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The time-dependent Ginzburg-Landau equation for the two-velocity difference model

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Chinese Physics B 2011年第8期20卷 130-135页

作者：吴淑贞程荣军葛红霞 Faculty of Science Ningbo University Department of Fundamental Course Ningbo Institute of TechnologyZhejiang University

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.

关键词： traffic flow two-velocity difference model TDGL equation mKdV equation

Cellular automaton model considering headway-distance effect

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Chinese Physics B 2008年第5期17卷 1863-1868页

作者：胡守信高坤汪秉宏陆玉凤 Department of Modern Physics and Nonlinear Science Center University of Science and Technology of China Department of Science Bengbu College Shanghai Academy of System Science

This paper presents a cellular automaton model for single-lane traffic flow. On the basis of the Nagel-Schreckenberg （NS） model, it further considers the effect of headway-distance between two successive cars on the randomization of the latter one. In numerical simulations, this model shows the following characteristics. （1） With a simple structure, this model succeeds in reproducing the hysteresis effect, which is absent in the NS model. （2） Compared with the slow-tostart models, this model exhibits a local fundamental diagram which is more consistent to empirical observations. （3） This model has much higher efficiency in dissolving congestions compared with the so-called NS model with velocitydependent randomization （VDR model）. （4） This model is more robust when facing traffic obstructions. It can resist much longer shock times and has much shorter relaxation times on the other hand. To summarize, compared with the existing models, this model is quite simple in structure, but has good characteristics.

关键词： traffic flow headway-distance phase-transition fundamental diagram

Optimal velocity functions for car-following models

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2010年第7期11卷 520-529页

作者： Milan BATISTA Elen TWRDY Faculty of Maritime Studies and Transport University of Ljubljana

The integral part of the optimal velocity car-following models is the optimal velocity function (OVF), which can be derived from measured velocity-spacing data. This paper discusses several characteristics of the OVF and presents regression analysis on two classical datasets, the Lincoln and Holland tunnels, with different possible OVFs. The numerical simulation of the formation of traffic congestion is conducted with three different heuristic OVFs, demonstrating that these functions give results similar to those of the famous Bando OVF (Bando et al., 1995). Also an alternative method is present for determining the sensitivity and model parameters based on a single car driving to a fixed barrier.

关键词： traffic flow Car following Optimal velocity function (OVF) traffic congestion

Multiple flux difference effect in the lattice hydrodynamic model

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Chinese Physics B 2012年第2期21卷 210-217页

作者：王涛高自友赵小梅 MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology Beijing Jiaotong UniversityBeijing 100044China College of Automation&Electronic Engineering Qingdao University of Science&TechnologyQingdao 266042China

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 reduetive 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.

关键词： flux difference lattice hydrodynamic model traffic flow mKdV equation

An improved cellular automaton model considering the effect of traffic lights and driving behaviour

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Chinese Physics B 2011年第4期20卷 197-203页

作者：何红弟卢伟真董力耘 Logistics Research Center and Shanghai Engineering Research Center of Shipping Logistics Information Shanghai Maritime University Department of Building and Construction City University of Hong Kong Shanghai Institute of Applied Mathematics and Mechanics Shanghai University

This paper proposes an improved cellular automaton model to describe the urban traffic flow with the consideration of traffic light and driving behaviour effects. Based on the model, the characteristics of the urban traffic flow on a single- lane road are investigated under three different control strategies, i.e., the synchronized, the green wave and the random strategies. The fundamental diagrams and time-space patterns of the traffic flows are provided for these strategies respectively. It finds that the dynamical transition to the congested flow appears when the vehicle density is higher than a critical level. The saturated flow is less dependent on the cycle time and the strategies of the traffic light control, while the critical vehicle density varies with the cycle time and the strategies. Simulated results indicate that the green wave strategy is proven to be the most effective one among the above three control strategies.

关键词： traffic flow cellular automaton control strategy vehicle density

A cellular automaton model for a bridge traffic bottleneck

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Acta Mechanica Sinica 2005年第3期21卷 305-309页

作者： Shifa Xiao Lingjiang Kong Muren Liu College of Physics & Information Engineering Guangxi Normal University Guilin 541004 China

A cellular automaton （CA） model is proposed in this paper to analyze a bridge traffic bottleneck. The simulation results with this model show that there are several phase transitions in the traffic average density, velocity and flow for each lane under a periodic boundary condition. An unstable phase in the traffic average density and velocity for the upstream and downstream lanes of the bridge is shown in a range of initial traffic densities. The critical points of the phase transitions and the phenomenon of the unstable phase found in the simulation are also explained with the mean-field theory.

关键词： traffic flow Cellular automata model Bridge-bottleneck Phase transition Unstable phase

A new coupled map car-following model considering drivers' steady desired speed

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Chinese Physics B 2014年第5期23卷 41-45页

作者：周桐孙棣华李华民刘卫宁 College of Automation Chongqing University Key Laboratory of Dependable Service Computing in Cyber Physical Society of Ministry of Education Chongqing University College of Computer Science Chongqing University

Based on the pioneering work of Konishi et al., in consideration of the influence of drivers＇ steady desired speed ef/ect on the traffic flow, we develop a new coupled map car-following model in the real world. By use of the control theory, the stability condition of our model is derived. The validity of the present theoretical scheme is verified via numerical simulation, confirming the correctness of our theoretical analysis.

关键词： traffic flow traffic congestion coupled map car-following model steady desired speed effect

The KdV-Burgers equation in a modified speed gradient continuum model

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Chinese Physics B 2013年第6期22卷 289-293页

作者：赖玲玲程荣军李志鹏葛红霞 Faculty of Science Ningbo University Ningbo Institute of Technology Zhejiang University College of Electronics and Information Engineering Tongji University

Based on the full velocity difference model, Jiang et al. put forward the speed gradient model through the micromacro linkage （Jiang R, Wu Q S and Zhu Z J 2001 Chin. Sci. Bull 46 345 and Jiang R, Wu Q S and Zhu Z J 2002 Trans. Res. B 36 405）. In this paper, the Taylor expansion is adopted to modify the model. The backward travel problem is overcome by our model, which exists in many higher-order continuum models. The neutral stability condition of the model is obtained through the linear stability analysis. Nonlinear analysis shows clearly that the density fluctuation in traffic flow leads to a variety of density waves. Moreover, the Korteweg-de Vries-Burgers （KdV-Burgers） equation is derived to describe the traffic flow near the neutral stability line and the corresponding solution for traffic density wave is derived. The numerical simulation is carried out to investigate the local cluster effects. The results are consistent with the realistic traffic flow and also further verify the results of nonlinear analysis.

关键词： traffic flow the speed gradient model KdV-Burgers equation

General solution of the modified Korteweg-de-Vries equation in the lattice hydrodynamic model

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Chinese Physics B 2010年第10期19卷 199-203页

作者：余寒梅程荣军葛红霞 Faculty of Science Ningbo University Department of Fundamental Course Ningbo Institute of Technology Zhejiang University

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.

关键词： traffic flow lattice hydrodynamic model mKdV equation