A velocity-difference-separation model for car-following theory

We introduce a velocity-difference-separation model that modifies the previous models in the literature. The improvement of this new model over the previous ones lies in that it not only theoretically retains many strong points of the previous ones, but also performs more realistically than others in the dynamical evolution of congestion. Furthermore, the proposed model is investigated with analytic and numerical methods, with the finding that it can demonstrate some complex physical features observed in real traffic such as the existence of three phases： free flow, synchronized flow, and wide moving jam; sudden flow drop in flow-density plane; and traffic hysteresis in transition between the free and the synchronized flow.

Feedback control scheme of traffic jams based on the coupled map car-following model

Based on the pioneering work of Konishi et al. [Phys. Rev. E （1999） 60 4000], a new feedback control scheme is presented to suppress traffic jams based on the coupled map car-following model under the open boundary condition. The effect of the safe headway on the traffic system is considered. According to the control theory, the condition under which traffic jams can be suppressed is analyzed. The results are compared with the previous results concerning congestion control. The simulations show that the suppression performance of our scheme on traffic jams is better than those of the previous schemes, although all the schemes can suppress traffic jams. The simulation results are consistent with theoretical analyses.

A new car-following model with consideration of the traffic interruption probability

In this paper, we present a new car-following model by taking into account the effects of the traffic interruption probability on the car-following behaviour of the following vehicle. The stability condition of the model is obtained by using the linear stability theory. The modified Korteweg-de Vries （KdV） equation is constructed and solved, and three types of traffic flows in the headway sensitivity space-stable, metastable, and unstable--are classified. Both the analytical and simulation results show that the traffic interruption probability indeed has an influence on driving behaviour, and the consideration of traffic interruption probability in the car-following model could stabilize traffic flow.

Car-following models of vehicular traffic

The Car-following models is a kind of microscopic simulation model for vehicular traffic, which describe the one-by-one following behaviors of vehicles in the same traffic lane. As a common traffic phenomenon, following behavior is of great importance in the micro-study of intelligent traffic control. Compared with other traffic-flow models, car-following model embodies the human factors and reflects the real traffic situation in a better way. This paper gives a systematic review of the development and actuality of car-following models by introducing and analyzing in detail the advantages and disadvantages of GHR model, OV model, CA model and fuzzy-logic model. In addition, local stability and asymptotic stability of car-following models are discussed in this paper.

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

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.

A control method for congested traffic in the coupled map car-following model

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 results axe compared with that presented by Konishi et al [Phys. Rev. 1999 E 60 4000-4007]. The simulation results show that the temporal behavior obtained by our method is better than that by the Konishi＇s et al. method, although both the methods could suppress the traffic jam. The simulation results are consistent with the theoretical analysis.

An Improved Car-Following Model for Multiphase Vehicular Traffic Flow and Numerical Tests

This paper attempts to introduce an improved difference model that modifies a car-following model, which takes the next-nearest-neighbor interaction into account. The hnprovement of this model over the previous one lies in that it performs more realistically in the dynamical motion for small delay time. The traffic behavior of the improved model is investigated with analytic and numerical methods with the finding that the new consideration could further stabilize traffic flow. And some simulation tests verify that the proposed model can demonstrate some complex physical features observed recently in real traffic such as the existence of three phases： free flow, coexisting flow, and jam flow; spontaneous formation of density waves; sudden flow drop in flow-density plane; traffic hysteresis in transition between the free and the coexisting flow. Furthermore, th.e improved model also predicts that the stable state to relative density in the coexisting flow is insusceptible to noise.

An improved car-following model with consideration of the lateral effect and its feedback control research

A car-following model is presented, in which the effects of non-motor vehicles on adjacent lanes are taken into ac- count. 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 simulation is used to demonstrate the advantage of the new model including the control signal; the results are consistent with the analytical ones

A new coupled-map car-following model based on a transportation supernetwork framework

A new car-following model is proposed by considering information from a number of preceding vehicles with intervehicle communication. A supernetwork architecture is first described, which has two layers： a traffic network and a communication network. The two networks interact with and depend on each other. The error dynamic system around the steady state of the model is theoretically analyzed and some nonjam criteria are derived. A simple control signal is added to the model to analyze the criteria of suppressing traffic jams. The corresponding numerical simulations confirm the correctness of the theoretical analysis. Compared with previous studies concerning coupled map models, the controlled model proposed in this paper is more reasonable and also more effective in the sense that it takes into account the formation of traffic congestion.

