Experimental and empirical investigations of traffic flow instability

Traffic instability is an important but undesirable feature of traffic flow. This paper reports our experimental and empirical studies on traffic flow instability. We have carried out a large scale experiment to study the car-following behavior in a 51-car-platoon. The experiment has reproduced the phenomena and confirmed the findings in our previous 25-car-platoon experiment, i.e., standard deviation of vehicle speeds increases in a concave way along the platoon. Based on our experimental results, we argue that traffic speed rather than vehicle spacing (or density) might be a better indicator of traffic instability, because vehicles can have different spacing under the same speed. For these drivers, there exists a critical speed between 30 km/h and 40 km/h, above which the standard deviation of car velocity is almost saturated (flat) along the 51-car-platoon, indicating that the traffic flow is likely to be stable. In contrast, below this critical speed, traffic flow is unstable and can lead to the formation of traffic jams. Traffic data from the Nanjing Airport Highway support the experimental observation of existence of a critical speed. Based on these findings, we propose an alternative mechanism of traffic instability: the competition between stochastic factors and the so-called speed adaptation effect, which can better explain the concave growth of speed standard deviation in traffic flow.     

Calibration of nonlinear car-following laws for traffic oscillation prediction

Frequency-domain analysis has been successfully used to (i) predict the amplification of traffic oscillations along a platoon of vehicles with nonlinear car-following laws and (ii) measure traffic oscillation properties (e.g., periodicity, magnitude) from field data. This paper proposes a new method to calibrate nonlinear car-following laws based on real-world vehicle trajectories, such that oscillation prediction (based on the calibrated car-following laws) and measurement from the same data can be compared and validated. This calibration method, for the first time, takes into account not only the driver’s car-following behavior but also the vehicle trajectory’s time-domain (e.g., location, speed) and frequency-domain properties (e.g., peak oscillation amplitude). We use Newell’s car-following model (1961) as an example and calibrate its parameters based on a penalty-based maximum likelihood estimation procedure. A series of experiments using Next Generation Simulation (NGSIM) data are conducted to illustrate the applicability and performance of the proposed approach. Results show that the calibrated car-following models are able to simultaneously reproduce observed driver behavior, time-domain trajectories, and oscillation propagation along the platoon with reasonable accuracy.     

Understanding the structure of hyper-congested traffic from empirical and experimental evidences

We study in this paper the structure of traffic under hypercongestion, which is a controversial issue between traditional two-phase traffic theory and Kerner’s three-phase theory. By analyzing video traffic data from a section of the Nanjing Airport Highway, it is found that traffic states inside hypercongestion are not homogeneous, which contradicts the existence of a “Homogeneous Congested Traffic” state claimed in two-phase traffic theory. Analysis of vehicle trajectories and velocities obtained from an experimental car-following study with a platoon of 25 vehicles also confirms the above findings. Furthermore, it is also found from the video traffic data that the structure of hypercongested traffic varies only slightly with location, which might be due to small jams inside hypercongested traffic merging into larger ones slowly and/or larger jams sometimes breaking into small ones. Finally, the implications of our observations on traffic modeling have been discussed.     

Vehicle headway modeling and its inferences in macroscopic/microscopic traffic flow theory: A survey

Vehicle headway distribution models are widely used in traffic engineering fields, since they reflect the fundamental uncertainty in drivers' car-following maneuvers and meanwhile provide a concise way to describe the stochastic feature of traffic flows. This paper presents a systematic review of vehicle headway distribution studies in the last few decades. Since it is impossible to enumerate the merits and drawbacks of all of existing distribution models, we emphasize four advances of headway distribution modeling in this paper. First, we highlight the chronicle of key assumptions on the existing distribution models and explain why this evolution occurs. Second, we show that departure headways measured for interrupted flows on urban streets and headways measured for uninterrupted flows on freeways have common features and can be simulated by a unified microscopic car-following model. The interesting finding helps gather two kinds of headway distribution models under one umbrella. Third, we review different approaches that aim to link microscopic car-following models and mesoscopic vehicle headway distribution models. Fourth, we show that both the point scattering on the density-flow plot and the shape of traffic flow breakdown curve implicitly depend on the vehicular headway distribution. These findings reveal pervasive connections between macroscopic traffic flow models and mesoscopic headway distribution. All these new insights bring new vigor into vehicle headway studies and open research frontiers in this field.     

