Traffic Oscillations Research Articles

Car following behavioral stochasticity analysis and modeling: Perspective from wave travel time

This paper analyzes the car following behavioral stochasticity based on two sets of field experimental trajectory data by measuring the wave travel time series τ˜n(t) of vehicle n. The analysis shows that (i) No matter the speed of leading vehicle oscillates significantly or slightly, τ˜n(t) might change significantly; (ii) A follower's τ˜n(t) can vary from run to run even if the leader travels at the same stable speed; (iii) Sometimes, even if the leader's speed fluctuates significantly, the follower can keep a nearly constant value of τ˜n(t). The Augmented Dickey-Fuller test indicates that the time series ξn(t)=dτ˜n(t)/dt follows a mean reversion process, no matter the oscillations fully developed or not. Based on the finding, a simple stochastic Newell model is proposed. The concave growth pattern of traffic oscillations has been derived analytically. Furthermore, simulation results demonstrate that the new model well captures both macroscopic characteristic of traffic flow evolution and microscopic characteristic of car following.

Platoon Trajectories Generation: A Unidirectional Interconnected LSTM-Based Car-Following Model

Car-following models have been widely applied and made remarkable achievements in traffic engineering. However, the traffic micro-simulation accuracy of car-following models in a platoon level, especially during traffic oscillations, still needs to be enhanced. Rather than using traditional individual car-following models, we proposed a new trajectory generation approach to generate platoon level trajectories given the first leading vehicle’s trajectory. In this article, we discussed the temporal and spatial error propagation issue for the traditional approach by a car following block diagram representation. Based on the analysis, we pointed out that error comes from the training method and the model structure. In order to fix that, we adopt two improvements on the basis of the traditional LSTM-based car-following model. We utilized a scheduled sampling technique during the training process to solve the error propagation in the temporal dimension. Furthermore, we developed a unidirectional interconnected LSTM model structure to extract trajectories features from the perspective of the platoon. As indicated by the systematic empirical experiments, the proposed novel structure could efficiently reduce the temporal-spatial error propagation. Compared with the traditional LSTM-based car-following model, the proposed model has almost 40% less error. The findings will benefit the design and analysis of micro-simulation for platoon-level car-following models.

Systematic Evaluation of a Multi-Lane Green-Driving Algorithm in a Mixed Connected Environment

Vehicles traveling under oscillated traffic have low energy efficiency and high air pollutant emissions. Green driving with the help of connected vehicles (CVs) attracts a lot of research effort to improve vehicle energy efficiency. However, it is very challenging to perform green driving on multi-lane freeways under a mixed connected environment. In the researchers’ previous work, one innovative green-driving algorithm was proposed to solve the multi-lane problem with only one CV. In this study, a systematic analysis of the algorithm is conducted to understand its benefits and limitations on smoothing traffic oscillations. The effect of the steady states and the number of lanes is also analyzed. In addition, the algorithm is extended to a more general scenario with multiple CVs. The extended system coordinates multiple CVs to form multiple moving bottlenecks to mitigate traffic oscillation more efficiently as well as providing more realistic instructions to CVs. The evaluation of the extended system concludes with the most effective strategies to control CVs to smooth oscillations.

The relationship between car following string instability and traffic oscillations in finite-sized platoons and its use in easing congestion via connected and automated vehicles with IDM based controller

This paper focuses on two fundamental issues in traffic flow modelling: string stability of car following (CF), and oscillation of traffic flow. Its aim is to explore the complementary use of CF instability analysis and oscillation analysis to compress and ease traffic congestion in a connected environment. Each of these topics has been extensively investigated in the literature. However, each topic has been investigated separately and, despite the inherent conceptual and empirical closeness of the two concepts, little effort has been devoted to untangling their relationship.To address this failing, we first define four types of oscillation – amplitude-decay oscillation, amplitude-ceiling oscillation, speed-deviation ceiling oscillation, and speed-deviation growth oscillation – and reveal their similarities and dissimilarities to CF instability. Based on the stability criterion, we then develop oscillation criteria to identify different types of oscillation by relaxing two unrealistic assumptions used in CF stability analysis (i.e., infinitely-long platoon and long-wavelength perturbation). Finally, to demonstrate how CF instability analysis and oscillation analysis can be combined to influence individual vehicle stability and improve traffic oscillations in a connected environment, a platoon of vehicles that experience an oscillation in the NGSIM data is used in a case study. In this case study, different control factors are used for different vehicle types: connected (but human-driven) vehicles, and automated vehicles.Our analysis shows that a higher stability of some individual vehicles can alleviate the oscillation severity for the platoon. It also shows that desired time gap and maximum acceleration are two promising parameters that can be used to both improve individual vehicle stability and significantly smooth the oscillation of the platoon in a connected and/or automated environment. Of particular note, when considering all of the factors explored in our analysis, adjustment of the desired time gap is the most effective factor in smoothing traffic oscillations.