A Model of Car-Following with Adaptive Headway

The performances of a well-known GHR car-following model was investigated by using numerical simulations in describing the acceleration and deceleration process induced by the motion of a leading car. It is shown that in GHR model vehicle is allowed to run arbitrarily close together if their speed are identical,and it waves aside even though the separation is larger than its desired distance. Based on these investigations, a modified GHR model which features a new nonlinear term which attempts to adjust the inter-vehicle spacing to a certain desired value was proposed accordingly to overcome these deficiencies. In addition, the analysis of the additive nonlinear term and steady-state flow of the new model were studied to prove its rationality.

A control method applied to mixed traffic flow for the coupled-map car-following model

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 model can exhibit a better effect as p = 0.65, which is a parameter in the optimal velocity function. The control scheme, which was proposed by Zhao and Gao, is introduced into the modified model and the feedback gain range is determined. In addition, a modified control method is applied to a mixed traffic system that consists of two types of vehicle. The range of gains is also obtained by theoretical analysis. Comparisons between our method and that of Zhao and Gao are carried out, and the corresponding numerical simulation results demonstrate that the temporal behavior of traffic flow obtained using our method is better than that proposed by Zhao and Gao in mixed traffic systems.

Traffic chaos and its prediction based on a nonlinear car-following model

This paper discusses the dynamic behavior and its predictions for a simulated traffic flow based on the nonlinear response of a vehicle to the leading car＇s movement in a single lane. Traffic chaos is a promising field, and chaos theory has been applied to identify and predict its chaotic movement. A simulated traffic flow is generated using a car-following model（ GM model）, and the distance between two cars is investigated for its dynamic properties. A positive Lyapunov exponent confirms the existence of chaotic behavior in the GM model. A new algorithm using a RBF NN （radial basis function neural network） is proposed to predict this traffic chaos. The experiment shows that the chaotic degree and predictable degree are determined by the first Lyapunov exponent. The algorithm proposed in this paper can be generalized to recognize and predict the chaos of short-time traffic flow series

Numerical Simulation of Motor Vehicles’ Courtesy Behavior on Crosswalk Based on Car-Following Model

In observing driver courtesy towards pedestrians at unsignalized crosswalks, a behavioral model was adopted in a simulation based on the GM Car-Following Model. The SIMI Motion Software was used to extract the vehicle operation data from Wenyi South Road and Hanyuan Road in Xi'an City. The parameters of the GM Car-Following Model were calibrated by genetic algorithm. The road simulation environment based on the Car-Following Model was constructed by MATLAB. In the case of no stopping, uniform deceleration avoidance with advance notice, emergency brake avoidance without advance notice, changes such as the displacement of the Car-Following queue, headway, speed, acceleration, and deceleration were analyzed by numerical simulation. The results show that when there is advance notice before the crosswalk, the minimum headway distances of Car1-Car2, Car2-Car3, Car3-Car4 and Car4-Car5 are 7.09 m, 7.38 m, 7.65 m, 7.91 m, and the average rates of change of the headway during deceleration are 0.78 m/s, 0.74 m/s, 0.71 m/s, 0.68 m/s respectively;in the absence of advance notice before the crosswalk, the minimum headway distances of Car1-Car2, Car2-Car3, Car3-Car4 and Car4-Car5 are 7.28 m, 7.75 m, 8.19 m, 8.59 m, and the average rates of change of the headway during deceleration are 1.57 m/s, 1.25 m/s, 1.04 m/s, 0.96 m/s, respectively. Therefore, in order to effectively prevent the occurrence of vehicle rear-end events, it's necessary to set traffic signs and markings on the preceding section of the intersection or road exhibiting behavioral comity.

Modeling and analysis of car-following behavior considering backward-looking effect

The car-following behavior can be influenced by its driver’s backward-looking effect.Especially in traffic congestion,if vehicles adjust the headway by considering backward-looking effect,the stability of traffic flow can be enhanced.A model of car-following behavior considering backward-looking effect was built using visual information as a stimulus.The critical stability conditions were derived by linear and nonlinear stability analyses.The results of parameter sensitivity analysis indicate that the stability of traffic flow was enhanced by considering the backward-looking effect.The spatiotemporal evolution of traffic flow of different truck ratios and varying degrees of backward-looking effect was determined by numerical simulation.This study lays a foundation for exploring the complex feature of car-following behavior and making the intelligent network vehicles control rules more consistent with human driver habits.

