with a passing constant, ensuring the existence of kink soliton solution for the mKdV equation. Findings: To validate our theoretical findings, we conducted numerical simulation, conclusively demonstrating that the integration of PDS with passing in the proposed model, can efficiently mitigate traffic congestion. When we fix the passing coefficient and vary the PDS coefficient, we identify the enlargement of stable region with small PDS values. Similarly, by fixing the PDS coefficient varying passing coefficient reveals the enlargement of stable region with small passing values. Novelty: Results displayed that the stability performance of the proposed model is higher than the existing LH model with passing and found that our proposed model performs better than existing models to alleviate traffic congestion and improve traffic flow. Keywords: Traffic flow, Lattice hydrodynamic model (LHM), Psychological driver sensitivity (PDS), Passing effect, Stability

Study on Energy Dissipation and Fuel Consumption in Lattice Hydrodynamic Model under Traffic Control

A lattice hydrodynamic traffic model considering the average optimal flow of multiple grids downstream as a feedback control is proposed. The energy dissipation and fuel consumption are investigated under the feedback control based on the lattice hydrodynamic traffic model. Through linear stability analysis, the stability condition of the model is obtained. The mKdV equation and its kink-antikink density wave solution are derived by using the reduced perturbation method of nonlinear analysis. The variation trends of density wave, energy dissipation, and fuel consumption under traffic control are studied by numerical simulations. The research shows that exerting the feedback control can effectively suppress traffic congestion and improve the stability of traffic system. Meanwhile, it can also reduce the energy dissipation and fuel consumption of traffic system.

Stability analysis of multiple-lattice self-anticipative density integration effect based on lattice hydrodynamic model in V2V environment* *Project sponsored by the Natural Science Foundation of Chongqing, China (Grant No. cstc2019jcyj-msxmX0265).

Under the environment of vehicle-to-vehicle (V2V) communication, the traffic information on a large scale can be obtained and used to coordinate the operation of road traffic system. In this paper, a new traffic lattice hydrodynamic model is proposed which considers the influence of multiple-lattice self-anticipative density integration on traffic flow in the V2V environment. Through theoretical analysis, the linear stability condition ofthe new model is derived and the stable condition can be enhanced when more-preceding-lattice self-anticipative density integration effect is taken into account. The property of the unstable traffic density wave in the unstable region is also studied according to thenonlinear analysis. It is shown that the unstable traffic density wave can be described by solving the modified Korteweg–de-Vries (mKdV) equation. Finally, the simulation results demonstrate the validity of the theoretical results. Both theoretical analysis and numerical simulations demonstrate that multiple-lattice self-anticipative density integrationeffect can enhance the stability of traffic flow system in the V2V environment.

Analysis of mixed traffic with connected and non-connected vehicles based on lattice hydrodynamic model

With the development of information technology, the communication between vehicle and vehicle(V2V), vehicle and infrastructure(V2I) promotes traffic efficiency and safety. In this work, we study the mixed traffic with connected and non-connected vehicles, and present the mixed traffic lattice hydrodynamic model. By using linear stability analysis, the stability conditions of the traffic system are obtained. The phase-plot shows that the communication range and permeability of connected vehicles have an important influence on the traffic system. Then we get the modified Korteweg-de Vries equation via nonlinear analysis. Furthermore, the numerical simulation results verify the theoretical results, and shows that increasing the communication range and permeability of connected vehicle will make the traffic system more stable.

A feedback control method with consideration of the next-nearest-neighbor interactions in a lattice hydrodynamic model

A feedback control method with consideration of the next-nearest-neighbor interactions is investigated in the lattice hydrodynamic traffic model. The stability condition is obtained by discussing the first-order transfer function G1 and the second-order transfer function G2. The solution of mKdV equation which describe the density wave are yielded by nonlinear analysis. Theoretical analysis result indicates that the feedback gain λ, the weight coefficient of the nearest-neighbor interaction and the next-nearest-neighbor interaction have a great impact on the improvement of the stability of traffic flow. Numerical simulations by analyzing the short-term, long-term behaviors and hysteresis loop of traffic flow verify that the impacts of the feedback gain λ, the nearest-neighbor weight and the next-nearest-neighbor weight on traffic control. The feedback control method considering the next-nearest-neighbor interactions displays the nonlocal characteristics in the implementation of local control process.

