Hongxia Ge

Ningbo University

In this paper, a modified continuum model considering the vehicle's taillight effect is presented. The high order fluid dynamics model of taillight effect is derived by means of the transformation from micro to macro. Combined with the continuous conservation equation of traffic flow, the linear and nonlinear analysis of the new macroscopic hydrody...

Taking account of the effect of the driver's memory, an extended car-following model is proposed in this paper. A control signal including the velocity contrast of considered car and the following car is taken into account in this extended model. Numerical simulations are implemented to prove that the application of the model can suppress the traff...

In the paper, an improved car-following model based on the full velocity difference model considering the influence of optimal velocity for leading vehicle on a single-lane road is proposed. The linear stability condition of the model is obtained by applying the linear stability theory. Through nonlinear analysis, the time-dependent Ginzburg–Landau...

Based on optimal velocity car following model, a new model considering traffic jerk is proposed to describe the jamming transition in traffic flow on a highway. Traffic jerk means the sudden braking and acceleration of vehicles, which has a significant impact on traffic movement. The nature of the model is researched by using linear and nonlinear a...

The delayed-feedback control method is applied for lattice hydrodynamic model of traffic flow. The linear stability condition with and without control signal are derived through linear and nonlinear analysis. Numerical simulation is carried out and the results confirm that the traffic congested can be suppressed efficiently by considering the contr...

Based on single-lane traffic model, a two-lane traffic model is presented considering the velocity difference control signal. The stability condition of the model is obtained by the control theory. The delayed feedback control signal is added to the two-lane model, and the corresponding stability condition is derived again. The numerical simulation...

In this paper, a new lattice model for bidirectional pedestrian flow on single path which involves the effect of friction parameter is presented. Linear stability analysis is used to obtain the stability condition. The modified Korteweg-de Vries (mKdV) equation and time-dependent Ginzburg-Landan (TDGL) equation are deduced by means of the reductive...

Car-following models are proposed to describe the jamming transition in traffic flow on a highway. In this paper, a new car-following model considering the driver's forecast effect is investigated to describe the traffic jam. The nature of the model is studied using linear and nonlinear analysis method. A thermodynamic theory is formulated to descr...

In the paper, two-lane traffic flow considering lane changing behaviors has been discussed based on the control theory, and the friction interference which is from the neighbor lane has been taken into account. By using the control method, the stability condition is derived. The feedback signals, which include vehicular information from both lanes,...

Ramps and sloping roads appear everywhere in the built environment. It is obvious that the movement pattern of people in the sloping path may be different as compared with the pattern on level roads. Previously, most of the studies, especially the mathematical and simulation models, on pedestrian movement consider the flow at level routes. This stu...

A new method is proposed to study the stability of the car-following model considering traffic interruption probability. The stability condition for the extended car-following model is obtained by using the Lyapunov function and the condition for no traffic jam is also given based on the control theory. Numerical simulations are conducted to demons...

A new control method to suppress traffic jams is proposed by considering headway of the front and rear. With the control signals or not the stability conditions are derived. It is shown that the vehicle speed fluctuation by the simulations disappears when the feedback control signals are introduced. Therefore, serious congestion will not occur in t...

In order to describe the car-following behavior more actually in real traffic, an extended car-following model incorporating the headway of arbitrary number of vehicles that precede and the relative velocity is proposed from the viewpoint of control. The stability condition of the extended model is obtained by using the linear stability theory. The...

Considered the effect of traffic anticipation in the real world, a new anticipation driving car following model (AD-CF) was proposed by Zheng et al. Based on AD-CF model, adopted an asymptotic approximation between the headway and density, a new continuum model is presented in this paper. The neutral stability condition is obtained by applying the...

In this paper, a car-following model considering anticipation-driving behavior is considered to describe the traffic jam. The nature of the model is investigated using linear and nonlinear analysis method. A thermodynamic theory is formulated for describing the phase transitions and critical phenomena, and the time-dependent Ginzburg-Landau equatio...

Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity, physics, engineering, and other areas of applications. In this paper, a meshfree method based on the moving Kriging interpolation is developed for a two-dimensional time-fractional diffusion equation. The shape function and its derivative...

In light of previous work [Phys. Rev. E 60 4000 (1999)], a modified coupled-map car-following model is proposed by considering the headways of two successive vehicles in front of a considered vehicle described by the optimal velocity function. The non-jam conditions are given on the basis of control theory. Through simulation, we find that our mode...

This paper focuses on a two-dimensional bidirectional pedestrian flow model which involves the next-nearest-neighbor effect. The Korteweg-de Vries equation is derived to describe the density wave of pedestrian congestion by nonlinear analysis. The soliton solution is obtained.

A car-following model is presented, in which the effects of non-motor vehicles on adjacent lanes are taken into account. A control signal including the velocity differences between the following vehicle and the target vehicle is introduced according to the feedback control theory. The stability condition for the new model is derived. Numerical simu...

A new continuum traffic flow model is proposed based on an improved car-following model, which takes the driverʼs forecast effect into consideration. The backward travel problem is overcome by our model and the neutral stability condition of the new model is obtained through the linear stability analysis. Nonlinear analysis shows clearly that the d...

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...

The present paper deals with the numerical solution of the coupled Schrödinger-KdV equations using the element-free Galerkin (EFG) method which is based on the moving least-square approximation. Instead of traditional mesh oriented methods such as the finite difference method (FDM) and the finite element method (FEM), this method needs only scatter...

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...

A generalized Fisher equation (GFE) relates the time derivative of the average of the intrinsic rate of growth to its variance. The exact mathematical result of the GFE has been widely used in population dynamics and genetics, where it originated. Many researchers have studied the numerical solutions of the GFE, up to now. In this paper, we introdu...

Based on the full velocity difference model, Jiang et al. put forward the speed gradient model through the micro-macro 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 overco...

Based on the anticipation lattice hydrodynamic models, which are described by the partial differential equations, the continuum version of the model is investigated through a reductive perturbation method. The linear stability theory is used to discuss the stability of the continuum model. The Korteweg–de Vries (for short, KdV) equation near the ne...

Based on an extended lattice hydrodynamic model considering the delay of the driver’s response in sensing headway, we get the time-dependent Ginzburg–Landau (for short, TDGL) equation to describe the transition and critical phenomenon in traffic flow by applying the reductive perturbation method. The corresponding solutions are obtained. Numerical...

In the Letter, a modified car-following model is presented, in which, the effects of vehicles (or non-motor vehicles) on other lanes without isolation belts are taken into account. The stability condition of the model is obtained by using the control theory method. To check the validity of the present theoretical scheme, the numerical simulation is...

Based on the coupled map car following model which was presented by Konishi et al. [Konishi KJ, Kokame H, Hirate K. Phys Rev E 1999;60:4000-7.] (for short, KKH), a modified coupled map car following model is proposed. In this model two successive vehicles’ headway distances in front of the considered one are incorporated in the optimal velocity (fo...

In this paper, we analyse the equal width (EW) wave equation by using the mesh-free reproducing kernel particle Ritz (kp-Ritz) method. The mesh-free kernel particle estimate is employed to approximate the displacement field. A system of discrete equations is obtained through the application of the Ritz minimization procedure to the energy expressio...

A car-following model which involves the effects of traffic interruption probability is further investigated. The stability condition of the model is obtained through the linear stability analysis. The reductive perturbation method is taken to derive the time-dependent Ginzburg-Landau (TDGL) equation to describe the traffic flow near the critical p...

A simple control method to suppress traffic congestion is proposed for the car-following model. The stability conditions are derived by using the control method, and the feedback signals, which act on our traffic system, are extended to the car-following model. The control signals will play an effect only if the traffic is congested. The correspond...

The element-free Galerkin (EFG) method is used in this paper to find the numerical solution to a regularized long-wave (RLW) equation. The Galerkin weak form is adopted to obtain the discrete equations, and the essential boundary conditions are imposed by the penalty method. The effectiveness of the EFG method of solving the RLW equation is investi...

