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.     

Method for investigating intradriver heterogeneity using vehicle trajectory data: A Dynamic Time Warping approach

After first extending Newell’s car-following model to incorporate time-dependent parameters, this paper describes the Dynamic Time Warping (DTW) algorithm and its application for calibrating this microscopic simulation model by synthesizing driver trajectory data. Using the unique capabilities of the DTW algorithm, this paper attempts to examine driver heterogeneity in car-following behavior, as well as the driver’s heterogeneous situation-dependent behavior within a trip, based on the calibrated time-varying response times and critical jam spacing. The standard DTW algorithm is enhanced to address a number of estimation challenges in this specific application, and a numerical experiment is presented with vehicle trajectory data extracted from the Next Generation Simulation (NGSIM) project for demonstration purposes. The DTW algorithm is shown to be a reasonable method for processing large vehicle trajectory datasets, but requires significant data reduction to produce reasonable results when working with high resolution vehicle trajectory data. Additionally, singularities present an interesting match solution set to potentially help identify changing driver behavior; however, they must be avoided to reduce analysis complexity.     

Applications of wavelet transform for analysis of freeway traffic: Bottlenecks, transient traffic, and traffic oscillations

This paper demonstrates the capabilities of wavelet transform (WT) for analyzing important features related to bottleneck activations and traffic oscillations in congested traffic in a systematic manner. In particular, the analysis of loop detector data from a freeway shows that the use of wavelet-based energy can effectively identify the location of an active bottleneck, the arrival time of the resulting queue at each upstream sensor location, and the start and end of a transition during the onset of a queue. Vehicle trajectories were also analyzed using WT and our analysis shows that the wavelet-based energies of individual vehicles can effectively detect the origins of deceleration waves and shed light on possible triggers (e.g., lane-changing). The spatiotemporal propagations of oscillations identified by tracing wavelet-based energy peaks from vehicle to vehicle enable analysis of oscillation amplitude, duration and intensity.     

Hysteresis in traffic flow revisited: An improved measurement method

This paper presents new insights on the hysteresis phenomenon in congested freeway traffic. It is found that existing theories based on different driver behavior for acceleration and deceleration are incomplete. The data suggests that one needs to consider aggressive and timid driver behavior as well. These findings are based on an improved method for measuring traffic flow variables from trajectory data consistently with kinematic wave theory.     

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.     

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.     

Incorporating human-factors in car-following models: A review of recent developments and research needs

Over the past decades there has been a considerable development in the modeling of car-following (CF) behavior as a result of research undertaken by both traffic engineers and traffic psychologists. While traffic engineers seek to understand the behavior of a traffic stream, traffic psychologists seek to describe the human abilities and errors involved in the driving process. This paper provides a comprehensive review of these two research streams.It is necessary to consider human-factors in CF modeling for a more realistic representation of CF behavior in complex driving situations (for example, in traffic breakdowns, crash-prone situations, and adverse weather conditions) to improve traffic safety and to better understand widely-reported puzzling traffic flow phenomena, such as capacity drop, stop-and-go oscillations, and traffic hysteresis. While there are some excellent reviews of CF models available in the literature, none of these specifically focuses on the human factors in these models.This paper addresses this gap by reviewing the available literature with a specific focus on the latest advances in car-following models from both the engineering and human behavior points of view. In so doing, it analyses the benefits and limitations of various models and highlights future research needs in the area.     

Driving behaviour models enabling the simulation of Advanced Driving Assistance Systems: revisiting the Action Point paradigm