Eco-Driving Algorithm with a Moving Bottleneck on a Single-Lane Road

Eco-driving strategies have been applied to smooth traffic flow and reduce greenhouse gas emissions along with air pollution. In this paper, we propose an eco-driving strategy to reduce traffic oscillation and smooth trajectories for connected vehicles following a moving bottleneck on a single-lane road. The eco-driving strategy, which leverages vehicle-to-vehicle (V2V) communications, designs advisory speed limits for each following vehicle through a control algorithm. The algorithm is based on the prediction of the following vehicle trajectories dictated by a moving bottleneck. The following vehicle trajectories are obtained by analytically solving the moving bottleneck problem in which the moving bottleneck speeds vary over time. In addition, the bounded acceleration rate is imposed in car-following behavior. The benefits of this strategy are demonstrated by applying it to four scenarios with different bottleneck movements. By simulating the scenarios with Newell’s car-following model with bounded acceleration and VT-Micro emission model, we find that both speed fluctuations and emissions are reduced with the algorithm in the scenarios in which the moving bottleneck has a constant speed, accelerates, decelerates and stops-and-goes. The results indicate that the proposed eco-driving algorithm can smooth traffic flow behind a moving bottleneck.

A study of relationships in traffic oscillation features based on field experiments

• Collect field trajectory data with periodic oscillation settings. • Propose a new time-domain method to estimate oscillation features. • Quantitatively reveal the relationships between traffic oscillation features. • Estimate a time gap function to improve the performance of car following models. Despite numerous theoretical models, only limited field experiments have been conducted to investigate traffic oscillation propagation, and the relationships between traffic oscillation features (e.g., period, speed variation, spacing and headway) have not received quantitative analysis. This study conducts a set of field experiments designed to inspect such relationships. In these experiments, 12 vehicles equipped with high-resolution global positioning system (GPS) devices following one another on public roads, and the lead vehicle was asked to move with designed trajectory profiles incorporating various parameters. Measurements of five features are extracted from processing the field vehicle trajectory data with a time-domain method. Frequency analysis is also proposed with the Fourier transform method to verify the effectiveness of the features measured by the time-domain method. Compared to the frequency-domain method, the time-domain method yields more measurements with comparable quality and is more robust on trajectories with a small number of oscillation cycles. Then, a series of linear regression analyses reveal a number of new findings on the relationships between these features. For example, the time gap between two consecutive vehicles is negatively correlated with the speed standard deviation of the preceding vehicle and the initial speed of the following vehicle. It is also positively correlated with the average speed of the preceding vehicle and the initial spacing. The findings are helpful in constructing new microscopic traffic models better describing traffic oscillation dynamics. To illustrate this benefit, revised car following models are proposed to capture the relationship between time gap and other features. The simulation results show that the revised models yield better prediction accuracy (in range of 18% to 40% with the oscillation experiment dataset and in range of 30–63% with the stationary experiment dataset) than the classical models on reproducing real-world trajectories.

Formalizing the heterogeneity of the vehicle-driver system to reproduce traffic oscillations

