Optimization of Wiedemann and Fritzsche car-following models for emission estimation

Recent studies have provided that the vehicle trajectories generated by car-following models may not represent the real driving characteristics, thus leading to significant emission estimation errors. In this paper, two of the most widely used car-following models, Wiedemann and Fritzsche models, were selected and analyzed based on the massive field car-following trajectories in Beijing. A numerical simulation method was designed to generate the following car’s trajectories by using the field trajectories as the input. By comparing the simulated and the filed data, the representativeness of the simulated regime fractions and VSP distributions were evaluated. Then, the mechanism of car-following models was investigated from the aspects of regime determination and the acceleration rule in each regime. Further, the regime threshold parameters and acceleration model were optimized for emission estimations. This study found that the “Following” regime threshold of SDX and the maximum acceleration in “Free Driving” regime are critical parameters for Wiedemann model. The differences between the Wiedemann simulated VSP distribution and the field one can be reduced separately by applying the optimized SDX and maximum acceleration model individually. However, a much sharper reduction was observed by optimizing both parameters simultaneously, and the emission estimation errors were further reduced, which were less than 4% in the case studies. Fritzsche model generated more realistic VSP distributions and emissions, while the maximum accelerations could be further optimized for high speed conditions.     

Trajectory data reconstruction and simulation-based validation against macroscopic traffic patterns

This paper shows that the behavior of driver models, either individually or entangled in stochastic traffic simulation, is affected by the accuracy of empirical vehicle trajectories. To this aim, a “traffic-informed” methodology is proposed to restore physical and platoon integrity of trajectories in a finite time–space domain, and it is applied to one NGSIM I80 dataset. However, as the actual trajectories are unknown, it is not possible to verify directly whether the reconstructed trajectories are really “nearer” to the actual unknowns than the original measurements. Therefore, a simulation-based validation framework is proposed, that is also able to verify indirectly the efficacy of the reconstruction methodology. The framework exploits the main feature of NGSIM-like data that is the concurrent view of individual driving behaviors and emerging macroscopic traffic patterns. It allows showing that, at the scale of individual models, the accuracy of trajectories affects the distribution and the correlation structure of lane-changing model parameters (i.e. drivers heterogeneity), while it has very little impact on car-following calibration. At the scale of traffic simulation, when models interact in trace-driven simulation of the I80 scenario (multi-lane heterogeneous traffic), their ability to reproduce the observed macroscopic congested patterns is sensibly higher when model parameters from reconstructed trajectories are applied. These results are mainly due to lane changing, and are also the sought indirect validation of the proposed data reconstruction methodology.     

A flexible traffic stream model and its three representations of traffic flow

To connect microscopic driving behaviors with the macro-correspondence (i.e., the fundamental diagram), this study proposes a flexible traffic stream model, which is derived from a novel car-following model under steady-state conditions. Its four driving behavior-related parameters, i.e., reaction time, calmness parameter, speed- and spacing-related sensitivities, have an apparent effect in shaping the fundamental diagram. Its boundary conditions and homogenous case are also analyzed in detail and compared with other two models (i.e., Longitudinal Control Model and Intelligent Driver Model). Especially, these model formulations and properties under Lagrangian coordinates provide a new perspective to revisit the traffic flow and complement with those under Eulerian coordinate. One calibration methodology that incorporates the monkey algorithm with dynamic adaptation is employed to calibrate this model, based on real-field data from a wide range of locations. Results show that this model exhibits the well flexibility to fit these traffic data and performs better than other nine models. Finally, a concrete example of transportation application is designed, in which the impact of three critical parameters on vehicle trajectories and shock waves with three representations (i.e., respectively defined in x-t, n-t and x-n coordinates) is tested, and macro- and micro-solutions on shock waves well agree with each other. In summary, this traffic stream model with the advantages of flexibility and efficiency has the good potential in level of service analysis and transportation planning.     

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.     

Adaptive cruise control design for active congestion avoidance

We present an adaptive cruise control (ACC) strategy where the acceleration characteristics, that is, the driving style automatically adapts to different traffic situations. The three components of the concept are the ACC itself, implemented in the form of a car-following model, an algorithm for the automatic real-time detection of the traffic situation based on local information, and a strategy matrix to adapt the driving characteristics (that is, the parameters of the ACC controller) to the traffic conditions. Optionally, inter-vehicle and infrastructure-to-car communication can be used to improve the accuracy of determining the traffic states. Within a microscopic simulation framework, we have simulated the complete concept on a road section with an on-ramp bottleneck, using empirical loop-detector data for an afternoon rush-hour as input for the upstream boundary. We found that the ACC vehicles improve the traffic stability and the dynamic road capacity. While traffic congestion in the reference scenario was completely eliminated when simulating a proportion of 25% ACC vehicles, travel times were already significantly reduced for much lower penetration rates. The efficiency of the proposed driving strategy even for low market penetrations is a promising result for a successful application in future driver assistance systems.     

