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.     

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.     

Towards data-driven car-following models

Car following models have been studied with many diverse approaches for decades. Nowadays, technological advances have significantly improved our traffic data collection capabilities. Conventional car following models rely on mathematical formulas and are derived from traffic flow theory; a property that often makes them more restrictive. On the other hand, data-driven approaches are more flexible and allow the incorporation of additional information to the model; however, they may not provide as much insight into traffic flow theory as the traditional models. In this research, an innovative methodological framework based on a data-driven approach is proposed for the estimation of car-following models, suitable for incorporation into microscopic traffic simulation models. An existing technique, i.e. locally weighted regression (loess), is defined through an optimization problem and is employed in a novel way. The proposed methodology is demonstrated using data collected from a sequence of instrumented vehicles in Naples, Italy. Gipps’ model, one of the most extensively used car-following models, is calibrated against the same data and used as a reference benchmark. Optimization issues are raised in both cases. The obtained results suggest that data-driven car-following models could be a promising research direction.     

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.     

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.     

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).     

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.     

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.     

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.     

Development and testing of a fully Adaptive Cruise Control system

Adaptive Cruise Control systems have been developed and introduced into the consumer market for over a decade. Among these systems, fully-adaptive ones are required to adapt their behaviour not only to traffic conditions but also to drivers’ preferences and attitudes, as well as to the way such preferences change for the same driver in different driving sessions. This would ideally lead towards a system where an on-board electronic control unit can be asked by the driver to calibrate its own parameters while he/she manually drives for a few minutes (learning mode). After calibration, the control unit switches to the running mode where the learned driving style is applied. The learning mode can be activated by any driver of the car, for any driving session and each time he/she wishes to change the current driving behaviour of the cruise control system.The modelling framework which we propose to implement comprises four layers (sampler, profiler, tutor, performer). The sampler is responsible for human likeness and can be calibrated while in learning mode. Then, while in running mode, it works together with the other modelling layers to implement the logic. This paper presents the overall framework, with particular emphasis on the sampler and the profiler that are explained in full mathematical detail. Specification and calibration of the proposed framework are supported by the observed data, collected by means of an instrumented vehicle. The data are also used to assess the proposed framework, confirming human-like and fully-adaptive characteristics.     

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 framework for user- and system-oriented optimisation of fuel efficiency and traffic flow in Adaptive Cruise Control

Fully automated vehicles could have a significant share of the road network traffic in the near future. Several commercial vehicles with full-range Adaptive Cruise Control (ACC) systems or semi-autonomous functionalities are already available on the market. Many research studies aim at leveraging the potential of automated driving in order to improve the fuel efficiency of vehicles. However, in the vast majority of those, fuel efficiency is isolated to the driving dynamics between a single follower-leader pair, hence overlooking the complex nature of traffic. Consequently fuel efficiency and the efficient use of the roadway capacity are framed as conflicting objectives, leading to fuel-economy control models that adopt highly conservative driving styles.This formulation of the problem could be seen as a user-optimal approach, where in spite of delivering savings for individual vehicles, there is the side-effect of the deterioration of traffic flow. An important point that is overlooked is that the inefficient use of roadway capacity gives rise to congested traffic and traffic breakdowns, which in return increases energy costs within the system. The optimisation methods used in these studies entail high computational costs and, therefore, impose a strict constraint on the scope of problem.In this study, the use of car-following models and the limitation of the search space of optimal strategies to the parameter space of these is proposed. The proposed framework enables performing much more comprehensive optimisations and conducting more extensive tests on the collective impacts of fuel-economy driving strategies. The results show that, as conjectured, a “short-sighted” user-optimal approach is unable to deliver overall fuel efficiency. Conversely, a system-optimal formulation for fuel efficient driving is presented, and it is shown that the objectives of fuel efficiency and traffic flow are in fact not only non-conflicting, but also that they could be viewed as one when the global benefits to the network are considered.     