Road traffic congestion is the result of various phenomena often of random nature and not directly observable with empirical experiments. This makes it difficult to clearly understand the empirically observed traffic instabilities. The vehicles’ acceleration/deceleration patterns are known to trigger instabilities in the traffic flow under congestion. It has been empirically observed that free-flow pockets or voids may arise when there is a difference in the speeds and the spacing between the follower and the leader increases. During these moments, the trajectory is dictated mainly by the characteristics of the vehicle and the behaviour of the driver and not by the interactions with the leader. Voids have been identified as triggers for instabilities in both macro and micro level, which influence traffic externalities such as fuel consumption and emissions. In the literature, such behaviour is usually reproduced by injecting noise to the results of car-following models in order to create fluctuations in the instantaneous vehicles’ acceleration.This paper proposes a novel car-following approach that takes as input the driver and the vehicle characteristics and explicitly reproduces the impact of the vehicle dynamics and the driver’s behaviour by adopting the Microsimulation Free-flow aCceleration (MFC) model. The congested part of the model corresponds to the Lagrangian discretization of the LWR model and guarantees a full consistency at the macroscopic scale with congested waves propagating accordingly to the first-order traffic flow theory.By introducing naturalistic variation in the driving styles (timid and aggressive drivers) and the vehicle characteristics (specification from different vehicle models), the proposed model can reproduce realistic traffic flow oscillations, similar to those observed empirically. An advantage of the proposed model is that it does not require the injection of any noise in the instantaneous vehicle accelerations.The proposed methodology has been tested by studying a) the traffic flow oscillations produced by the model in a one-lane road uphill simulation scenario, b) the ability of the model to reproduce car-following instabilities observed in three car-following trajectory datasets and c) the ability of the model to produce realistic fuel consumption estimates. The results prove the robustness of the proposed model and the ability to describe traffic flow oscillations as a consequence of the combination of driving style and vehicle’s technical specifications.

Deep Reinforcement Learning-Based Vehicle Driving Strategy to Reduce Crash Risks in Traffic Oscillations

The primary objective of this study is to propose a deep reinforcement learning-based driving strategy for individual vehicles to mitigate oscillations and optimize traffic safety in stop-and-go waves. A deep deterministic policy gradient (DDPG)-based driving strategy, which requires information that is directly obtained by in-vehicle sensors, is proposed for system performance optimization. Two typical scenarios were simulated based on simulation software (SUMO): (i) the leading vehicle slowed down according to real trajectory data to produce one oscillation; (ii) the leading vehicle conducted several abrupt decelerations with various degrees of disturbance to produce multiple oscillations. The DDPG agents interacted with the SUMO platform to determine the optimal acceleration of vehicles that can reduce crash risks in various stop-and-go waves. The results showed that the proposed DDPG-based driving strategy successfully reduced the crash risk by 68.9%–78.4%. Scenarios with different penetration rates of DDPG agents and in various flow rates were compared to test the effect of the proposed strategy. The DDPG-based driving strategy reduced crash risk more with the increase of penetration rate and this strategy performed better when applied in the scenario with a high traffic flow rate. The proposed strategy is compared with the adaptive cruise control and jam-absorbing driving strategies. Results showed the proposed strategy outperformed other oscillation mitigating strategies in reducing crash risks.

Impact of Stochasticity on Traffic Flow Dynamics in Macroscopic Continuum Models

Stochasticity is an indispensable factor for describing real traffic situations. Recent experimental study has shown that a model spanning a two-dimensional speed–spacing (or speed–density) relationship has the potential to reproduce the characteristics of traffic flow in both experiments and empirical observations. This paper studies the impact of stochasticity on traffic flow in macroscopic models utilizing the stochastic flow–density relationship. Numerical analysis is conducted under the periodic boundary to study the impact of stochasticity on stability. Traffic flow upstream of a bottleneck is also investigated to study the impact of stochasticity on the oscillation growth feature. It is shown that there is only a quantitative difference for model stability after introducing stochasticity. In contrast, a qualitative change of the traffic oscillation growth feature can be clearly observed. With the introduction of stochasticity, traffic oscillations begin to grow in a concave way along the road. Sensitivity analysis is also performed. It is found that, under the stochastic flow–density relationship: (i) with the decrease of relaxation time, the second-order model becomes stable; (ii) the smaller the propagation speed of small disturbance, the much stronger the traffic oscillation; (iii) the larger the fluctuation range, the sooner the traffic oscillation fully develops; and (iv) the changing probability has trivial impact on the simulation results. Finally, model calibration and validation are conducted. It is shown that the experimental spatiotemporal patterns can be captured by macroscopic models under the stochastic flow–density relationship, especially the second-order model.