Study on the continuous delayed optimal flow on traffic stability in a new macro traffic model

The influence of the continuous delayed optimal flow on traffic stability is studied based on a new traffic lattice hydrodynamic model in this paper. Linear analysis derives the model’s linear stable condition and it shows that the stability of traffic flow is enhanced by considering the continuous delayed optimal flow. Also the feature of the unstable traffic flow is uncovered by the solution of the mKdV equation with nonlinear analysis. Finally, numerical simulation is carried out to intuitively show the stabilization effect of the continuous delayed optimal flow on traffic flow and the continuous delayed optimal flow should be considered in traffic theory.

Research on the stabilization effect of continuous self-delayed traffic flux in macro traffic modeling

A modified macro traffic lattice hydrodynamic model is proposed by considering the continuous self-delayed traffic flux information on traffic stability. Via linear stability theory, the influence of the continuous self-delayed traffic flux on traffic stability is derived. It reveals that the stable region in the density-sensitivity space can be enlarged by taking the continuous self-delayed traffic flux into account. Furthermore, the nonlinear feature of density wave in the unstable region is studied and it is consistent with the kink-antikink solution of the mKdV equation. Also numerical simulation is conducted to further verify the analytical results and it is shown that the continuous self-delayed traffic flux information can improve the stable level of traffic flow significantly.

Effect of density integration on the stability of a new lattice hydrodynamic model

A novel traffic lattice hydrodynamic model considering the effect of density integration is proposed and analyzed in the paper. Via linear stability theory, linear stability condition of the new model is derived, which reveals an improvement of traffic stability by considering the integration of continuous historical density information. Moreover, the nonlinear properties of the extended model are revealed through nonlinear analysis. The propagating backwards kink–antikink waves are generated by deriving the mKdV equation near the critical point and verified by numerical simulation. All the results show that the density integration effect can suppress traffic congestion efficiently in traffic lattice hydrodynamic modeling.

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

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 microscopic model in form of angular variables into macroscopic one is deduced. Consequently, a corresponding continuum traffic flow model on curved road is derived. The critical condition for the steady traffic flow is obtained. Meanwhile, the stability condition of this continuum traffic model is compared with one of the microscopic model and lattice hydrodynamic traffic model on curved road. By nonlinear analysis, the KdV–Burgers equation which describes the density wave near the neutral stability line is derived. Furthermore, the numerical simulations are carried out to verify the validity of this macroscopic traffic. Results indicate the radius of curved road have a great impact on the formation of traffic jams. Local clustering effects in the state of instability of traffic flow give rise to the stop&go traffic jams. Numerical simulation also indicates the unstable region is shrunken under the increasing strength of the angular velocity difference.

Lattice hydrodynamic modeling of traffic flow with consideration of historical current integration effect

A new traffic lattice hydrodynamic model with consideration of historical current integration effect is proposed in this paper and the influence of current integration effect on traffic flow is studied through linear and nonlinear analyses. The linear stability condition obtained by linear analysis reveals that the traffic stability can be enhanced by considering the impact of historical current integration effect. Also the nonlinear analysis shows that the traffic density wave in the unstable region near the critical point can be described by the kink–antikink solution of the mKdV equation. Finally, numerical simulation is carried out to verify the analytical results and it is proved that the historical current integration effect can improve the stability of traffic flow importantly.

Effects of speed deviation and density difference in traffic lattice hydrodynamic model with interruption

An extended lattice hydrodynamic model is proposed by incorporating the effects of speed deviation, traffic interruption probability and the density difference between the leading and the following lattice. The stability condition of the extended model is obtained by using the linear stability theory. Based on nonlinear analysis method, the mKdV equation is derived. Therefore, the propagation behavior of traffic jam can be described by the kink-antikink soliton solution of the mKdV equation. Numerical simulation demonstrated that the traffic flow will be more stable and it is more consistent with real traffic with the consideration of effects of speed deviation and traffic interruption probability and the density difference.