On the network connectivity of platoon-based vehicular cyber-physical systems

In the past few years, vehicular ad hoc networking (VANET) has attracted significant attention and many fundamental issues have been investigated, such as network connectivity, medium access control (MAC) mechanism, routing protocol, and quality of service (QoS). Nevertheless, most related work has been based on simplified assumptions on the underlying vehicle traffic dynamics, which has a tight interaction with VANET in practice. In this paper, we try to investigate VANET performance from the vehicular cyber-physical system (VCPS) perspective. Specifically, we consider VANET connectivity of platoon-based VCPSs where all vehicles drive in platoon-based patterns, which facilitate better traffic performance as well as information services. We first propose a novel architecture for platoon-based VCPSs, then we derive the vehicle distribution under platoon-based driving patterns on a highway. Based on the results, we further investigate inter-platoon connectivity in a bi-directional highway scenario and evaluate the expected time of safety message delivery among platoons, taking into account the effects of system parameters, such as traffic flow, velocity, platoon size and transmission range. Extensive simulations are conducted which validate the accuracy of our analysis. This study will be helpful to understand the behavior of VCPSs, and will be helpful to improve vehicle platoon design and deployment.     

Experimental study and modeling of car-following behavior under high speed situation

To investigate the car-following behavior under high speed driving conditions, we performed a set of 11-car-platoon experiments on Hefei airport highway. The formation and growth of oscillations have been analyzed and compared with that in low speed situations. It was found that there is considerable heterogeneity for the same driver over different runs of the experiment. This intra-driver heterogeneity was quantitatively depicted by a new index and incorporated in an enhanced two-dimensional intelligent driver model. Using both the new high-speed and the previous low-speed experimental data, the new and three existing models were calibrated. Simulation results show that the enhanced model outperforms the three existing car-following models that do not take into account this intra-driver heterogeneity in reproducing the essential features of the traffic in the experiments.     

Enhanced cooperative car-following traffic model with the combination of V2V and V2I communication

Vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communication are emerging components of intelligent transport systems (ITS) based on which vehicles can drive in a cooperative way and, hence, significantly improve traffic flow efficiency. However, due to the high vehicle mobility, the unreliable vehicular communications such as packet loss and transmission delay can impair the performance of the cooperative driving system (CDS). In addition, the downstream traffic information collected by roadside sensors in the V2I communication may introduce measurement errors, which also affect the performance of the CDS. The goal of this paper is to bridge the gap between traffic flow modelling and communication approaches in order to build up better cooperative traffic systems. To this end, we aim to develop an enhanced cooperative microscopic (car-following) traffic model considering V2V and V2I communication (or V2X for short), and investigate how vehicular communications affect the vehicle cooperative driving, especially in traffic disturbance scenarios. For these purposes, we design a novel consensus-based vehicle control algorithm for the CDS, in which not only the local traffic flow stability is guaranteed, but also the shock waves are supposed to be smoothed. The IEEE 802.11p, the defacto vehicular networking standard, is selected as the communication protocols, and the roadside sensors are deployed to collect the average speed in the targeted area as the downstream traffic reference. Specifically, the imperfections of vehicular communication as well as the measured information noise are taken into account. Numerical results show the efficiency of the proposed scheme. This paper attempts to theoretically investigate the relationship between vehicular communications and cooperative driving, which is needed for the future deployment of both connected vehicles and infrastructure (i.e. V2X).     

