Full Velocity Difference Model Research Articles

Traffic model for the dynamical behavioral study of a traffic system imposing push and pull effects

In this study, a novel traffic model, namely the push-pull model (PPM), has been developed considering not only forward-looking effects but also how focal vehicles are influenced by their following vehicle. The developed model represents a traffic flow field whose flow is significantly different from the conventional full velocity difference model in the congestion region but is analogous to the actual traffic flow system. We focused on linear analysis, nonlinear analysis, and numerical simulation to validate our model. Linear stability analysis determines the stability condition, delineating stable and unstable regions of traffic flow. The phase diagram of stability analysis demonstrates that the PPM has a crucial positive impact on traffic flow stabilization. In the case of nonlinearity, a kink-antikink soliton solution is generated from the modified Korteweg-de Vries equation, which is derived from the push-pull effect model to interpret traffic congestion. Furthermore, to check the validity of the theoretical results of this model, a numerical simulation has been conducted, demonstrating significant suppression of traffic congestion by considering push and pull effects.

Car-following model based on spatial expectation effect in connected vehicle environment: modeling, stability analysis and identification

In driving situations, if drivers have advanced access to downstream traffic conditions ahead of time, they may modify their driving behavior accordingly. This proactive approach can help reduce frequent acceleration and deceleration of vehicles and minimize traffic congestion. This paper considers the average headway of downstream vehicles to predict the traffic conditions of downstream roads. Based on the full velocity difference (FVD) model, we propose a car-following model that incorporates spatial expectation effect (SEFVD). Firstly, a linear stability analysis is performed on the SEFVD model, and the results indicate that the critical value of the SEFVD model is relatively small, and the stabilization region increases gradually with the number of vehicles downstream. Secondly, employing perturbation amplitudes on a virtual circular road, a numerical simulation of the SEFVD model is carried out and compared with the FVD model. The results demonstrate that the SEFVD model has the ability to suppress the formation of traffic oscillations and stabilize vehicle formation more quickly. Simulation results for the 11 cars starting from a traffic signal indicate that the delay time and kinematic wave speed of the SEFVD model are within reasonable limits. To evaluate the changes in energy use, we also carried out energy consumption experiments. The experimental findings show that the SEFVD model uses less energy compared to the FVD model. Finally, the parameters of the models are calibrated and verified by using NGSIM data. The total calibration error of the SEFVD model (m = 2) decreases by 42.97% compared to the FVD model, and the total validation error decreases by 29.3%. The results show that the proposed model can fit the actual data well, and the fitting error is smaller.

A mixed-flow model for heterogeneous vehicles enforcing a movement control protocol utilizing a vehicular size-based equilibrium speed function

This work addressed the effect of heterogeneous vehicle sizes on traffic flow fields by introducing a movement control protocol. Considering a continuum traffic model, a new equilibrium velocity function that is dependent on traffic density was introduced to account for the effect of vehicle size. The established model showed a quantitative comparison between the Optimal Velocity and Full Velocity Difference models. A neutral stability test was carried out to evaluate the model's capability of neutralizing flow fields. The density wave behavior near a critical point was portrayed by deducing the Korteweg–de Vries–Burgers equation through a nonlinear analysis. A series of numerical simulations, the outcomes of which agreed well with the analytical results, was performed to observe the overall flow field scenario.

Effects of connected automated vehicle on stability and energy consumption of heterogeneous traffic flow system

With the development of intelligent and interconnected traffic system, a convergence of traffic stream is anticipated in the foreseeable future, where both connected automated vehicle (CAV) and human driven vehicle (HDV) will coexist. In order to examine the effect of CAV on the overall stability and energy consumption of such a heterogeneous traffic system, we first take into account the interrelated perception of distance and speed by CAV to establish a macroscopic dynamic model through utilizing the full velocity difference (FVD) model. Subsequently, adopting the linear stability theory, we propose the linear stability condition for the model through using the small perturbation method, and the validity of the heterogeneous model is verified by comparing with the FVD model. Through nonlinear theoretical analysis, we further derive the KdV-Burgers equation, which captures the propagation characteristics of traffic density waves. Finally, by numerical simulation experiments through utilizing a macroscopic model of heterogeneous traffic flow, the effect of CAV permeability on the stability of density wave in heterogeneous traffic flow and the energy consumption of the traffic system is investigated. Subsequent analysis reveals emergent traffic phenomena. The experimental findings demonstrate that as CAV permeability increases, the ability to dampen the propagation of fluctuations in heterogeneous traffic flow gradually intensifies when giving system perturbation, leading to enhanced stability of the traffic system. Furthermore, higher initial traffic density renders the traffic system more susceptible to congestion, resulting in local clustering effect and stop-and-go traffic phenomenon. Remarkably, the total energy consumption of the heterogeneous traffic system exhibits a gradual decline with CAV permeability increasing. Further evidence has demonstrated the positive influence of CAV on heterogeneous traffic flow. This research contributes to providing theoretical guidance for future CAV applications, aiming to enhance urban road traffic efficiency and alleviate congestion.