In the field of Intelligent Transportation Systems (ITS), one of the most promising sub-functions is that of Advanced Driver Assistance Systems (ADAS). Development of an effective ADAS, and one that is able to gain drivers’ acceptance, hinges on the development of a human-like car-following model, and this is particularly important in order to ensure the driver is always ‘in the (vehicle control) loop’ and is able to recover control safely in any situation where the ADAS may release control. One of the most commonly used models of car-following is that of the Action Point (AP) (psychophysical) paradigm. However, while this is widely used in both micro-simulation models and behavioural research, the approach is not without its weaknesses. One of these, the potential redundancy of some of the identified APs, is examined in this paper and its basic structure validated using microscopic driving behaviour collected on thirteen subjects in Italy. Another weakness in practical application of the Action Point theory is the identification of appropriate thresholds, accounting for the perception, reaction and adjustment of relative speed (or spacing) from the leading vehicle. This article shows that this identification is problematic if the Action Point paradigm is analysed in a traditional way (car-following spirals), while it is easier if the phenomenon is analysed in terms of car-following ‘waves’, related to Time To Collision (TTC) or the inverse of TTC. Within this new interpretative framework, the observed action points can be observed to follow a characteristically linear pattern. The identification of the most significant variables to be taken into account, and their characterisation by means of a simple linear pattern, allows for the formulation of more efficient real-time applications, thereby contributing to the development and diffusion of emerging on-board technologies in the field of vehicle control and driver’s assistance.     

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.     

Analyzing fluctuations in car-following

Many car-following models predict a stable car-following behavior with a very small fluctuation around an equilibrium value g¹ of the net headway g with zero speed-difference Δv between the following and the lead vehicle. However, it is well-known and additionally demonstrated by data in this paper, that the fluctuations are much larger than these models predict. Typically, the fluctuation in speed difference is around ±2 m/s, while the fluctuation in the net time headway T = g/v can be as big as one or even two seconds, which is as large as the mean time headway itself. By analyzing data from loop detectors as well as data from vehicle trajectories, evidence is provided that this randomness is not due to driver heterogeneity, but can be attributed to an internal stochasticity of the driver itself. A final model-based analysis supports the hypothesis, that the preferred headway of the driver is the parameter that is not kept constant but fluctuates strongly, thus causing the even macroscopically observable randomness in traffic flow.     

Validation of the Rakha-Pasumarthy-Adjerid car-following model for vehicle fuel consumption and emission estimation applications

The Rakha-Pasumarthy-Adjerid (RPA) car-following model has been demonstrated to successfully replicate empirical driver car-following behavior. However, the validity of this model for fuel consumption and emission (FC/EM) estimation has yet to be studied. This paper attempts to address this research need by analyzing the applicability of the model for FC/EM estimation and comparing its performance to other state-of-practice car-following models; namely, the Gipps, Fritzsche and Wiedemann models. Naturalistic empirical data are employed to generate ground truth car-following events. The model-generated second-by-second Vehicle Specific Power (VSP) distributions for each car-following event are then compared to the empirical distributions. The study demonstrates that the generation of realistic VSP distributions is critical in producing accurate FC/EM estimates and that the RPA model outperforms the other three models in producing realistic vehicle trajectory VSP distributions and robust FC/EM estimates. This study also reveals that the acceleration behavior within a car-following model is one of the major contributors to producing realistic VSP distributions. The study further demonstrates that the use of trip-aggregated results may produce erroneous conclusions given that second-by-second errors may cancel each other out, and that lower VSP distribution errors occasionally result in greater bias in FC/EM estimates given the large deviation of the distribution at high VSP levels. Finally, the results of the study demonstrate the validity of the INTEGRATION micro-simulator, given that it employs the RPA car-following model, in generating realistic VSP distributions, and thus in estimating fuel consumption and emission levels.     

A car-following model considering asymmetric driving behavior based on long short-term memory neural networks

Asymmetric driving behavior is a critical characteristic of human driving behaviors and has a significant impact on traffic flow. In consideration of the asymmetric driving behavior, this paper proposes a long short-term memory (LSTM) neural networks (NN) based car-following (CF) model to capture realistic traffic flow characteristics by incorporating the driving memory. The NGSIM data are used to calibrate and validate the proposed CF model. Meanwhile, three characteristics closely related to the asymmetric driving behavior are investigated: hysteresis, discrete driving, and intensity difference. The simulation results show the good performance of the proposed CF model on reproducing realistic traffic flow features. Moreover, to further demonstrate the superiority of the proposed CF model, two other CF models including recurrent neural network based CF model and asymmetric full velocity difference model, are compared with LSTM-NN model. The results reveal that LSTM-NN model can capture the asymmetric driving behavior well and outperforms other models.     