Based on the microscopic two velocity difference model, a macroscopic model called speed viscous continuum model is developed to describe traffic flow. The relative velocities are added to the motion equation, which leads to viscous effects in continuum model. The viscous continuum model overcomes the backward travel problem, which exists in many h...

The present paper deals with the numerical solution of time-fractional partial differential equations using the element-free Galerkin (EFG) method, which is based on the moving least-square approximation. Compared with numerical methods based on meshes, the EFG method for time-fractional partial differential equations needs only scattered nodes ins...

In this paper, an extended car-following model considering the delay of the driver’s response in sensing headway is proposed to describe the traffic jam. It is shown that the stability region decreases when the driver’s physical delay in sensing headway increases. The phase transition among the freely moving phase, the coexisting phase, and the uni...

Based on the optimal velocity (OV) model, a new car-following model for traffic flow with the consideration of the driver's forecast effect (DFE) was proposed by Tang et al., which can be used to describe some complex traffic phenomena better. Using an asymptotic approximation between the headway and density, we obtain a new macro continuum version...

A modified coupled map car-following model is proposed, in which two successive vehicle headways in front of the considering vehicle is incorporated into the optimal velocity function. The steady state under certain conditions is obtained. An error system around the steady state is studied further. Moreover, the condition for the state having no tr...

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 correspondi...

Based on the pioneer work of Konishi et al, a new coupled map car-following model is presented by considering the headway distance of two successive vehicles in front. The feedback control method presented by Zhao-Gao is utilized to suppress the traffic congestion in the coupled map car-following model. According to the control theory, the conditio...

A weakly nonlinear evolution equation with control term is considered using the analytic method. From the perturbation theory, the solution of the corresponding equation is obtained. And the functions of asymptotic solution for the equation are studied.

A class of relative rotation nonlinear dynamical model with nonlinear damping force and forcing periodic force is investigated. First, a homotopic mapping is constructed, and then the initial approximate solution is determined. Finally, using the homotopic mapping method, the arbitrarily degree approximation for corresponding model is found.

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 ar...

Steady-state heat conduction problems arisen in connection with various physical and engineering problems where the functions satisfy a given partial differential equation and particular boundary conditions, have attracted much attention and research recently. These problems are independent of time and involve only space coordinates, as in Poisson'...

Based on the pioneer work of Konishi et al., a new control method is proposed to suppress the traffic congestion in the coupled map (CM) car-following model under open boundary condition. The influence of the following car to the system has been considered. Our method and that presented by Konishi et al. [Phys. Rev. E 60 (1999) 4000] are compared....

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...

The present paper deals with the numerical solution of a two-dimensional linear hyperbolic equation by using the element-free Galerkin (EFG) method which is based on the moving least-square approximation for the test and trial functions. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforce...

Based on the pioneer work of Konishi et al, a new control method is presented to suppress the traffic congestion in the coupled map (CM) car-following model under an open boundary. A control signal concluding the velocity differences of the two vehicles in front is put forward. The condition under which the traffic jam can be contained is analyzed....

The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but is also closely connected with the microscopic car following model. The modified Korteweg-de Vries (mKdV) equation about the density wave in congested traffic has been derived near the critical point since Nagatani first proposed it. But the K...

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...

A modified coupled map car-following model is proposed for a one-way with the application of intelligent transportation system to describe the dynamic characteristics of one-way traffic flow and the control of traffic congestion. Based on the present model and the theory of feedback control, the stability criteria are given for the change of speed...

A lattice hydrodynamic model is proposed by incorporating the anticipation effect. The linear and nonlinear methods are used to analyze the model, and the results show that considering “backward looking” effect leads to the stabilization of the system. Numerical simulation confirms that our model is more reasonable for describing the real traffic f...

The traffic flow controlled by a traffic light on a single-lane roadway is studied by using a modified NaSch model proposed by the authors, in which the randomization is dependent on the local density of the preceding time step. The flow-density diagrams are obtained and three different traffic density regions, i.e., undersaturated traffic, saturat...