A multi-commodity Lighthill–Whitham–Richards model of lane-changing traffic flow

Systematic lane changes can seriously deteriorate traffic safety and efficiency inside lane-drop, merge, and other bottleneck areas. In our previous studies (Jin, 2010a, Jin, 2010b), a phenomenological model of lane-changing traffic flow was proposed, calibrated, and analyzed based on a new concept of lane-changing intensity. In this study, we further consider weaving and non-weaving vehicles as two commodities and develop a multi-commodity, behavioral Lighthill–Whitham–Richards (LWR) model of lane-changing traffic flow. Based on a macroscopic model of lane-changing behaviors, we derive a fundamental diagram with parameters determined by car-following and lane-changing characteristics as well as road geometry and traffic composition. We further calibrate and validate fundamental diagrams corresponding to a triangular car-following fundamental diagram with NGSIM data. We introduce an entropy condition for the multi-commodity LWR model and solve the Riemann problem inside a homogeneous lane-changing area. From the Riemann solutions, we derive a flux function in terms of traffic demand and supply. Then we apply the model to study lane-changing traffic dynamics inside a lane-drop area and show that the smoothing effect of HOV lanes is consistent with observations in existing studies. The new theory of lane-changing traffic flow can be readily incorporated into Cell Transmission Model, and this study could lead to better strategies for mitigating bottleneck effects of lane-changing traffic flow.     

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.     

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.     

Agent-based simulation framework for mixed traffic of cars,pedestrians and trams

In this paper, we report on the construction of a new framework for simulating mixed traffic consisting of cars, trams, and pedestrians that can be used to support discussions about road management, signal control, and public transit. Specifically, a layered road structure that was designed for car traffic simulations was extended to interact with an existing one-dimensional (1D) car-following model and a two-dimensional (2D) discrete choice model for pedestrians. The car model, pedestrian model, and interaction rules implemented in the proposed framework were verified through simulations involving simple road environments. The resulting simulated values were in near agreement with the empirical data. We then used the proposed framework to assess the impact of a tramway extension plan for a real city. The simulation results showed that the impact of the proposed tramway on existing car traffic would not be serious, and by extension, implied that the proposed framework could help stakeholders decide on expansion scenarios that are satisfactory to both tram users and private car owners.     

Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts

Despite the availability of large empirical data sets and the long history of traffic modeling, the theory of traffic congestion on freeways is still highly controversial. In this contribution, we compare Kerner’s three-phase traffic theory with the phase diagram approach for traffic models with a fundamental diagram. We discuss the inconsistent use of the term “traffic phase” and show that patterns demanded by three-phase traffic theory can be reproduced with simple two-phase models, if the model parameters are suitably specified and factors characteristic for real traffic flows are considered, such as effects of noise or heterogeneity or the actual freeway design (e.g. combinations of off- and on-ramps). Conversely, we demonstrate that models created to reproduce three-phase traffic theory create similar spatiotemporal traffic states and associated phase diagrams, no matter whether the parameters imply a fundamental diagram in equilibrium or non-unique flow-density relationships. In conclusion, there are different ways of reproducing the empirical stylized facts of spatiotemporal congestion patterns summarized in this contribution, and it appears possible to overcome the controversy by a more precise definition of the scientific terms and a more careful comparison of models and data, considering effects of the measurement process and the right level of detail in the traffic model used.     

A two-dimensional simulation model for modelling turning vehicles at mixed-flow intersections

The turning behavior is one of the most challenging driving maneuvers under non-protected phase at mixed-flow intersections. Currently, one-dimensional simulation models focus on car-following and gap-acceptance behaviors in pre-defined lanes with few lane-changing behaviors, and they cannot model the lateral and longitudinal behaviors simultaneously, which has limitation in representing the realistic turning behavior. This paper proposes a three-layered “plan-decision-action” (PDA) framework to obtain acceleration and angular velocity in the turning process. The plan layer firstly calculates the two-dimensional optimal path and dynamically adjusts the trajectories according to interacting objects. The decision layer then uses the decision tree method to select a suitable behavior in three alternatives: car-following, turning and yielding. Finally, in the action layer, a set of corresponding operational models specify the decided behavior into control parameters. The proposed model is tested by reproducing 210 trajectories of left-turn vehicles at a two-phase mixed-flow intersection in Shanghai. As a result, the simulation reproduces the variation of trajectories, while the coverage rate of the trajectories is 88.8%. Meanwhile, both the travel time and post-encroachment time of simulation and empirical turning vehicles are similar and do not show statistically significant difference.     