Exploring Heterogeneity in Car-Following Behaviors Based on Driver Visual Characteristics: Modeling and Calibration

To investigate the heterogeneity of car-following behaviors across different vehicle combinations from the perspective of driver visual characteristics, the NGSIM dataset from I-80 and US-101 highways was selected and distinct car-following segments were extracted for analysis. Firstly, all the effective vehicle trajectories were extracted and categorized into different vehicle types based on their widths, resulting in four combination types of car-following segments. Visual angle and its change rate were introduced as variables representing driver visual characteristics. Additionally, one-way analysis of variance (ANOVA) was used to compare these variables with traditional ones. The driver’s visual characteristic variables were then incorporated to improve the full velocity difference (FVD) model. Genetic algorithms were employed to calibrate the model under different car-following types, revealing pronounced behavioral variations. After implementing the enhanced drivers’ visual angle (DVA) model, substantial reductions in calibration and validation errors were observed, with calibration errors decreasing by 51.93% and 42.22% and validation errors decreasing by 56.61% and 45.26%. This indicates the DVA model’s remarkable adaptability and stability. Lastly, through a sensitivity analysis of errors, the DVA model demonstrated greater robustness toward the improved error evaluation function. By integrating drivers’ visual characteristics, this study provides in-depth insights into heterogeneous car-following behaviors, enhancing our understanding of driver behaviors and micro-traffic simulation systems.

An improved car-following model considering the influence of multiple preceding vehicles in the same and two adjacent lanes

To investigate the driver's car-following behavior in multiple lanes, this study develops an improved multi-lane full velocity difference (FVD) model. This model considers the positions and widths of multiple preceding vehicles in the same lane in the longitudinal direction, as well as the lateral offset distances of the immediately preceding vehicles in the same and two adjacent lanes in the lateral direction. Based on the linear stability analysis, it is found that an increase in the lateral offset distances between a vehicle and its predecessors in the same lane is negative to the traffic flow stability, whereas an increase in the widths of front vehicles in the same lane within a certain range is beneficial to the traffic flow stability. These theoretical findings are verified by numerical simulations. With the use of a publicly available dataset of vehicle trajectories from Southeast University, this study extracts the microscopic traffic flow parameters of the following vehicles and their associated vehicles on urban roads in China. Through parameter calibration and model comparison, it is found that the developed improved multi-lane FVD model has greater adaptability than the conventional FVD model and existing improved FVD models, and its mean absolute error and root mean square error are to some extent optimized. With the rapid development of connected vehicle technology, the developed multi-lane FVD model can be used to assist drivers in making rational behavioral decisions and improve traffic flow stability.

Modeling and simulation of traffic flow based on memory effect and driver characteristics

In this paper, an improvement of the full velocity difference model is presented, which comprehensively considers driver characteristics which include aggressive and timid behaviors and memory effect. The stability condition of the improved model is obtained by making use of the small perturbation method. The Burgers, Korteweg–de Vries and modified Korteweg–de Vries equations are derived by means of the reductive perturbation method. Finally, through numerical simulation, the traffic flow evolution process of the improved model under two typical conditions is observed. The first is the starting process, and the second is the propagation process of disturbance in traffic flow. The results of numerical simulation and theoretical analysis demonstrate that the multiple driver characteristics considered in the improved model have important influences on traffic flow stability and the ease of traffic jams, and the model can quickly recover to its original state in case of the disturbance. • A new car following model is presented, which considers memory effect and driver characteristics including aggressive and timid behaviors. • The stability conditions of the extended model are obtained with the use of the small perturbation method. • The Burgers, Korteweg–de Vries and modified Korteweg–de Vries equations are derived by means of the reduced perturbation method. • The starting process and the propagation process of disturbance are carried out, the results are much closer to actual traffic.