A high fidelity traffic simulation model based on cellular automata and car-following concepts

A high fidelity cell based traffic simulation model (CELLSIM) has been developed for simulation of high volume of traffic at the regional level. Straightforward algorithms and efficient use of computational resources make the model suitable for real time traffic simulation. The model formulation uses concepts of cellular automata (CA) and car-following (CF) models, but is more detailed than CA models and has realistic acceleration and deceleration models for vehicles. A simple dual-regime constant acceleration model has been used that requires minimal calculation compared to detailed acceleration models used in CF models. CELLSIM is simpler than most CF models; a simplified car-following logic has been developed using preferred time headway. Like CA models, integer values are used to make the model run faster. Space is discretized in small intervals and a new concept of percent space occupancy (SOC) is used to measure traffic congestion. CELLSIM performs well in congested and non-congested traffic conditions. It has been validated comprehensively at the macroscopic and microscopic levels using two sets of field data. Comparison of field data and CELLSIM for trajectories, average speed, density and volume show very close agreement. Statistical comparison of macroscopic parameters with other CF models indicates that CELLSIM performs as good as detailed CF models. Stability analyses conducted using mild and severe disturbances indicate that CELLSIM performs well under both conditions.     

Behavior-based consistency-seeking models as deployment alternatives to dynamic traffic assignment models

This paper proposes a behavior-based consistency-seeking (BBCS) model as an alternative to the dynamic traffic assignment paradigm for the real-time control of traffic systems under information provision. The BBCS framework uses a hybrid probabilistic–possibilistic model to capture the day-to-day evolution and the within-day dynamics of individual driver behavior. It considers heterogeneous driver classes based on the broad behavioral characteristics of drivers elicited from surveys and past studies on driver behavior. Fuzzy logic and if–then rules are used to model the various driver behavior classes. The approach enables the modeling of information characteristics and driver response to be more consistent with the real-world. The day-to-day evolution of driver behavior characteristics is reflected by updating the appropriate model parameters based on the current day’s experience. The within-day behavioral dynamics are reactive and capture drivers’ actions vis-à-vis the ambient driving conditions by updating the weights associated with the relevant if–then rules. The BBCS model is deployed by updating the ambient driver behavior class fractions so as to ensure consistency with the real-time traffic sensor measurements. Simulation experiments are conducted to investigate the real-time applicability of the proposed framework to a real-world network. The results suggest that the approach can reasonably capture the within-day variations in driver behavior model parameters and class fractions in the traffic stream. Also, they indicate that deployment-capable information strategies can be used to influence system performance. From a computational standpoint, the approach is real-time deployable.     

Modelling supported driving as an optimal control cycle: Framework and model characteristics

Driver assistance systems support drivers in operating vehicles in a safe, comfortable and efficient way, and thus may induce changes in traffic flow characteristics. This paper puts forward a receding horizon control framework to model driver assistance and cooperative systems. The accelerations of automated vehicles are controlled to optimise a cost function, assuming other vehicles driving at stationary conditions over a prediction horizon. The flexibility of the framework is demonstrated with controller design of Adaptive Cruise Control (ACC) and Cooperative ACC (C-ACC) systems. The proposed ACC and C-ACC model characteristics are investigated analytically, with focus on equilibrium solutions and stability properties. The proposed ACC model produces plausible human car-following behaviour and is unconditionally locally stable. By careful tuning of parameters, the ACC model generates similar stability characteristics as human driver models. The proposed C-ACC model results in convective downstream and absolute string instability, but not convective upstream string instability observed in human-driven traffic and in the ACC model. The control framework and analytical results provide insights into the influences of ACC and C-ACC systems on traffic flow operations.     

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 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.     

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.     

A Framework for Developing Driving Cycles with On‐Road Driving Data

Abstract

This paper attempts to propose a framework on driving cycle development based on a thorough review of 101 transient driving cycles. A comparison of the driving cycles highlighted that Asian driving is the slowest but most aggressive while European driving is the fastest and smoothest. Further review of the cycle development methodologies identified three major elements for developing a driving cycle; test route selection, data collection and cycle construction methods. A framework was eventually proposed based on these findings and recommendations from this review. First, traffic activity patterns and quantitative statistics should be considered in determining the test routes. Speed data can be collected by using chase car method, on‐board measurement techniques or their hybrid. As for the construction of driving cycle, the matching approach has been more commonly used. It is recommended that the tendency of zero change in acceleration, which has been commonly ignored in the literature, and the application of succession probability at second‐by‐second level should be further explored. A fifth mode, creeping, is also recommended for modal analysis for characterizing urban congested driving conditions.