Modelling and Simulation for Train Movement Control Using Car-Following Strategy

Based on optimM velocity car-following model, in this paper, we propose a new railway tramc model for describing the process of train movement control. In the proposed model, we give an improved form of the optimal velocity function V^opt, which is considered as the desired velocity function for train movement control under different control conditions. In order to test the proposed model, we simulate and analyze the trajectories of train movements, moreover, discuss the relationship curves between the train allowable velocity and the site of objective point in detail. Analysis results indicate that the proposed model can well capture some realistic futures of train movement control.

Considering Backward Effect in Coupled Map Car-Following Model

Based on the pioneer work of Konishi et al,a new control method is proposed to suppress the trafficcongestion in the coupled map (CM) car-following model under open boundary condition.The influence of the followingcar to the system has been considered.Our method and that presented by Konishi et al.[Phys.Rev.E 60 (1999) 4000]are compared.Although both the methods could suppress the traffic jam,the simulation results show that the temporalbehavior obtained by ours is better than that proposed by the Konishi's et al.The simulation results are consistent withthe theoretical analysis.

Improved Car-Following Model Considering Modified Backward Optimal Velocity and Velocity Difference with Backward-Looking Effect

In this paper, a new traffic flow model called the forward-backward velocity difference (FBVD) model based on the full velocity difference model is proposed to investigate the backward-looking effect by applying a modified backward optimal velocity using generalized backward maximum speed. The FBVD model belongs to the family of microscopic models that consider spatiotemporally continuous formulations. Neutral stability conditions of the discrete car-following model are derived using the linear stability theory. The stability analysis results prove that the modified backward optimal velocity has a significant positive effect in stabilizing the traffic flow. Through nonlinear analysis, a kink-antikink solution is derived from the modified Korteweg-de Vries equation of the FBVD model to explain traffic congestion of the model. The validity of this theoretical model is checked using numerical results, according to which traffic jams were found to have been significantly diminished by the introduction of the modified backward optimal velocity.

A car-following model with the anticipation effect of potential lane changing

In this paper, a new car-following model is presented, taking into account the anticipation of potential lane changing by the leading vehicle. The stability condition of the model is obtained by using the linear stability theory. The modified Korteweg-de Vries （KdV） equation is constructed and solved, and three types of traffic flow in the headway-sensitivity space, namely stable, metastable and unstable ones, are classified. Both the analytical and simu- lation results show that anxiety about lane changing does indeed have an influence on driving behavior and that a consideration of lane changing probability in the car-following model could stabilize traffic flows. The quantitative relationship between stability improvement and lane changing probability is also investigated.

ONE-DIMENSIONAL CELLULAR AUTOMATON MODEL OFTRAFFIC FLOW BASED ON CAR-FOLLOWING IDEA

An improved one-dimensional CA ( Cellular Automaton) traffic model was proposed to describe the highway traffic under the periodic boundary conditions. This model was based on the idea of the car-following model, which claims that the motion of a vehicle at one time step depends on both its headway and the synchronous motion of the front vehicle, thus including indirectly the influence of its sub-neighboring vehicle. It? addition, the so-called safety distance was introduced to consider the deceleration behavior of vehicles and the stochastic factor was taken into account by introducing the deceleration probability. Meanwhile, the conditional deceleration in the model gives a better description of the phenomena observed on highways. It is found that there exists the metastability and hysteresis effect of traffic flow in the neighborhood of critical density under different initial conditions. Since this model gives a reasonable depiction of the motion of a single vehicle, it is easy to be extended to the case of traffic flow tinder the control of traffic lights in cities.

Simulating train movement in railway traffic using a car-following model

Based on a car-following model, in this paper, we propose a new traffic model for simulating train movement in railway traffic. In the proposed model, some realistic characteristics of train movement are considered, such as the distance headway and the safety stopping distance. Using the proposed traffic model, we analyse the space-time diagram of traffic flow, the trajectory of train movement, etc. Simulation results demonstrate that the proposed model can be successfully used for simulating the train movement. Some complex phenomena can be reproduced, such as the complex acceleration and deceleration of trains and the propagation of train delay.