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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. 相似文献
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By introducing a flow difference effect, a modified lattice two-lane traffic flow model is proposed, which is proved to be capable of improving the stability of traffic flow. Both the linear stability condition and the kink-antikink solution derived from the modified Korteweg-de Vries (mKdV) equation are analyzed. Numerical simulations verify the theoretical analysis. Furthermore, the evolution laws under different disturbances in the metastable region are studied. 相似文献
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General solution of the modified Korteweg-de-Vries equation in the lattice hydrodynamic model 下载免费PDF全文
Traffic congestion is related to various density waves, which might be described by the nonlinear wave equations, such as the Burgers, Korteweg-de-Vries (KdV) and modified Korteweg-de-Vries (mKdV) equations. In this paper, the mKdV equations of four different versions of lattice hydrodynamic models, which describe the kink--antikink soliton waves are derived by nonlinear analysis. Furthermore, the general solution is given, which is applied to solving a new model --- the lattice hydrodynamic model with bidirectional pedestrian flow. The result shows that this general solution is consistent with that given by previous work. 相似文献
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Stability analysis of multiple-lattice self-anticipative density integration effect based on lattice hydrodynamic model in V2V environment 下载免费PDF全文
Geng Zhang 《中国物理 B》2021,30(12):120201-120201
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 of the 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 the nonlinear 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 integration effect can enhance the stability of traffic flow system in the V2V environment. 相似文献
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A new lattice hydrodynamic traffic flow model with a consideration of multi-anticipation effect 总被引:1,自引:0,他引:1 下载免费PDF全文
We present a new multi-anticipation lattice hydrodynamic model based on the traffic anticipation effect in the real world.Applying the linear stability theory,we obtain the linear stability condition of the model.Through nonlinear analysis,we derive the modified Korteweg-de Vries equation to describe the propagating behaviour of a traffic density wave near the critical point.The good agreement between the simulation results and the analytical results shows that the stability of traffic flow can be enhanced when the multi-anticipation effect is considered. 相似文献
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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. 相似文献
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By introducing the traffic anticipation effect in the real world into the original lattice hydrodynamic model, we present a new anticipation effect lattice hydrodynamic (AELH) model, and obtain the linear stability condition of the model by applying the linear stability theory. Through nonlinear analysis, we derive the Burgers equation and Korteweg-de Vries (KdV) equation, to describe the propagating behaviour of traffic density waves in the stable and the metastable regions, respectively. The good agreement between simulation results and analytical results shows that the stability of traffic flow can be enhanced when the anticipation effect is considered. 相似文献
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A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow.Based on the two-velocity difference model,the time-dependent Ginzburg-Landau (TDGL) equation under certain condition is derived to describe the traffic flow near the critical point through the nonlinear analytical method.The corresponding two solutions,the uniform and the kink solutions,are given.The coexisting curve,spinodal line and critical point are obtained by the first and second derivatives of the thermodynamic potential.The modified Korteweg de Vries (mKdV) equation around the critical point is derived by using the reductive perturbation method and its kink-antikink solution is also obtained.The relation between the TDGL equation and the mKdV equation is shown.The simulation result is consistent with the nonlinear analytical result. 相似文献
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A new two-dimensional lattice hydrodynamic model considering the turning capability of cars is proposed. Based on this model, the stability condition for this new model is obtained by using linear stability analysis. Near the critical point, the modified KdV equation is deduced by using the nonlinear theory. The results of numerical simulation indicate that the critical point a c increases with the increase of the fraction p of northbound cars which continue to move along the positive y direction for c = 0.3, but decreases with the increase of p for c = 0.7. The results also indicate that the cars moving along only one direction (eastbound or northbound) are most stable. 相似文献