Do cooperative systems make drivers’ car-following behavior safer?

The main goal of in-vehicle technologies and co-operative services is to reduce congestion and increase traffic safety. This is achieved by alerting drivers on risky traffic conditions ahead of them and by exchanging traffic and safety related information for the particular road segment with nearby vehicles. Road capacity, level of service, safety, and air pollution are impacted to a large extent by car-following behavior of drivers. Car-following behavior is an essential component of micro-simulation models. This paper investigates the impact of an infrastructure-to-vehicle (I2V) co-operative system on drivers’ car-following behavior. Test drivers in this experiment drove an instrumented vehicle with and without the system. Collected trajectory data of the subject vehicle and the vehicle in front, as well as socio-demographic characteristics of the test drivers were used to estimate car-following models capturing their driving behavior with and without the I2V system. The results show that the co-operative system harmonized the behavior of drivers and reduced the range of acceleration and deceleration differences among them. The observed impact of the system was largest on the older group of drivers.     

Influences of the driver’s bounded rationality on micro driving behavior,fuel consumption and emissions

In this paper, we propose an extended car-following model to study the influences of the driver’s bounded rationality on his/her micro driving behavior, and the fuel consumption, CO, HC and NO_X of each vehicle under two typical cases, where Case I is the starting process and Case II is the evolution process of a small perturbation. The numerical results indicate that considering the driver’s bounded rationality will reduce his/her speed during the starting process and improve the stability of the traffic flow during the evolution of the small perturbation, and reduce the total fuel consumption, CO, HC and NO_X of each vehicle under the above two cases.     

A rule-based neural network approach to model driver naturalistic behavior in traffic

This paper proposes a rule-based neural network model to simulate driver behavior in terms of longitudinal and lateral actions in two driving situations, namely car-following situation and safety critical events. A fuzzy rule based neural network is constructed to obtain driver individual driving rules from their vehicle trajectory data. A machine learning method reinforcement learning is used to train the neural network such that the neural network can mimic driving behavior of individual drivers. Vehicle actions by neural network are compared to actions from naturalistic data. Furthermore, this paper applies the proposed method to analyze the heterogeneities of driving behavior from different drivers’ data.Driving data in the two driving situations are extracted from Naturalistic Truck Driving Study and Naturalistic Car Driving Study databases provided by the Virginia Tech Transportation Institute according to pre-defined criteria. Driving actions were recorded in instrumented vehicles that have been equipped with specialized sensing, processing, and recording equipment.     

A pattern recognition algorithm for assessing trajectory completeness

Vehicular trajectories are widely used for car-following (CF) model calibration and validation, as they embody characteristics of individual driving behaviour (each trajectory reflects an individual driver). Previous studies have highlighted that the trajectories should contain all the major vehicular interactions (driving regimes) between the leader and the follower for reliable CF model calibration and validation. Based on Dynamic Time Warping and Bottom-Up algorithms, this paper develops a pattern recognition algorithm for vehicle trajectories (PRAVT) to objectively, accurately, and automatically differentiate different driving regimes in a trajectory and then select the most complete trajectories (i.e. trajectories containing a maximum number of regimes). PRAVT is rigorously tested using synthetic data and then applied to the NGSIM data. We have observed that the NGSIM data are dominated by the trajectories which contain only three regimes, namely acceleration, deceleration, and following, 77% of the trajectories lack the standstill regime, and no trajectory in the NGSIM data is complete. These findings’ impact on how to properly utilize NGSIM data can be profound. Given the extensive use of the NGSIM data in the traffic flow community, this paper also provides insights about the types of regimes contained in each trajectory of the NGSIM data.     