Brake light cellular automaton model with advanced randomization for traffic breakdown

Traffic breakdown is one of the most important empirical phenomena in traffic flow theory. Unfortunately, it cannot be simulated by many traffic flow models. In order to clarify its mechanism, the new brake light cellular automaton model has been proposed. Comparing with previous brake light models, three different aspects have been considered: (i) drivers tend to take large decelerations if the time gap is smaller than the safe time gap and the leading vehicle’s brake light is on; (ii) the brake light rule is set according to the reality; (iii) the randomization rule is put forward before the acceleration rule to weaken the impact of brake light on driving behaviors. Analyses show that the new model can explain the mechanism of traffic breakdown and the failures of other brake light models. Simulations confirm that all empirical features of traffic breakdown are successfully reproduced. At last, brake light models are calibrated and validated by the I-80 empirical data provided by NGSIM. Results show that the performance of the new model is the best and models in the three-phase theory are not necessarily better than models in the fundamental diagram approach and vice versa, at least for the brake light models.     

Categorization of the lane change decision process on freeways

Traffic operations for new road layouts are often simulated using microscopic traffic simulation packages. These traffic simulation packages usually simulate traffic on freeways by a combination of a car-following model and a lane change model. The car-following models have gained attention of researchers and are well calibrated versus data. The proposed lane change models are often representations of assumed reasonable behavior, not necessarily corresponding to reality. The current simulation packages apply solely one specific type of model for car-following or lane changing for all vehicles during the simulation. This paper investigates the decision process of lane changing maneuvers for a variety of drivers based on a two-stage test-drive. Participants are asked to take a drive on a freeway in the Netherlands in a camera-equipped vehicle. Afterwards, the drivers are asked to comment on their choices related to lane and speed choice, while watching the video. This paper reveals that different drivers have completely different strategies to choose lanes, and the choices to change lane are related to their speed choice. Four distinct strategies are empirically found. These strategies differ not only in parameter values, as is currently being modeled in most simulation packages, but also in their reasoning. Most remarkably, all drivers perceive their strategy as an obvious behavior and expect all other drivers to drive in a similar way. In addition to the interviews of the participants in the test-drive, 11 people who did not take part in the experiment were interviewed and questioned on lane change decisions. Moreover, the findings of this study have been presented to various groups of audience with different backgrounds (about 150 people). Their comments and feedback on the derived driving strategies have added some value to this study. The findings in this paper form a starting point for developing a novel lane change model which considers four different driving strategies among the drivers on freeway. This is a significant contribution in the area of driving behavior modeling, since the existing microscopic simulators consider only one type of lane change models for all drivers during the simulation. This could lead to significant changes in the way lane changes on freeways are modeled.     

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).     

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.     

Online calibration for microscopic traffic simulation and dynamic multi-step prediction of traffic speed

Simulating driving behavior in high accuracy allows short-term prediction of traffic parameters, such as speeds and travel times, which are basic components of Advanced Traveler Information Systems (ATIS). Models with static parameters are often unable to respond to varying traffic conditions and simulate effectively the corresponding driving behavior. It has therefore been widely accepted that the model parameters vary in multiple dimensions, including across individual drivers, but also spatially across the network and temporally. While typically on-line, predictive models are macroscopic or mesoscopic, due to computational and data considerations, nowadays microscopic models are becoming increasingly practical for dynamic applications. In this research, we develop a methodology for online calibration of microscopic traffic simulation models for dynamic multi-step prediction of traffic measures, and apply it to car-following models, one of the key models in microscopic traffic simulation models. The methodology is illustrated using real trajectory data available from an experiment conducted in Naples, using a well-established car-following model. The performance of the application with the dynamic model parameters consistently outperforms the corresponding static calibrated model in all cases, and leads to less than 10% error in speed prediction even for ten steps into the future, in all considered data-sets.     

On some experimental features of car-following behavior and how to model them

We have carried out car-following experiments with a 25-car-platoon on an open road section to study the relation between a car’s speed and its spacing under various traffic conditions, in the hope to resolve a controversy surrounding this fundamental relation of vehicular traffic. In this paper we extend our previous analysis of these experiments, and report new experimental findings. In particular, we reveal that the platoon length (hence the average spacing within a platoon) might be significantly different even if the average velocity of the platoon is essentially the same. The findings further demonstrate that the traffic states span a 2D region in the speed-spacing (or density) plane. The common practice of using a single speed-spacing curve to model vehicular traffic ignores the variability and imprecision of human driving and is therefore inadequate. We have proposed a car-following model based on a mechanism that in certain ranges of speed and spacing, drivers are insensitive to the changes in spacing when the velocity differences between cars are small. It was shown that the model can reproduce the experimental results well.     

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.