A Trajectory Compensation Method Considering the Car-Following Behavior for Data Missing of Millimeter-Wave Radar in Roadside Detection Applications.

Concerning roadside traffic detection applications, and to address the millimeter-wave radar's missing data problem caused by target occlusion or the absence of features in low-speed conditions, this paper proposes a trajectory compensation method regarding car-following behavior. Referring to the installation scheme of the detector, a coordinate transformation method is presented to unify the radar spatial coordinates with the road coordinates. Considering the driver's car-following behavior, the optimal velocity model (OV), full velocity difference model (FVD), and the full velocity difference and acceleration (FVDA) model are applied for tracking the vehicle's trajectory related to the movement of the vehicle ahead. Finally, a data compensation scheme is presented. Taking actual trajectory data as samples, the proposed methods are verifiably useful for compensating for missing data and reconstructing target trajectories. Statistical results of different missing data trajectories demonstrate the rationality of the application of car-following models for the missing data compensation, and the FVDA model performs well compared with the OV and FVD models.

On the driver's stochastic nature in car-following behavior: Modeling and stabilizing based on the V2I environment

<abstract> <p>The driver's stochastic nature is one of the important causes of traffic oscillation. To better describe the impact of the driver's stochastic characteristics on car-following behavior, we propose a stochastic full velocity difference model (SFVDM) considering the stochastic variation of the desired velocity. In order to mitigate traffic oscillation caused by driving stochasticity, we further propose a stable speed guidance model (S-SFVDM) by leveraging vehicle-to-infrastructure communication. Stochastic linear stability conditions are derived to demonstrate the prominent influence of the driver's stochasticity on the stability of traffic flow and the improvement of traffic flow stability by the proposed guidance strategy, respectively. We present numerical tests to demonstrate the effectiveness of the proposed models. The results show that the SFVDM can capture the traffic oscillation caused by the driver's stochastic desired velocity and reproduce the same disturbance growth pattern as in the field experiment. The results also indicate that the S-SFVDM can significantly expand the stable area of traffic flow to decrease the negative impact on traffic flow stability caused by the driver's stochastic nature.</p> </abstract>

Vehicle type-dependent heterogeneous car-following modeling and road capacity analysis

Due to the lack of natural driving databases containing heterogeneous traffic in the existing heterogeneous car-following modeling research, there is an urgent need for the support of a large amount of measured trajectory data for modeling. To this end, four different car-following modes of heterogeneous traffic under the influence of different vehicle types are extracted from the HighD data set, with which the statistical characteristics of the following car speed, speed difference, gap, time headway and acceleration in each mode are studied separately. Moreover, the correlation analysis of two parameters in speed-gap and speed difference-gap is carried out. On this basis, the intelligent driver model (IDM) and the full velocity difference (FVD) model are, respectively, employed to model the car-following characteristics in each mode. The results show that the existence of the truck in the following vehicle pair makes the following vehicle tend to maintain a larger gap and a smaller following speed, that is, larger time headway and gap. With the increase of trucks’ ratio, the capacity of traffic decreases. The research can lay the foundation for more accurate mixed traffic flow modeling of heterogeneous human driving vehicles, and even subsequent research on heterogeneous traffic characteristics under a mixture of human driving vehicles and autonomous vehicles.

A Fuzzy Full Velocity Difference Model Based on Driver’s Perception Characteristics

The perception characteristics of drivers greatly vary with the status of traffic flow. To designate the vehicle trajectory more accurately, a driver’s perception headway coefficient is introduced, and a fuzzy full velocity difference (FVD) model is proposed in this paper. Consistent with the control theory, the stability conditions of the improved model are derived. Through the fuzzy control method, the input and output items of the control rule are constructed, respectively. The genetic algorithm is operated to calibrate the model parameters of timid and aggressive drivers. Eventually, the effectiveness of the model is verified by simulations. The research results show that, with the decrease of driver’s perception headway coefficient, the stability range of the traffic flow gradually increases, which is beneficial. Additionally, the average root means square percentage errors (RMSPE) values of the full velocity difference (FVD) model, the intelligent driver model (IDM), and the proposed model are, respectively, 0.312, 0.308, and 0.213. Compared with IDM and FVD models, the proposed model can accurately describe the local velocity variations and determine the car-following behavior of the human driving vehicle better.