Statistical inference for two-regime stochastic car-following models

This paper presents the formulation of a family of two-regime car-following models where both free-flow and congestion regimes obey statistically independent random processes. This formulation generalizes previous efforts based on Brownian and geometric Brownian acceleration processes, each reproducing a different feature of traffic instabilities. The probability density of vehicle positions turns out to be analytical in our model, and therefore parameters can be estimated using maximum likelihood. This allows us to test a wide variety of hypotheses using statistical inference methods, such as the homogeneity of the driver/vehicle population and the statistical significance of the impacts of roadway geometry. Using data from two car-following experiments, we find that (i) model parameters are similar across repeated experiments within the same dataset but different across datasets, (ii) the acceleration error process is closer to a Brownian motion, and (iii) drivers press the gas pedal harder than usual when they come to an upgrade segment. Additionally, we explain the cause of traffic oscillations traveling downstream, which were observed both in the field data and in our simulations. The model is flexible so that newer vehicle technologies can be incorporated to test such hypotheses as differences in the car-following parameters of automated and regular vehicles, when data becomes available.

A new two-lane lattice hydrodynamic model with the introduction of driver’s predictive effect

This paper devises a new two-lane lattice hydrodynamic model (TLHM) to explore driver’s predictive effect (DPE) on traffic oscillation. First, a linear approach is conducted to analytically predict the DPE on traffic performance. Theoretical analysis shows that with the help of DPE, the traffic flow stability will be gradually enhanced. Then, nonlinear analysis is implemented to explore the characteristics of traffic oscillation when sensitivity coefficient is near the critical point. The modified KdV equation derived from the new model and its analytical solution related kink–antikink density waves are obtained. Finally, numerical experiments show that the DPE can effectively dampen the growth of oscillation, which is well consistent with the theoretical analysis of the new model.

Defining Highway Node Acceptance Capacity (HNAC): Theoretical Analysis and Data Simulation

A new concept of Highway Node Acceptance Capacity (HNAC) is proposed in this paper inspired by a field data observation. To understand HNAC in microscopic view, boundary condition of successful merging is found using car-following behaviours and lane-changing rules, which could also explain traffic oscillations. In macroscopic view, linear positive relationship between HNAC and background traffic volume is obtained based on moving bottleneck. To determine the explicit form of the relationship, data simulation considering car-following behaviours and traffic flow theory is used. In the results, the synchronization phenomenon of oscillation in on-ramp (with respect to main road) and intersected road is found. The explicit equation of HNAC is determined based on standard deviation and correlation coefficient analysis, and also proved to be accurate with model validation, which is helpful in studies related to propagation mechanism of traffic emergencies on highway network.

Trajectory Planning Method for Mixed Vehicles Considering Traffic Stability and Fuel Consumption at the Signalized Intersection

Traffic lights force vehicles to stop frequently at signalized intersections, which leads to excessive fuel consumption, higher emissions, and travel delays. To address these issues, this study develops a trajectory planning method for mixed vehicles at signalized intersections. First, we use the intelligent driver car-following model to analyze the string stability of traffic flow upstream of the intersection. Second, we propose a mixed-vehicle trajectory planning method based on a trigonometric model that considers prefixed traffic signals. The proposed method employs the proportional-integral-derivative (PID) model controller to simulate the trajectory when connected vehicles (equipped with internet access) follow the optimal advisory speed. Essentially, only connected vehicle trajectories need to be controlled because normal vehicles simply follow the connected vehicles according to the Intelligent Driver Model (IDM). The IDM model aims to minimize traffic oscillation and ensure that all vehicles pass the signalized intersection without stopping. The results of a MATLAB simulation indicate that the proposed method can reduce fuel consumption and NOx, HC, CO2, and CO concentrations by 17%, 22.8%, 17.8%, 17%, and 16.9% respectively when the connected vehicle market penetration is 50 percent.

A probability lane-changing model considering memory effect and driver heterogeneity

Lane changing is one of the basic driving behaviours, which may induce traffic oscillations and incidents. However, it is difficult to well model the lane-changing decision process due to the complex traffic status. To promote the prediction accuracy of lane-changing decisions, this paper presents a probability lane-changing model by taking into account the memory effect. That is, the lane-changing decision model considers a series of trajectory data rather than the data of a specific time utilized in most existing models. Furthermore, the drivers are classified in terms of lane-changing trajectories, which is expected to further promote the prediction accuracy of the lane-changing decision model. Calibrations and validations are carried out based on the NGSIM data, which indicate that the proposed model can significantly promote the prediction accuracy of lane-changing decisions.

