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.     

Freeway traffic oscillations: Microscopic analysis of formations and propagations using Wavelet Transform

In this paper we identify the origins of stop-and-go (or slow-and-go) driving and measure microscopic features of their propagations by analyzing vehicle trajectories via Wavelet Transform. Based on 53 oscillation cases analyzed, we find that oscillations can be originated by either lane-changing maneuvers (LCMs) or car-following (CF) behavior. LCMs were predominantly responsible for oscillation formations in the absence of considerable horizontal or vertical curves, whereas oscillations formed spontaneously near roadside work on an uphill segment. Regardless of the trigger, the features of oscillation propagations were similar in terms of propagation speed, oscillation duration, and amplitude. All observed cases initially exhibited a precursor phase, in which slow-and-go motions were localized. Some of them eventually transitioned into a well-developed phase, in which oscillations propagated upstream in queue. LCMs were primarily responsible for the transition, although some transitions occurred without LCMs. Our findings also suggest that an oscillation has a regressive effect on car-following behavior: a deceleration wave of an oscillation affects a timid driver (characterized by larger response time and/or minimum spacing) to become less timid and an aggressive driver less aggressive, although this change may be short-lived. An extended framework of Newell’s CF model is able to describe the regressive effect with two additional parameters with reasonable accuracy, as verified using vehicle trajectory data.     

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.     

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.     

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.     

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.     

A probabilistic stationary speed–density relation based on Newell’s simplified car-following model

Probabilistic models describing macroscopic traffic flow have proven useful both in practice and in theory. In theoretical investigations of wide-scatter in flow–density data, the statistical features of flow density relations have played a central role. In real-time estimation and traffic forecasting applications, probabilistic extensions of macroscopic relations are widely used. However, how to obtain such relations, in a manner that results in physically reasonable behavior has not been addressed. This paper presents the derivation of probabilistic macroscopic traffic flow relations from Newell’s simplified car-following model. The probabilistic nature of the model allows for investigating the impact of driver heterogeneity on macroscopic relations of traffic flow. The physical features of the model are verified analytically and shown to produce behavior which is consistent with well-established traffic flow principles. An empirical investigation is carried out using trajectory data from the New Generation SIMulation (NGSIM) program and the model’s ability to reproduce real-world traffic data is validated.     

The kinematic wave model with finite decelerations: A social force car-following model approximation

This paper derives a five-parameter social force car-following model that converges to the kinematic wave model with triangular fundamental diagram. Analytical solutions for vehicle trajectories are found for the lead-vehicle problem, which exhibit clockwise and counter-clockwise hysteresis depending on the model’s parameters and the lead vehicle trajectory. When coupled with a stochastic vehicle dynamics module, the model is able to reproduce periods and amplitudes of stop-and-go waves, as reported in the field. The model’s stability conditions are analysed and its trajectories are compared to real data.     

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.     

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.     

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.     

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.     

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).     

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.     

A lane-change trajectory model from drivers’ vision view

Car-following and Lane-changing are two fundamental tasks during driving. While many car-following models can be applied, relatively, only a few lane-changing models have been developed. Classical lane-changing models mainly focus on drivers’ lane selection and gap acceptance behaviors, but very limited research has paid attention to formulating detailed lane-changing trajectories. This research aims to fill the gap by proposing a lane-changing trajectory model, which is built directly from drivers’ vision view, to model detailed lane-changing trajectories. A large amount of data of reference angles, defined as the angle changes between the drivers’ vision angle and left or right lane line, were first extracted from the videos recorded by the vehicle traveling data recorders (VTDRs) installed in 11 taxies. A comprehensive data analysis indicates that same drivers show similarity of their daily lane-changing habit but with variety, and different drivers’ lane-change trajectory data show different lane-change “personality” including aggressive or non-aggressive behaviors. Based on these findings, this paper then proposed a hyperbolic tangent lane-change trajectory model to describe drivers’ detailed lane-change trajectories. The model is verified using both real data and simulation. The results show the proposed lane-change trajectory model can successfully describe drivers’ lane-changing trajectories. More importantly, some parameters in the model are directly associated to drivers’ driving characteristics during lane-change. With this unique feature, the proposed model can generate driver-specific lane-change trajectories. Such improvement could contribute to the future development of Advanced Driver Assistance Systems (ADAS).     

