Continuum modeling for two-lane traffic flow with consideration of the traffic interruption probability

Considering the effects that the probability of traffic interruption and the friction between two lanes have on the car-following behaviour, this paper establishes a new two-lane microscopic car-following model. Based on this microscopic model, a new macroscopic model was deduced by the relevance relation of microscopic and macroscopic scale parameters for the two-lane traffic flow. Terms related to lane change are added into the continuity equations and velocity dynamic equations to investigate the lane change rate. Numerical results verify that the proposed model can be efficiently used to reflect the effect of the probability of traffic interruption on the shock, rarefaction wave and lane change behaviour on two-lane freeways. The model has also been applied in reproducing some complex traffic phenomena caused by traffic accident interruption.

Continuum modeling for two-lane traffic flow

In this paper, we study the continuum modeling of traffic dynamics for two-lane freeways. A new dynamics model is proposed, which contains the speed gradient-based momentum equations derived from a car-following theory suited to two-lane traffic flow. The conditions for securing the linear stability of the new model are presented. Numerical tests are can＇ied out and some nonequilibrium phenomena are observed, such as small disturbance instability, stop-and-go waves, local clusters and phase transition.

Continuum models for freeways with two lanes and numerical tests

This paper deals with the continuum modeling of traffic dynamics for freeways with two lanes where the faster vehicles are allowed to travel on both lanes while the slower vehicles are allowed to travel on one lane only. The speed gradient-based momentum equation is used to develop the traffic models for each lane. Using the proposed models, some nonequilibrium phenomena such as small disturbance instability and stop-and-go waves, together with results from numerical tests are investigated. The conditions for keeping the models’linear stability are presented.

Lane changing analysis for two-lane traffic flow

In this paper, the two-lane traffic are studied by using the lane-changing rules in the car-following models. The simulation show that the frequent lane changing occurs when the lateral distance in car following activities is considered and it gives rise to oscillating waves. In contrast, if the lateral distance is not considered （or considered occasionally）, the lane changing appears infrequently and soliton waves occurs. This implies that the stabilization mechanism no longer functions when the lane changing is permitted. Since the oscillating and soliton waves correspond to the unstable and metastable flow regimes, respectively, our study verifies that a phase transition may occur as a result of the lane changing.

Cellular Automaton Models of Highway Traffic Flow Considering Lane-Control and Speed-Control

As two kinds of management modes of highway traffic control,lane-control,and speed-control produce different effect under different conditions.In this paper,traffic flow cellular automaton models for four-lane highway system with two opposing directions under the above two modes are established considering car and truck mixed running. Through computer numerical simulating,the fundamental diagrams with different parameters are obtained,and after the analysis of density-flux diagrams,the variation discipline of flux with traffic density under different control models is gained.The results indicate that,compared with lane-control,utilization ratio of road can be further improved with speed-control when the truck number increases.The research result is of great significance for reasonable providing theoretical guidance for highway traffic control.

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

In this paper, the viscous continuum traffic flow model for a single lane is extended to the traffic flow for two-lane freeways. The proposed model is a higher-order continuum model considering the coupling and lane changing effects of the vehicles on two adjacent lanes. It results from integrating the Taylor series expansion of the viscous continuum traffic flow model proposed by Ge （2006 Physiea A 371 667） into the multi-lane model presented by Daganzo （1997 Transpn. Res. B 31 83）. Our proposed model may be used to describe non-anisotropic behaviour because of lane changing in multi-lane traffic. A linear stability analysis is given and the neutral stability condition is obtained. Also, issues related to lane changing, shock waves and rarefaction waves, local clustering and phase transition are investigated through a simulation experiment. The simulation results show that the proposed model is capable of explaining some particular traffic phenomena commonly observable in real world traffic flow.

Threshold values of traffic flow for the provision of exclusive bus lanes

A simulation network model was established using VISSIM software and verified by the T- test. The model took into consideration the road conditions, pedestrian crossing, traffic composi- tion, bus stops and traffic signal. The operating characteristics of buses and cars under different flow conditions were studied using the simulation model, and the speed-flow models of buses and cars were established based on the simulation results. Finally, the threshold values of traffic flow for the provision of exclusive bus lanes was determined with the target of optimal travel benefits （per capi- ta） , which would provide a basis for the planning and design of exclusive bus lanes on urban roads.

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

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.

Flow difference effect in the two-lane lattice hydrodynamic model

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. Futhermore, the evolution laws under different disturbances in the metastable region are studied.

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 study on the effects of the transit parking time on traffic flow based on cellular automata theory

This paper mainly deals with the effects of transit stops on vehicle speeds and conversion lane numbers in a mixed traffic lane. Based on thorough research of traffic flow and cellular automata theory, it calibrates the cellular length and the running speed. Also, a cellular automata model for mixed traffic flow on a two-lane system under a periodic boundary condition is presented herewith, which also takes into consideration the harbour-shaped transit stop as well. By means of computer simulation, the article also studies the effects of bus parking time on the traffic volume, the transit speed and the fast lane speed at the same time. The results demonstrate that, with the increase of the bus parking time, the traffic volume of the transit stop and the transit speed decrease while the fast lane speed increases. This result could help calculate the transit delay correctly and make arrangements for transit routes reasonably and scientifically.

