A stochastic two-dimensional intelligent driver car-following model with vehicular dynamics

The law of vehicle movement has long been studied under the umbrella of microscopic traffic flow models,especially the car-following(CF)models.These models of the movement of vehicles serve as the backbone of traffic flow analysis,simulation,autonomous vehicle development,etc.Two-dimensional(2D)vehicular movement is basically stochastic and is the result of interactions between a driver's behavior and a vehicle's characteristics.Current microscopic models either neglect 2D noise,or overlook vehicle dynamics.The modeling capabilities,thus,are limited,so that stochastic lateral movement cannot be reproduced.The present research extends an intelligent driver model(IDM)by explicitly considering both vehicle dynamics and 2D noises to formulate a stochastic 2D IDM model,with vehicle dynamics based on the stochastic differential equation(SDE)theory.Control inputs from the vehicle include the steer rate and longitudinal acceleration,both of which are developed based on an idea from a traditional intelligent driver model.The stochastic stability condition is analyzed on the basis of Lyapunov theory.Numerical analysis is used to assess the two cases:(i)when a vehicle accelerates from a standstill and(ii)when a platoon of vehicles follow a leader with a stop-and-go speed profile,the formation of congestion and subsequent dispersion are simulated.The results show that the model can reproduce the stochastic 2D trajectories of the vehicle and the marginal distribution of lateral movement.The proposed model can be used in both a simulation platform and a behavioral analysis of a human driver in traffic flow.

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.

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 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 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 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 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 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

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.

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.

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.

Car-following Model and Its Stability under Ice and Snowfall Conditions

In order to describe the behavior of the car under ice and snowfall conditions more realistically,a vehicle following model based on the full velocity difference model is proposed under the premise of considering the speed difference and various kinds of ice and snowfall conditions. Under various road conditions,it obtains the critical stability curve of the model,and verifies that the worse the road condition is,the less stable the traffic flow is. In addition,the method of nonlinear analysis is used to obtain the solution of the kink density wave in the space headway under the unstable region. Finally,the conclusions are verified by numerical simulation,that worse road conditions,which means the road surface friction coefficient is small,will lead to greater instability region and worse anti-interference ability of traffic flow,and even cause more congestion and accidents. The conclusions make great contributions to handling the traffic jams and security issues under ice and snowfall conditions.

A novel car-following model by sharing cooperative information transmission delayed effect under V2X environment and its additional energy consumption

A novel car-following model is offered based on the cooperative information transmission delayed effect involving headway and velocity under V2 X environment.The stability conditions and m Kd V equation of the new model are obtained via the linear and nonlinear analysis.Through numerical simulation,the variation trend of headway and hysteresis phenomenon are studied.In addition,we investigate the additional energy consumption of the vehicle during acceleration.In brief,theoretical analysis and simulation results confirm that the new car-following model based on the cooperative information transmission delayed effect can improve traffic stability and reduce additional energy consumption.

Calibration of Car-Following Models Considering the Impacts of Warning Messages from Tablet/Smartphone Application

The phenomenon of car-following is special in traffic operations. Traditional car-following models can well describe the reactions of the movements between two concessive vehicles in the same lane within a certain distance. With the invention of connected vehicle technologies, more and more advisory messages are in development and applied in our daily lives, some of which are related to the measures and warnings of speed and headway distance between the two concessive vehicles. Such warnings may change the conventional car-following mechanisms. This paper intends to consider the possible impacts of in-vehicle warning messages to improve the traditional car-following models, including the General Motor (GM) Model and the Linear (Helly) Model, by calibrating model parameters using field data from an arterial road in Houston, Texas, U.S.A. The safety messages were provided by a tablet/smartphone application. One exponent was applied to the GM model, while another one applied to the Linear (Helly) model, both were on the stimuli term “difference in velocity between two concessive vehicles”. The calibration and validation were separately conducted for deceleration and acceleration conditions. Results showed that, the parameters of the traditional GM model failed to be properly calibrated with the interference of in-vehicle safety messages, and the parameters calibrated from the traditional Linear (Helly) Model with no in-vehicle messages could not be directly used in the case with such messages. However, both updated models can be well calibrated even if those messages were provided. The entire research process, as well as the calibrated models and parameters could be a reference in the on-going connected vehicle program and micro/macroscopic traffic simulations.

A Data-Driven Car-Following Model Based on the Random Forest

The car-following models are the research basis of traffic flow theory and microscopic traffic simulation. Among the previous work, the theory-driven models are dominant, while the data-driven ones are relatively rare. In recent years, the related technologies of Intelligent Transportation System (ITS) re- presented by the Vehicles to Everything (V2X) technology have been developing rapidly. Utilizing the related technologies of ITS, the large-scale vehicle microscopic trajectory data with high quality can be acquired, which provides the research foundation for modeling the car-following behavior based on the data-driven methods. According to this point, a data-driven car-following model based on the Random Forest (RF) method was constructed in this work, and the Next Generation Simulation (NGSIM) dataset was used to calibrate and train the constructed model. The Artificial Neural Network (ANN) model, GM model, and Full Velocity Difference (FVD) model are em- ployed to comparatively verify the proposed model. The research results suggest that the model proposed in this work can accurately describe the car- following behavior with better performance under multiple performance indicators.

Stabilization strategy of a car-following model with multiple time delays of the drivers

An extended car-following model with multiple delays is constructed to describe driver's driving behavior.Through stability analysis,the stability condition of this uncontrolled model is given.To dampen the negative impact of the driver's multiple delays(i.e.,stability condition is not satisfied),a novel control strategy is proposed to assist the driver in adjusting vehicle operation.The control strategy consists of two parts:the design of control term as well as the design of the parameters in the term.Bifurcation analysis is performed to illustrate the necessity of the design of parameters in control terms.In the course of the design of parameters in the control term,we improve the definite integral stability method to reduce the iterations by incorporating the characteristics of bifurcation,which can determine the appropriate parameters in the control terms more quickly.Finally,in the case study,we validate the control strategy by utilizing measured data and configuring scenario,which is closer to the actual traffic.The results of validation show that the control strategy can effectively stabilize the unstable traffic flow caused by driver's delays.

Stabilisation analysis of multiple car-following model in traffic flow

An improved multiple car-following model is proposed by considering the arbitrary number of preceding cars, which includes both the headway and the velocity difference of multiple preceding cars. The stability condition of the extended model is obtained by using the linear stability theory. The modified Korteweg-de Vries equation is derived to describe the traffic behaviour near the critical point by applying the nonlinear analysis. Traffic flow can be also divided into three regions： stable metastable and unstable regions. Numerical simulation is in accordance with the analytical result for the model. And numerical simulation shows that the stabilisation of traffic is increasing by considering the information of more leading cars and there is unavoidable effect on traffic flow from the multiple leading cars information.

Multiple car-following model of traffic flow and numerical simulation

On the basis of the full velocity difference （FVD） model, an improved multiple car-following （MCF） model is proposed by taking into account multiple information inputs from preceding vehicles. The linear stability condition of the model is obtained by using the linear stability theory. Through nonlinear analysis, a modified Korteweg-de Vries equation is constructed and solved. The traffic jam can thus be described by the klnk-antikink soliton solution for the mKdV equation. The improvement of this new model over the previous ones lies in the fact 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, numerical simulation of traffic dynamics shows that the proposed model can avoid the disadvantage of negative velocity that occurs at small sensitivity coefficients λ in the FVD model by adjusting the information on the multiple leading vehicles. No collision occurs and no unrealistic deceleration appears in the improved model.

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.