The novel lattice hydrodynamic model is presented by incorporating the “backward looking” effect. The stability condition for the the model is obtained using the linear stability theory. The result shows that considering one following site in vehicle motion leads to the stabilization of the system compared with the original lattice hydrodynamic mod...

A modified cellular automaton model for traffic flow on highway is proposed with a novel concept about the variable security gap. The concept is first introduced into the original Nagel–Schreckenberg model, which is called the non-sensitive driving cellular automaton model. And then it is incorporated with a sensitive driving NaSch model, in which...

In the light of the optimal velocity model, a two velocity difference model for a car-following theory is put forward considering navigation in modern traffic. To our knowledge, the model is an improvement over the previous ones theoretically, because it considers more aspects in the car-following process than others. Then we investigate the proper...

In this paper, the reproducing kernel particle method (RKPM) is used for finding the solution of a two-dimensional parabolic inverse problem with a source control parameter, and the corresponding discrete equations are obtained. Comparing with the numerical methods based on mesh, the reproducing kernel particle method only needs the scattered nodes...

In this paper the new continuum traffic flow model proposed by Jiang et al is developed based on an improved car-following model, in which the speed gradient term replaces the density gradient term in the equation of motion. It overcomes the wrong-way travel which exists in many high-order continuum models. Based on the continuum version of car-fol...

Based on the Nagel-Schreckenberg (NaSch) model of traffic flow, a modified cellular automaton (CA) traffic model with the density-dependent randomization (abbreviated as the DDR model) is proposed to simulate traffic flow. The fundamental diagram obtained by simulation shows the ability of this modified NaSch model to capture the essential features...

Based on the Nagel-Schreckenberg (NaSch) model of traffic flow, a new cellular automaton (CA) traffic model is proposed to simulate microscopic traffic flow. The probability p is a variable which contains a randomly selected term for each individual driver and a density-dependent term which is the same for all drivers. When the rational probability...

Without Abstract

A modified coupled map car-following model is proposed for a one-way with the application of intelligent transportation system to describe the dynamic characteristics of one-way traffic flow and the control of traffic congestion. Based on the present model and the theory of feedback control，the stability criteria are given for the change of speed o...

An extended car following model is proposed by incorporating intelligent transportation system and the backward looking effect under certain condition in traffic flow. The neutral stability condition of this model is obtained by using the linear stability theory. The results show that anticipating the behavior of vehicles preceding and following on...

A new traffic flow model called density viscous continuum model is developed to describe traffic more reasonably. The two delay time scales are taken into consideration, differing from the model proposed by Xue and Dai [Phys. Rev. E 68 (2003) 066123]. Moreover the relative density is added to the motion equation from which the viscous term can be d...

The jams in the congested traffic reveal various density waves. Some of them are described by the nonlinear wave equations: the Korteweg–de-Vries (KdV) equation, the Burgers equation and the modified KdV equation. An extended car following model are proposed in previous work, and the kink-antikink solution has been obtained from the mKdV equation....

The jams in the congested traffic are related with various density waves, which might be governed by the nonlinear wave equations, such as the Korteweg–de-Vries (KdV) equation, the Burgers equation and the modified Korteweg–de-Vries (mKdV) equation. Three different versions of optimal velocity models are examined. The stability conditions of the mo...

A novel cellular automaton model for traffic flow on highway is proposed considering Intelligent Transportation System (ITS). Based on the Nagel-Schreckenberg model (NS for short), it includes effective gap and brake light. Moreover, a novel concept about the variable security gap is introduced. The simulation shows that the road capacity of the mo...

Two lattice traffic models are proposed by incorporating a cooperative driving system. The lattice versions of the hydrodynamic model of traffic flow are described by the differential-difference equation and difference-difference equation, respectively. The stability conditions for the two models are obtained using the linear stability theory. The...

An extended car following model is proposed by incorporating an intelligent transportation system in traffic. The stability condition of this model is obtained by using the linear stability theory. The results show that anticipating the behavior of more vehicles ahead leads to the stabilization of traffic systems. The modified Korteweg-de Vries equ...