Study on varying time delay on traffic stability in a novel lattice hydrodynamic model

A novel traffic lattice hydrodynamic model with consideration of varying time delay is proposed. The asymptotic stability condition of the new model is derived in the form of linear matrix inequality through Lyapunov stability theory and the traffic disturbance appearing in the new model can be suppressed under this stable condition. Numerical simulation shows that varying time delay affects the stability of traffic flow importantly and the traffic flow with consideration of varying time delay is more likely to develop into traffic congestion.

Stability analysis of feedforward anticipation optimal flux difference in traffic lattice hydrodynamic theory

Recently, the influence of driver's individual behaviors on traffic stability is research hotspot with the fasting developing transportation cyber-physical systems. In this paper, a new traffic lattice hydrodynamic model is proposed with consideration of driver's feedforward anticipation optimal flux difference. The neutral stability condition of the new model is obtained through linear stability analysis theory. The results show that the stable region will be enlarged on the phase diagram when the feedforward anticipation optimal flux difference effect is taken into account. In order to depict traffic jamming transition properties theoretically, the mKdV equation near the critical point is derived via nonlinear reductive perturbation method. The propagation behavior of traffic density waves can be described by the kink–antikink solution of the mKdV equation. Numerical simulations are conducted to verify the analytical results and all the results confirms that traffic stability can be enhanced significantly by considering the feedforward anticipation optimal flux difference in traffic lattice hydrodynamic theory.

Phase transition of a new lattice hydrodynamic model with consideration of on-ramp and off-ramp

A new traffic lattice hydrodynamic model with consideration of on-ramp and off-ramp is proposed in this paper. The influence of on-ramp and off-ramp on the stability of the main road is uncovered by theoretical analysis and computer simulation. Through linear stability theory, the neutral stability condition of the new model is obtained and the results show that the unstable region in the phase diagram is enlarged by considering the on-ramp effect but shrunk with consideration of the off-ramp effect. The mKdV equation near the critical point is derived via nonlinear reductive perturbation method and the occurrence of traffic jamming transition can be described by the kink–antikink soliton solution of the mKdV equation. From the simulation results of space-time evolution of traffic density waves, it is shown that the on-ramp can worsen the traffic stability of the main road but off-ramp is positive in stabilizing the traffic flow of the main road.

Effect of explicit lane changing in traffic lattice hydrodynamic model with interruption

In this paper, the explicit lane changing effect for two-lane traffic system with interruption is studied based on lattice hydrodynamic model. Through linear stability analysis, the neutral stability criterion for the two-lane traffic system is derived, and the density–sensitivity space is divided into the stable and unstable regions by the neutral stability curve. By applying nonlinear reductive perturbation method, the Burgers equation and modified Korteweg–de Vries (mKdV) equation are obtained to depict the density waves in the stable and unstable regions, respectively. Numerical simulations confirm the theoretical results showing that the traffic characteristics in the stable and unstable regions can be described respectively by the triangular shock waves of the Burgers equation and the kink–antikink solution of the mKdV equation. Also it is proved that lane changing can average the traffic situation of each lane for two-lane traffic system and enhance the stability of traffic flow, but traffic interruption of the current lattice can deteriorate the stable level of traffic flow and easily result in traffic congestion.

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.

Analysis of anticipation driving effect in traffic lattice hydrodynamic model with on-ramp

A new traffic lattice hydrodynamic model with on-ramp is proposed with consideration of driver’s anticipation effect according to transportation cyber physical systems. The neutral stability condition of the new model is obtained through linear stability analysis theory. The results show that the stable region on the phase diagram will be enlarged by considering driver’s anticipation effect but shrunk with the consideration of on-ramp effect. In order to depict traffic jamming transition, the modified Korteweg-de Vries (mKdV) equation near the critical point is derived via nonlinear reductive perturbation method. The propagation behavior of traffic density wave can be described by the kink–antikink solution of the mKdV equation. Numerical simulations are conducted to verify the analytical results, and all the results confirm that both driver’s anticipation effect and on-ramp effect affect the traffic stability of the main road importantly.