From behavioral psychology to acceleration modeling: Calibration,validation, and exploration of drivers’ cognitive and safety parameters in a risk-taking environment

We investigate a utility-based approach for driver car-following behavioral modeling while analyzing different aspects of the model characteristics especially in terms of capturing different fundamental diagram regions and safety proxy indices. The adopted model came from an elementary thought where drivers associate subjective utilities for accelerations (i.e. gain in travel times) and subjective dis-utilities for decelerations (i.e. loss in travel time) with a perceived probability of being involved in rear-end collision crashes. Following the testing of the model general structure, the authors translate the corresponding behavioral psychology theory – prospect theory – into an efficient microscopic traffic modeling with more elaborate stochastic characteristics considered in a risk-taking environment.After model formulation, we explore different model disaggregate and aggregate characteristics making sure that fidelity is kept in terms of equilibrium properties. Significant effort is then dedicated to calibrating and validating the model using microscopic trajectory data. A modified genetic algorithm is adopted for this purpose while focusing on capturing inter-driver heterogeneity for each of the parameters. Using the calibration exercise as a starting point, simulation sensitivity analysis is performed to reproduce different fundamental diagram regions and to explore rear-end collisions related properties. In terms of fundamental diagram regions, the model in hand is able to capture traffic breakdowns and different instabilities in the congested region represented by flow-density data points scattering. In terms of incident related measures, the effect of heterogeneity in both psychological factors and execution/perception errors on the accidents number and their distribution is studied. Through sensitivity analysis, correlations between the crash-penalty, the negative coefficient associated with losses in speed, the positive coefficient associated with gains in speed, the driver’s uncertainty, the anticipation time and the reaction time are retrieved. The formulated model offers a better understanding of driving behavior, particularly under extreme/incident conditions.     

Stochastic eco-routing in a signalized traffic network

In this paper, an eco-routing algorithm is developed for vehicles in a signalized traffic network. The proposed method incorporates a microscopic vehicle emission model into a Markov decision process (MDP). Instead of using GPS-based vehicle trajectory data, which are used by many existing eco-routing algorithm, high resolution traffic data including vehicle arrival and signal status information are used as primary inputs. The proposed method can work with any microscopic vehicle model that uses vehicle trajectories as inputs and gives related emission rates as outputs. Furthermore, a constrained eco-routing problem is proposed to deal with the situation where multiple costs present. This is done by transferring the original MDP based formulation to a linear programming formulation. Besides the primary cost, additional costs are considered as constraints. Two numerical examples are given using the field data obtained from City of Pasadena, California, USA. The eco-routing algorithm for single objective is compared against the traditional shortest path algorithm, Dijkstra’s algorithm. Average reductions of CO emission around 20% are observed.     

Do microscopic merging models reproduce the observed priority sharing ratio in congestion?

A classical way to represent vehicle interactions at merges at the microscopic scale is to combine a gap-acceptance model with a car-following algorithm. However, in congested conditions (when a queue spills back on the major road), outputs of such a combination may be irrelevant if anticipatory aspects of vehicle behaviours are disregarded (like in single-level gap-acceptance models). Indeed, the insertion decision outcomes are so closely bound to the car-following algorithm that irrelevant results are produced. On the one hand, the insertion decision choice is sensitive to numerical errors due to the car-following algorithm. On the other hand, the priority sharing process observed in congestion cannot be correctly reproduced because of the constraints imposed by the car-following on the gap-acceptance model. To get over these issues, more sophisticated gap-acceptance algorithms accounting for cooperation and aggressiveness amongst drivers have been recently developed (multi-level gap-acceptance models). Another simpler solution, with fewer parameters, is investigated in this paper. It consists in introducing a relaxation procedure within the car-following rules and proposing a new insertion decision algorithm in order to loosen the links between both model components. This approach will be shown to accurately model the observed flow allocation pattern in congested conditions at an aggregate scale.     

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.