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.

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 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 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.

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.

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.

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 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

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.

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.

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.

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.

Car-following model featured with factors reflecting emergency evacuation situation

A new emergency evacuation car-following model （EECM） is proposed. The model aims to capture the main characteristics of traffic flow and driver behavior under an emergency evacuation, and it is developed on the basis of minimum safety distances with parts of the drivers＇ abnormal behavior in a panic emergency situation. A thorough questionnaire survey is undertaken among drivers of different ages. Based on the results from the survey, a safety-distance car-following model is formulated by taking into account two new parameters： a differential distributing coefficient and a driver＇ s experiential decision coefficient, which are used to reflect variations of driving behaviors under an emergency evacuation situation when compared with regular conditions. The formulation and derivation of the new model, as well as its properties and applicability are discussed. A case study is presented to compare the car-following trajectories using observed data under regular peak-hour traffic conditions and theoretical EECM results. The results indicate the consistency of the analysis of assumptions on the EECM and observations.

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.

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.

Study on Performances of Car-following Models Induced by Motions of a Leading Car

This paper investigated the performances of a well-known car-following model with numerical simulations in describing the deceleration process induced by the motion of a leading car. A leading car with a pre-specilied speed profile was used to test the above model. The results show that this model is to some extent deficient in performing the process aforementioned. Modifications of the model to overcome these deficiencies were demonstrated anda modified car-following model was proposed accordingly. Furthermore, the delay time of car motion of the new model were studied.

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.