带有最优流量信息中断期望影响的一类新格子模型

交通中断是导致交通扰动的一个重要因素.为研究最优流量信息中断的期望行为对交通流稳定性的影响,基于Nagatani’s模型考虑最优流量中断概率的影响,提出一类新的格子流体力学模型.首先,根据线性稳定分析方法,得到新模型的线性稳定条件;其次,通过非线性稳定理论,获得该模型的modified Korteweg-de Vries(mKdV)方程,并根据求解方程得到的扭结-反扭结孤立波解描述交通堵塞的演变过程;最后,通过仿真算例验证了理论分析结果.结果表明,考虑最优流量中断期望影响的新格子流体力学模型比Nagatani’s模型更稳定,当添加最优流量信息中断的期望影响时,交通流的稳定性得到显著提高.

长隧道路段货车限道措施的数值模拟——以甬莞高速角洞岙隧道路段为例

基于实际交通录像分析得出的边界条件和货车影响距离,提出了含有长隧道的双车道元胞自动机交通流模型.模拟结果与实际交通数据对比,吻合较好,表明模型能够准确反映实际交通流的特性.数值模拟显示,货车的存在增加了隧道路段交通拥堵的发生概率,且这种影响随货车比增加而增强.为降低货车对隧道交通的影响,提出了货车限道措施,并开展数值模拟,结果表明,货车限道措施能显著提升左车道的车速,在大进车率时也能提升右车道的车速,在高货车比时流量提升效果显著.

A new traffic model on compulsive lane-changing caused by off-ramp

In the field of traffic flow studies, compulsive lane-changing refers to lane-changing （LC） behaviors due to traffic rules or bad road conditions, while free LC happens when drivers change lanes to drive on a faster or less crowded lane. LC studies based on differential equation models accurately reveal LC influence on traffic environment. This paper presents a second-order partial differential equation （PDE） model that simulates both compulsive LC behavior and free LC behavior, with lane-changing source terms in the continuity equation and a lane-changing viscosity term in the momentum equation. A specific form of this model focusing on a typical compulsive LC behavior, the ＇off-ramp problem＇, is derived. Numerical simulations are given in several cases, which are consistent with real traffic phenomenon.

A new traffic model with a lane-changing viscosity term

In this paper, a new continuum traffic flow model is proposed, with a lane-changing source term in the continuity equation and a lane-changing viscosity term in the acceleration equation. Based on previous literature, the source term addresses the impact of speed difference and density difference between adjacent lanes, which provides better precision for free lane-changing simulation; the viscosity term turns lane-changing behavior to a ＂force＂ that may influence speed distribution. Using a flux-splitting scheme for the model discretization, two cases are investigated numerically. The case under a homogeneous initial condition shows that the numerical results by our model agree well with the analytical ones; the case with a small initial disturbance shows that our model can simulate the evolution of perturbation, including propagation,dissipation, cluster effect and stop-and-go phenomenon.

Traffic dynamical characteristics and nonlinear density waves with consideration of navigation

In this dissertation, based on the existing macroscopic and microscopic models for traffic flow, several improved mathematical models in accordance with the rapid development of intelligent transportation system （ITS） are proposed, and the corresponding theoretical analysis and numerical simulation are performed. In addition, the relationships between macroscopic and microscopic traffic models are examined, in which emphasis is particularly laid on the investigation of the various nonlinear density waves in traffic flows. The contents of the dissertation are as follows.

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

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.

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

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.

Application of singular perturbation method in analyzing traffic density waves

Car following model is one of microscopic models for describing traffic flow. Through linear stability analysis, the neutral stability lines and the critical points are obtained for the different types of car following models and two modified models. The singular perturbation method has been used to derive various nonlinear wave equations, such as the Kortewegde-Vries （KdV） equation and the modified Korteweg-de-Vries （mKdV） equation, which could describe different density waves occurring in traffic flows under certain conditions. These density waves are mainly employed to depict the formation of traffic jams in the congested traffic flow. The general soliton solutions are given for the different types of car following models, and the results have been used to the modified models efficiently.

基于换道时间分布的交通流随机微分方程

在总结随机交通流理论发展的基础上,提出考虑换道时间随机性的随机交通流动力学方程,给出包括换道行为的交通流方程数值解法.解法结合换道时间的密度分解和偏微分方程的差分求解,对快速路交织区车流速度在时空上的演变概率进行求解,得到交通流速度演变趋势的随机可能性,并表达为速度变化的概率密度.求解结果表明,交通流动力学随机微分方程及其数值解法能够描述复杂交通流的随机特性,速度概率密度函数弥补了其他交通流方程难以表达的车流速度随机特征,为深入研究拥堵工况的交通流演变规律提供了新研究手段,也为交通设施和交通控制设计提供了通行能力之类的参量在可靠性上的理论分析方法.