Stop-and-go traffic analysis: Theoretical properties,environmental impacts and oscillation mitigation

This study aims (i) to analyze theoretical properties of a recently proposed describing-function (DF) based approach (Li and Ouyang, 2011; Li et al., 2012) for traffic oscillation quantification, (ii) to adapt it for estimating fuel consumption and emission from traffic oscillation and (iii) to explore vehicle control strategies of smoothing traffic with advanced technologies. The DF approach was developed to predict traffic oscillation propagation across a platoon of vehicles following each other by a nonlinear car-following law with only the leading vehicle’s input. We first simplify the DF approach and prove a set of properties (e.g., existence and uniqueness of its solution) that assure its prediction is always consistent with observed traffic oscillation patterns. Then we integrate the DF approach with existing estimation models of fuel consumption and emission to analytically predict environmental impacts (i.e., unit-distance fuel consumption and emission) from traffic oscillation. The prediction results by the DF approach are validated with both computer simulation and field measurements. Further, we explore how to utilize advantageous features of emerging sensing, communication and control technologies, such as fast response and information sharing, to smooth traffic oscillation and reduce its environmental impacts. We extend the studied car-following law to incorporate these features and apply the DF approach to demonstrate how these features can help dampen the growth of oscillation and environmental impact measurements. For information sharing, we convert the corresponding extended car-following law into a new fixed point problem and propose a simple bisecting based algorithm to efficiently solve it. Numerical experiments show that these new car-following control strategies can effectively suppress development of oscillation amplitude and consequently mitigate fuel consumption and emission.     

Dissipation of stop-and-go waves via control of autonomous vehicles: Field experiments

Traffic waves are phenomena that emerge when the vehicular density exceeds a critical threshold. Considering the presence of increasingly automated vehicles in the traffic stream, a number of research activities have focused on the influence of automated vehicles on the bulk traffic flow. In the present article, we demonstrate experimentally that intelligent control of an autonomous vehicle is able to dampen stop-and-go waves that can arise even in the absence of geometric or lane changing triggers. Precisely, our experiments on a circular track with more than 20 vehicles show that traffic waves emerge consistently, and that they can be dampened by controlling the velocity of a single vehicle in the flow. We compare metrics for velocity, braking events, and fuel economy across experiments. These experimental findings suggest a paradigm shift in traffic management: flow control will be possible via a few mobile actuators (less than 5%) long before a majority of vehicles have autonomous capabilities.     

Modeling chain collisions in vehicular networks with variable penetration rates

The vehicular ad hoc network has great potential in improving traffic safety. One of the most important and interesting issues in the research community is the safety evaluation with limited penetration rates of vehicles equipped with inter-vehicular communications. In this paper, a stochastic model is proposed for analyzing the vehicle chain collisions. It takes into account the influences of different penetration rates, the stochastic nature of inter-vehicular distance distribution, and the different kinematic parameters related to driver and vehicle. The usability and accuracy of this model is tested and proved by comparative experiments with Monte Carlo simulations. The collision outcomes of a platoon in different penetration rates and traffic scenarios are also analyzed based on this model. These results are useful to provide theoretical insights into the safety control of a heterogeneous platoon.     

Heterogeneous platoon flow dispersion model based on truncated mixed simplified phase‐type distribution of travel speed

Existing research on platoon dispersion models either describe homogeneous traffic flow feature, or are in lack of analytical solutions. By analyzing the field data, the truncated mixed simplified phase‐type distribution is proved to be capable of capturing the characteristics of heterogeneous traffic flow with an excellent fitting result. In light of this, we derive a generic heterogeneous platoon dispersion model with truncated mixed simplified phase‐type of speed in the forms of integrable functions. Numerical case studies are conducted to compare the performance of the proposed model and the conventional models (i.e., the Robertson model and truncated mixed Gaussian model). The results show that the proposed model not only better captures the platoon dispersion laws of heterogeneous traffic flow, but also presents higher computational efficiency, which provides practical implications on traffic signal control. Copyright © 2017 John Wiley & Sons, Ltd.     