Investigation of car-following models in disordered traffic using trajectory data obtained from unmanned aerial vehicles

ABSTRACT Car-following models are the cornerstones of microscopic traffic simulation tools and intelligent transportation systems, but the applicability of car-following models to disordered traffic have not been investigated in detail with longer trajectory dataset. To address this gap, two car-following models namely, Intelligent Driver Model (IDM) and Full Velocity Difference Model (FVDM) are calibrated using trajectory data collected on an urban arterial road in Chennai, India using Unmanned Aerial Vehicles. The raw data are smoothed for noise removal and the car-following pairs are identified based on the lateral overlap and following duration. The models are calibrated by minimizing the deviations between the observed and simulated longitudinal gaps between leader and follower using genetic algorithm. The obtained errors are between 2.5% and 19.5%, which are comparable with standard ranges of error reported in literature. The optimal parameter values represent the distinct characteristics of disordered traffic in comparison with the homogeneous traffic.

Use of an Improved Car-Following Model to Explain the Influence of Traffic Composition on Saturation Headway at Signalized Intersections

Previous studies mainly used statistical methods to analyze the impact of traffic composition on saturation flow rate from the mesolevel, and there is insufficient research on how traffic composition affects driving behavior. Thus, the purpose of this paper is to establish a more accurate car-following model, establish the relationship between microbehavior and mesostatistical regularity, and explain the influence of vehicle composition on saturation headway. In this paper, an improved full velocity difference (FVD) model is proposed, which abstracts the driver characteristics of a heterogeneous flow into four scenarios: car-car, car-bus, bus-car, and bus-bus. The measured data are used to calibrate and verify the basic FVD and the improved FVD models. The performance of the improved model is significantly improved. The RMSE and RMSPE are reduced by 15.29% and 22.32%, respectively. Finally, through numerical simulation experiments, the variation of saturation headway with different proportions of buses is analyzed. The saturation headway increases with the increase of the proportion of heavy vehicles. Moreover, another important finding is that the saturation headway is not significantly influenced by the position of the buses but only by the proportion of the buses. The research results could provide theoretical support for the control and management of fleets composed of different vehicles at intersections.

Incorporation of Human Factors to a Data-Driven Car-Following Model

In recent years, there have been intensive efforts to consider human factors (HFs) in the modeling of human driver behavior. In particular, “engineering” car-following models widely used in traffic simulation have been extended to include HFs. This extension is needed to generate critical situations, which are often attributable to human error. However, incorporation of reaction processes requires advanced models that take driver predictions and delayed responses into account. In this paper, a methodology for integrating HFs into driver behavior modeling is developed based on a long short-term memory architecture. The proposed methodology employed a three-layer psychological concept: perception, information processing, and action. The perception layer modeled (imperfect) estimation of visually received stimuli. Information processing included short-term memory and the projection of perceived stimuli into the near future. The executed action, based on the sensed as well as anticipated dynamic driving state, was delayed by the perception–reaction time. To represent individual differences among driver types, the available training dataset was classified in four clusters according to observable driver characteristics. The methodology was demonstrated with data recorded at an urban signalized intersection. Model performance was compared with that of two established engineering models, the intelligent driver model and the (extended) full velocity difference model. The results indicated that the human driver model developed here showed superior performance in replicating real-world trajectories compared with existing models and was able to represent the varying driving strategies of different groups.

Integrated-Hybrid Framework for Connected and Autonomous Vehicles Microscopic Traffic Flow Modelling

In this study, a novel traffic flow modeling framework is proposed considering the impact of driving system and vehicle mechanical behavior as two different units on the traffic flow. To precisely model the behavior of Connected and Autonomous (CA) vehicles, three submodels are proposed as a novel microscopic traffic flow framework, named Integrated-Hybrid (IH) model. Focusing on the realization of the car following behavior of CA vehicles, the driving system (vehicle control system) and the vehicle mechanical system are modeled separately and linked by throttle and brake actuators model. The IH model constitutes the key part of the Full Velocity Difference (FVD) model considering the mechanical capability of vehicles and dynamic collision avoidance strategies to ensure the safety of following distance between two consecutive vehicles. Linear stability conditions are derived for each model and developing methodology for each submodel is discussed. Our simulations revealed that the IH model successfully generates velocity and acceleration profiles during car following maneuvers and throttle angle/brake information in connected vehicles environment can effectively improve traffic flow stability. The vehicles’ departure and arrival process while passing through a signal-lane with a traffic light considering the anticipation driving behavior and throttle angle/brake information of direct leading vehicle was explored. Our numerical results demonstrated that the IH model can capture the velocity fluctuations, delay times, and kinematic waves efficiently in traffic flow.