Modeling car-following behavior on urban expressways in Shanghai: A naturalistic driving study

Although car-following behavior is the core component of microscopic traffic simulation, intelligent transportation systems, and advanced driver assistance systems, the adequacy of the existing car-following models for Chinese drivers has not been investigated with real-world data yet. To address this gap, five representative car-following models were calibrated and evaluated for Shanghai drivers, using 2100 urban-expressway car-following periods extracted from the 161,055 km of driving data collected in the Shanghai Naturalistic Driving Study (SH-NDS). The models were calibrated for each of the 42 subject drivers, and their capabilities of predicting the drivers’ car-following behavior were evaluated.The results show that the intelligent driver model (IDM) has good transferability to model traffic situations not presented in calibration, and it performs best among the evaluated models. Compared to the Wiedemann 99 model used by VISSIM®, the IDM is easier to calibrate and demonstrates a better and more stable performance. These advantages justify its suitability for microscopic traffic simulation tools in Shanghai and likely in other regions of China. Additionally, considerable behavioral differences among different drivers were found, which demonstrates a need for archetypes of a variety of drivers to build a traffic mix in simulation. By comparing calibrated and observed values of the IDM parameters, this study found that (1) interpretable calibrated model parameters are linked with corresponding observable parameters in real world, but they are not necessarily numerically equivalent; and (2) parameters that can be measured in reality also need to be calibrated if better trajectory reproducing capability are to be achieved.     

Evaluation of the General Motors based car-following models and a proposed fuzzy inference model

This paper evaluates the properties of the General Motors (GM) based car-following models, identifies their characteristics, and proposes a fuzzy inference logic based model that can overcome some of the shortcomings of the GM based models. This process involves developing a framework for evaluating a car-following model and comparing the behavior predicted by the GM models with the behavior observed under the real world situation. For this purpose, an instrumented vehicle was used to collect data on the headway and speeds of two consecutive vehicles under actual traffic conditions. Shortcomings of the existing GM based models are identified, in particular, the stability conditions were analyzed in detail. A fuzzy-inference based model of car-following is developed to represent the approximate nature of stimulus–response process during driving. This model is evaluated using the same evaluation framework used for the GM models and the data obtained by the instrumented test vehicle. Comparison between the performance of the two models show that the proposed fuzzy inference model can overcome many shortcomings of the GM based car-following models, and can be useful for developing the algorithm for the adaptive cruise control for automated highway system (AHS).     

Characterization of traffic oscillation propagation under nonlinear car-following laws

Unlike linear car-following models, nonlinear models generally can generate more realistic traffic oscillation phenomenon, but nonlinearity makes analytical quantification of oscillation characteristics (e.g, periodicity and amplitude) significantly more difficult. This paper proposes a novel mathematical framework that accurately quantifies oscillation characteristics for a general class of nonlinear car-following laws. This framework builds on the describing function technique from nonlinear control theory and is comprised of three modules: expression of car-following models in terms of oscillation components, analyses of local and asymptotic stabilities, and quantification of oscillation propagation characteristics. Numerical experiments with a range of well-known nonlinear car-following laws show that the proposed approach is capable of accurately predicting oscillation characteristics under realistic physical constraints and complex driving behaviors. This framework not only helps further understand the root causes of the traffic oscillation phenomenon but also paves a solid foundation for the design and calibration of realistic nonlinear car-following models that can reproduce empirical oscillation characteristics.     

Impact of stop-and-go waves and lane changes on discharge rate in recovery flow

In an effort to uncover traffic conditions that trigger discharge rate reductions near active bottlenecks, this paper analyzed individual vehicle trajectories at a microscopic level and documented the findings. Based on an investigation of traffic flow involving diverse traffic situations, a driver’s tendency to take a significant headway after passing stop-and-go waves was identified as one of the influencing factors for discharge rate reduction. Conversely, the pattern of lane changers caused a transient increase in the discharge rate until the situation was relaxed after completing the lane-changing event. Although we observed a high flow from the incoming lane changers, the events ultimately caused adverse impacts on the traffic such that the disturbances generated stop-and-go waves. Based on this observation, we regard upstream lane changes and stop-and-go waves as the responsible factors for the decreased capacity at downstream of active bottlenecks. This empirical investigation also supports the resignation effect, the regressive effect, and the asymmetric behavioral models in differentiating acceleration and deceleration behaviors.