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Time-dependent Ginzburg-Landau equation for lattice hydrodynamic model describing pedestrian flow 下载免费PDF全文
A thermodynamic theory is formulated to describe the phase transition and critical phenomena in pedestrian flow. Based on the extended lattice hydrodynamic pedestrian model taking the interaction of the next-nearest-neighbor persons into account, the time-dependent Ginzburg-Landau (TDGL) equation is derived to describe the pedestrian flow near the critical point through the nonlinear analysis method. The corresponding two solutions, the uniform and the kink solutions, are given. The coexisting curve, spinodal line, and critical point are obtained by the first and second derivatives of the thermodynamic potential. 相似文献
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The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but also connected with the microscopic car following model closely. The modified Korteweg-de Vries (mKdV) equation related to the density wave in a congested traffic region has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail for the car following model. We devote ourselves to obtaining the KdV equation from the original lattice hydrodynamic models and the KdV soliton solution to describe the traffic jam. Especially, we obtain the general soliton solution of the KdV equation and the mKdV equation. We review several lattice hydrodynamic models, which were proposed recently. We compare the modified models and carry out some analysis. Numerical simulations are conducted to demonstrate the nonlinear analysis results. 相似文献
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A novel lattice model integrating the cooperative deviation of density and optimal flux under V2X environment 下载免费PDF全文
Guang-Han Peng 《中国物理 B》2023,32(1):18902-018902
A novel lattice hydrodynamic model is proposed by integrating the cooperative deviation of density and optimal flux under vehicle to X (V2X) environment. According to the theoretical analysis, the stability conditions and the mKdV equations affected by the cooperative deviation of traffic information are explored. And the density wave, hysteresis loop and energy consumption of the traffic flow have been investigated via numerical simulation. The results indicate that the cooperative deviation of density and optimal flux can effectively alleviate the traffic congestion. More importantly, our new consideration can reduce fuel consumption and exhaust emission under the V2X environment. 相似文献
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In this paper, a new lattice hydrodynamic model is proposed by taking delay feedback and flux change rate effect into account in a single lane. The linear stability condition of the new model is derived by control theory. By using the nonlinear analysis method, the mKDV equation near the critical point is deduced to describe the traffic congestion. Numerical simulations are carried out to demonstrate the advantage of the new model in suppressing traffic jam with the consideration of flux change rate effect in delay feedback model. 相似文献
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《Physics letters. A》2020,384(27):126668
Lane markings are painted on the ground to permit movement turns along traffic lanes at signalized junctions. Drivers have to follow the guidance to turn different directions to enter different downstream lanes. A new two-dimensional lattice hydrodynamic model is proposed to model the effects of a shared lane marking. The control method is used to analyze the model and new stability conditions are derived. A shared lane marking can divert traffic with different directions to enter different downstream lanes. Under different turning proportion, intensities of traffic at downstream vary. Results show that the traffic diversion could influence the flow stability. Shared lane marking is able to divert traffic flows to different downstream lanes. A feedback control signal is added in the proposed model. Revised stability conditions are obtained using the proposed control method. Numerical simulations present the results for the stability under different traffic conditions. 相似文献
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The Korteweg-de Vires equation for the bidirectional pedestrian flow model considering the next-nearest-neighbor effect 下载免费PDF全文
This paper focuses on a two-dimensional bidirectional pedestrian flow model which involves the next-nearest-neighbor effect. The stability condition and the Korteweg-de Vries (KdV) equation are derived to describe the density wave of pedestrian congestion by linear stability and nonlinear analysis. Through theoretical analysis, the soliton solution is obtained. 相似文献
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通过线性稳定性分析,得到了多前车速度差模型的稳定性条件, 并发现通过调节多前车信息,使交通流的稳定区域明显扩大. 通过约化摄动方法 研究了该模型的非线性动力学特性:在稳定流区域,得到了描述密度波的Burgers方程;在交 通流的不稳定区域内,在临界点附近获得了描述车头间距的修正的Korteweg-de Vries (modified Korteweg-de Vries, mKdV)方程; 在亚稳态区域内,在中性稳定曲线附近获得了描述车头间距 的KdV方程. Burgers的孤波解、mKdV方程的扭结-反扭结波解及KdV方程的 孤波解描述了交通流堵塞现象. 相似文献
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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. 相似文献