Steady-state performance and dynamic performance of heterogeneous platoons under a connected environment

Under the vehicle-to-vehicle (V2V) environment, the steady-state performance and the dynamic performance are both crucial for the traffic system. This paper proposes an in-depth methodology to provide some insights into the comprehensive changes of steady-state performance and dynamic performance of a heterogeneous platoon, which contains human-driven vehicles (HDVs) and connected and automated vehicles (CAVs). To further understand the impacts of various feedback information, an improved full velocity difference model that incorporates multiple feedback communicating information is developed. Based on the transfer function, the stability and steady-state error are proposed to characterize the steady-state performance, while the degree of fluctuation and duration of fluctuation are used to measure the dynamic performance. On the one hand, a key finding is that there are inconsistencies in steady-state and dynamic performance under particular feedback information. The acceleration or spacing feedback information can enhance the steady-state performance while degrading the dynamic performance. The speed difference feedback information yields the opposite result. On the other hand, it is discovered that compared to several types of feedback information, combining just one type of information is enough to boost the platoon performance. When the number of CAVs is considerable, combining two types of information will considerably increase the duration time. Therefore it is important to find the key feedback information for the platoon performance. The main purpose of this paper is to present a methodology of platoon performance analysis instead of discussing the various traffic scenarios. As a result, while certain results may alter in some specific scenarios, the proposed methodology and core contribution remain applicable to various traffic scenarios.

Bifurcation Analysis of Aggressive and Cautious Driving Behavior in Full Velocity Difference Model

Bifurcation Analysis of Aggressive and Cautious Driving Behavior in Full Velocity Difference Model

The “backward-looking” effect in the continuum model considering a new backward equilibrium velocity function

In this paper, a new continuum traffic model is developed considering the backward-looking effect through a new positive backward equilibrium speed function. As compared with the conventional full velocity difference model, the backward equilibrium velocity function, which is largely acceptably grounded from mathematical and physical perspectives, plays an important role in significantly enhancing the stability of the traffic flow field. A linear stability condition is derived to demonstrate the flow neutralization capacity of the model, whereas the Korteweg–de Vries–Burgers equation and the attendant analytical solution are deduced using nonlinear analysis to observe the traffic flow behavior near the neutral stability condition. A numerical simulation, used to determine the flow stability enhancement efficiency of the model, is also conducted to verify the theoretical results.

A microscopic traffic flow model for sharing information from a vehicle to vehicle by considering system time delay effect

In this study, we propose an information-sharing traffic flow model by considering multiple preceding cars and system time delay effect to reproduce a more likely flow field given the dissemination of intelligent transportation systems with wireless communication. The flow field would be robustly stable and efficient if the information on each vehicle’s dynamics could be shared without time delay. However, a realistic situation inevitably entails some time delay, resulting from mechanical and control systems. The proposed model is validated by the neutral stability condition through linear stability theory, thus confirming that the proposed model substantially increases the stability of a traffic flow field compared with the conventional full velocity difference model (optimal velocity model). The modified Korteweg–de Vries equation is derived and analyzed for nonlinear analysis. A numerical simulation is also conducted to justify the proposed model.

Analysis of road capacity and pollutant emissions: Impacts of Connected and automated vehicle platoons on traffic flow

Connected and Automated Vehicles (CAV) are currently not intelligent enough to deal with complex traffic conditions. CAVs traveling in platoons can reduce external interference and further improve road capacity. Therefore, a mixed traffic capacity gain formula was constructed, considering both communication interaction and size limitations of CAV platoons. CAVs are divided into three types in a mixed traffic environment in terms of different states and positions. A model was constructed to examine how several parameters affect capacity, and these capacity-improving parameters were used to indicate coefficients of headway gains. Additionally, an empirical formula for pollutant emissions with different headway gains is applied in the mixed traffic. A series of microsimulations are tested based on the improved Full Velocity Difference (FVD) model and CAV models which are established as discrete steps based on the above analyses. The simulation results are highly consistent with the theoretical analyses, demonstrating the universality of this model. Finally, it indicated that the overall optimal size of CAV platoons is between 5 and 10 when taking both the road capacity and pollutant emissions into consideration.