Stability Analysis of Stochastic Linear Car-Following Models

Recent scholars have developed a number of stochastic car-following models that have successfully captured driver behavior uncertainties and reproduced stochastic traffic oscillation propagation. Whereas elegant frequency domain analytical methods are available for stability analysis of classic deterministic linear car-following models, there lacks an analytical method for quantifying the stability performance of their peer stochastic models and theoretically proving oscillation features observed in the real world. To fill this methodological gap, this study proposes a novel analytical method that measures traffic oscillation magnitudes and reveals oscillation characteristics of stochastic linear car-following models. We investigate a general class of stochastic linear car-following models that contain a linear car-following model and a stochastic noise term. Based on frequency domain analysis tools (e.g., Z-transform) and stochastic process theories, we propose analytical formulations for quantifying the expected speed variances of a stream of vehicles following one another according to one such stochastic car-following model, where the lead vehicle is subject to certain random perturbations. Our analysis on the homogeneous case (where all vehicles are identical) reveals two significant phenomena consistent with recent observations of traffic oscillation growth patterns from field experimental data: A linear stochastic car-following model with common parameter settings yields (i) concave growth of the speed oscillation magnitudes and (ii) reduction of oscillation frequency as oscillation propagates upstream. Numerical studies verify the universal soundness of the proposed analytical approach for both homogeneous and heterogeneous traffic scenarios, and both asymptotically stable and unstable underlying systems, as well as draw insights into traffic oscillation properties of a number of commonly used car-following models. Overall, the proposed method, as a stochastic peer, complements the traditional frequency-domain analysis method for deterministic car-following models and can be potentially used to investigate stability responses and mitigate traffic oscillation for various car-following behaviors with stochastic components.

Managing Lane Changing of Algorithm-Assisted Drivers

Theoretical models of vehicular traffic ascribe the fundamental cause of velocity oscillations and stop-and-go waves to suboptimal or unpredictable human driving behavior. In this paper we ask: if vehicles were controlled or assisted by algorithms, and hence driven optimally, would these phenomena simply go away? If not, how should a regulator manage algorithm-assisted vehicular traffic for a smooth flow? We study these questions in the context of a mandatory lane-changing scenario with mixed traffic, i.e., an algorithm-assisted driver on a curtailed lane that has to merge to an adjacent free lane with a relatively dense platoon of human drivers. In a stylized model of algorithm-assisted driving, we liken the blocked-lane driver to a rational self-interested agent, whose objective is to minimize her expected travel time through the blockage, deciding (a) at what velocity to move, and (b) whether to merge to the free lane, if given the opportunity (adequate gap). Moving at higher velocities reduces travel time, but also reduces the probability of finding a large enough gap to merge. We analyze the problem via dynamic programming, and we show that the optimal policy has a surprising structure: in the presence of uncertainty on adequate-sized gaps in the target lane, it may be optimal for the blocked-lane driver, in certain parameter regimes, to oscillate between high and low velocities while attempting to merge. Hence, traffic oscillations can arise not just due to suboptimal or unpredictable human driving behavior, but also endogenously, as the outcome of a driver’s rational, optimizing behavior. We draw out structural similarities to bang-bang control. As velocity oscillations are known to be detrimental to a smooth traffic flow, we provide sufficient conditions on the velocity limits so that traffic oscillations while merging, due to such optimizing behavior, do not arise at optimality. Finally, we investigate the fundamental flow-density and travel time-density diagrams through traffic micro-simulations. We establish that the proposed approach exhibits consistently near-optimal performance, in a broad variety of traffic conditions.

Event-triggered Varying Speed Limit Control of Stop-and-go Traffic

This paper develops event-triggered boundary control strategies for varying speed limit (VSL) located at a freeway segment. The stop-and-go traffic oscillations are suppressed by regulating the velocity of vehicles that leave the segment. The controlled velocity signal is only updated when a event triggering condition is satisfied. Compared with the continuous input signal, the event-based controller presents as a more realistic setting to implement by VSL on a digital platform which allows the adaptation time for drivers to follow the advisory speed. The traffic dynamics of density and velocity are described with linearized Aw-Rascle-Zhang (ARZ) macroscopic traffic partial differential equation (PDE) model which results in a 2 × 2 coupled hyperbolic system. The event-triggered boundary controllers rely on the emulation of the full state backstepping boundary feedback and two different Lyapunov-based event-triggered strategies to determine the time instants at which the control value must be sampled/updated. One of the event-triggered strategies makes use of a dynamic triggering condition under which it is possible to state the existence of a uniform minimal dwell-time (independent of initial conditions). The exponential stability under event-triggered control is achieved and validated with numerical simulations.