Human-like autonomous car-following model with deep reinforcement learning

This study proposes a framework for human-like autonomous car-following planning based on deep reinforcement learning (deep RL). Historical driving data are fed into a simulation environment where an RL agent learns from trial and error interactions based on a reward function that signals how much the agent deviates from the empirical data. Through these interactions, an optimal policy, or car-following model that maps in a human-like way from speed, relative speed between a lead and following vehicle, and inter-vehicle spacing to acceleration of a following vehicle is finally obtained. The model can be continuously updated when more data are fed in. Two thousand car-following periods extracted from the 2015 Shanghai Naturalistic Driving Study were used to train the model and compare its performance with that of traditional and recent data-driven car-following models. As shown by this study’s results, a deep deterministic policy gradient car-following model that uses disparity between simulated and observed speed as the reward function and considers a reaction delay of 1 s, denoted as DDPGvRT, can reproduce human-like car-following behavior with higher accuracy than traditional and recent data-driven car-following models. Specifically, the DDPGvRT model has a spacing validation error of 18% and speed validation error of 5%, which are less than those of other models, including the intelligent driver model, models based on locally weighted regression, and conventional neural network-based models. Moreover, the DDPGvRT demonstrates good capability of generalization to various driving situations and can adapt to different drivers by continuously learning. This study demonstrates that reinforcement learning methodology can offer insight into driver behavior and can contribute to the development of human-like autonomous driving algorithms and traffic-flow models.     

Nonlinear finite-time consensus-based connected vehicle platoon control under fixed and switching communication topologies

This paper proposes nonlinear consensus-based control strategies for a connected vehicle (CV) platoon under different communication topologies. In particular, pinning control based consensus protocols are proposed by incorporating the car-following interactions between CVs under fixed and switching communication topologies. The finite-time stability and consensus of the proposed protocols are rigorously analyzed using the LaSalle’s invariance principle and Lyapunov technique. The theoretical analyses investigate the impacts of communication topology on convergence and stability of CV platoon. This study conducts numerical experiments for a CV platoon under four scenarios: (i) Fixed communication topology with time-invariant leader, (ii) fixed communication topology with time-variant leader, (iii) switching communication topology with time-invariant leader, and (iv) switching communication topology with time-variant leader. Simulations results illustrate the effectiveness of the proposed protocols in terms of convergence time and stability with respect to position and velocity profiles.     

Macroscopic traffic flow propagation stability for adaptive cruise controlled vehicles

Traffic flow propagation stability is concerned about whether a traffic flow perturbation will propagate and form a traffic shockwave. In this paper, we discuss a general approach to the macroscopic traffic flow propagation stability for adaptive cruise controlled (ACC) vehicles. We present a macroscopic model with velocity saturation for traffic flow in which each individual vehicle is controlled by an adaptive cruise control spacing policy. A nonlinear traffic flow stability criterion is investigated using a wavefront expansion technique. Quantitative relationships between traffic flow stability and model parameters (such as traffic flow and speed, etc.) are derived for a generalized ACC traffic flow model. The newly derived stability results are in agreement with previously derived results that were obtained using both microscopic and macroscopic models with a constant time headway (CTH) policy. Moreover, the stability results derived in this paper provide sufficient and necessary conditions for ACC traffic flow stability and can be used to design other ACC spacing policies.     

Platoon-based traffic flow model for estimating breakdown probability at single-lane expressway bottlenecks

This study investigates the mechanism of traffic breakdown and establishes a traffic flow model that precisely simulates the stochastic and dynamic processes of traffic flow at a bottleneck. The proposed model contains two models of stochastic processes associated with traffic flow dynamics: a model of platoon formation behind a bottleneck and a model of speed transitions within a platoon. After these proposed models are validated, they are applied to a simple one-way, one-lane expressway section containing a bottleneck, and the stochastic nature of traffic breakdown is demonstrated through theoretical exercises.     

Intelligent cruise control systems and traffic flow stability

There are two kinds of stability associated with traffic flow problems – string stability (or car-following stability) and traffic flow stability. We provide a clear distinction between traffic flow stability and string stability, and such a distinction has not been recognized in the literature, thus far. String stability is stability with respect to intervehicular spacing; intuitively, it ensures the knowledge of the position and velocity of every vehicle in the traffic, within reasonable bounds of error, from the knowledge of the position and velocity of a vehicle in the traffic. String stability is analyzed without adding vehicles to or removing vehicles from the traffic. On the other hand, traffic flow stability deals with the evolution of traffic velocity and density in response to the addition and/or removal of vehicles from the flow. Traffic flow stability can be guaranteed only if the velocity and density solutions of the coupled set of equations is stable, i.e., only if stability with respect to automatic vehicle following and stability with respect to density evolution is guaranteed. Therefore, the flow stability and critical capacity of any section of a highway is dependent not only on the vehicle following control laws and the information used in their synthesis, but also on the spacing policy employed by the control system. Such a dependence has practical consequences in the choice of a spacing policy for adaptive cruise control laws and on the stability of the traffic flow consisting of vehicles equipped with adaptive cruise control features on the existing and future highways. This critical dependence is the subject of investigation here.     

A control theoretic formulation of green driving strategies based on inter-vehicle communications

Various green driving strategies have been proposed to smooth traffic flow and lower pollutant emissions and fuel consumption in stop-and-go traffic. In this paper, we present a control theoretic formulation of distributed, cooperative green driving strategies based on inter-vehicle communications (IVCs). The control variable is the advisory speed limit, which is designed to smooth a following vehicle’s speed profile without changing its average speed. We theoretically analyze the performance of a constant independent and three simple cooperative green driving strategies and present three rules for effective and robust strategies. We then develop a distributed cooperative green driving strategy, in which the advisory speed limit is first independently calculated by each individual vehicle and then averaged among green driving vehicles through IVC. By simulations with Newell’s car-following model and the Comprehensive Modal Emissions Model (CMEM), we demonstrate that such a strategy is effective and robust independently as well as cooperatively for different market penetration rates of IVC-equipped vehicles and communication delays. In particular, even when 5% of the vehicles implement the green driving strategy and the IVC communication delay is 60 s, the fuel consumption can be reduced by up to 15%. Finally we discuss some future extensions.     

A simple nonparametric car-following model driven by field data

Car-following models are always of great interest of traffic engineers and researchers. In the age of mass data, this paper proposes a nonparametric car-following model driven by field data. Different from most of the existing car-following models, neither driver’s behaviour parameters nor fundamental diagrams are assumed in the data-driven model. The model is proposed based on the simple k-nearest neighbour, which outputs the average of the most similar cases, i.e., the most likely driving behaviour under the current circumstance. The inputs and outputs are selected, and the determination of the only parameter k is introduced. Three simulation scenarios are conducted to test the model. The first scenario is to simulate platoons following real leaders, where traffic waves with constant speed and the detailed trajectories are observed to be consistent with the empirical data. Driver’s rubbernecking behaviour and driving errors are simulated in the second and third scenarios, respectively. The time–space diagrams of the simulated trajectories are presented and explicitly analysed. It is demonstrated that the model is able to well replicate periodic traffic oscillations from the precursor stage to the decay stage. Without making any assumption, the fundamental diagrams for the simulated scenario coincide with the empirical fundamental diagrams. These all validate that the model can well reproduce the traffic characteristics contained by the field data. The nonparametric car-following model exhibits traffic dynamics in a simple and parsimonious manner.     

Eco-driving advisory strategies for a platoon of mixed gasoline and electric vehicles in a connected vehicle system

As electric vehicles (EVs) have gained an increasing market penetration rate, the traffic on urban roads will tend to be a mix of traditional gasoline vehicles (GVs) and EVs. These two types of vehicles have different energy consumption characteristics, especially the high energy efficiency and energy recuperation system of EVs. When GVs and EVs form a platoon that is recognized as an energy-friendly traffic pattern, it is critical to holistically consider the energy consumption characteristics of all vehicles to maximize the energy efficiency benefit of platooning. To tackle this issue, this paper develops an optimal control model as a foundation to provide eco-driving suggestions to the mixed-traffic platoon. The proposed model leverages the promising connected vehicle technology assuming that the speed advisory system can obtain the information on the characteristics of all platoon vehicles. To enhance the model applicability, the study proposes two eco-driving advisory strategies based on the developed optimal control model. One strategy provides the lead vehicle an acceleration profile, while the other provides a set of targeted cruising speeds. The acceleration-based eco-driving advisory strategy is suitable for platoons with an automated leader, and the speed-based advisory strategy is more friendly for platoons with a human-operated leader. Results of numerical experiments demonstrate the significance when the eco-driving advisory system holistically considers energy consumption characteristics of platoon vehicles.