Impacts of cooperative adaptive cruise control platoons on emissions under traffic oscillation

Previous studies have shown that cooperative adaptive cruise control (CACC) vehicles have capability to improve traffic flow stability and reduce emissions and fuel consumption. However, previous studies did not investigate the relevance between these two aspects. To address this issue, we calculated stability conditions of traffic flow using car-following models. Simulations are also performed to evaluate reductions of emissions and fuel consumption under traffic oscillations. We also compared results of stability and emissions for exploring intrinsic relevance between them. Results show that stability could qualitatively influence reductions of emissions and fuel consumption, which provides potential method to reduce emissions and fuel consumption.

Optimal jam-absorption driving strategy for mitigating rear-end collision risks with oscillations on freeway straight segments

Traffic oscillations (or stop-and-go waves) in freeway traffic jam cause large variation of vehicle speed and remarkably reduce travel safety. Previous jam-absorption driving strategies focused on the operational side and did not consider the safety effects caused by the controlled vehicle on freeways. In this paper, we proposed an optimal jam-absorption driving strategy to mitigate traffic oscillations and rear-end collision risks on freeway straight segments. Firstly, the proposed strategy determined the starting and ending point of an oscillation at the temporal and spatial dimensions based on the Wavelet Transform (WT) and the steady equilibrium condition of car-following driving. Then different controlled vehicles were evaluated by the given absorbing speeds. Various measurements were considered to evaluate the safety performance of the strategies. The optimal solution was obtained which guided the controlled vehicle to move slowly at the optimal jam-absorbing speed, and created a gap to eliminate the downstream oscillation timely but avoid causing secondary wave in the upstream traffic. The Intelligent Driver Model (IDM) was modified to build the simulation platform in a connected environment. The results showed that our proposed strategy effectively reduced the severity of traffic oscillations, or even fully eliminate the oscillations. The optimal strategy reduced the surrogate safety measures by 93.53 %–94.78 %, and decreased the total travel time by 1.27 %. We also compared our strategy with previous strategies and the results suggested that ours had better performances.

Traffic Oscillations Mitigation in Vehicle Platoon Using a Car-Following Control Model for Connected and Autonomous Vehicle

Traffic oscillations often occur in road traffic, they make traffic flow unstable, unsafe and inefficient. Emerging connected and autonomous vehicle (CAV) technologies are potential solutions to mitigating the traffic oscillations for the advantages that CAVs are controllable and cooperative. In order to study a control strategy and the effectiveness of CAVs in mitigating traffic oscillations and improving traffic flow and analyse the characteristics of homogeneous traffic flow made up of CAVs and heterogeneous traffic flow made up of CAVs and RVs when traffic oscillations appear in traffic flow. Firstly, the formation and propagation of traffic oscillations in a platoon of RVs are simulated and analysed. Then, a car-following control model is built to control the longitudinal motion of CAVs, and real-time information of preceding CAV is used in the model and this can make the motion of CAVs more cooperative. The model reflects an idea named “slow-in” and “fast-out,” and this idea is helpful to mitigate traffic oscillations. Then, numerical simulations of homogeneous traffic flow of a platoon of CAVs and simulations of heterogeneous traffic flow containing CAVs and RVs are conducted, and different penetration rates (0, 0.2, 0.4, 0.6, 0.8, and 1) of CAVs are considered in the simulations of heterogeneous traffic flow. The characteristics and evolution of traffic flow are analysed and some indexes reflecting traffic efficiency and stability are calculated and analysed. Simulation results show that there are smaller velocity fluctuation, less stopping time and shorter length of road occupied when vehicle platoon contains CAVs (penetration rates are from 0.2 to 1) compared to the platoon containing only RVs (without CAVs). As for the heterogeneous traffic flow containing CAVs and RVs, these three indexes decrease with the increase of penetration rates (from 0.2 to 1) of CAVs. These results indicate that CAVs with the car-following control model in vehicle platoon are beneficial for mitigating traffic oscillations and improving traffic flow.