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.     

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.     

A field evaluation case study of the environmental and energy impacts of traffic calming

This study quantifies the energy and environmental impact of a selection of traffic calming measures using a combination of second-by-second floating-car global positioning system data and microscopic energy and emission models. It finds that traffic calming may result in negative impacts on vehicle fuel consumption and emission rates if drivers exert aggressive acceleration levels to speed up to their journeys. Consequently by eliminating sharp acceleration maneuvers significant savings in vehicle fuel consumption and emission rates are achievable through driver education. The study also demonstrates that high emitting vehicles produce CO emissions that are up to 25 times higher than normal vehicle emission levels while low emitting vehicles produce emissions that are 15–35% of normal vehicles. The relative increases in vehicle fuel consumption and emission levels associated with the sample traffic calming measures are consistent and similar for normal, low, and high emitting vehicles.     

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.     

Are vehicle trajectories simulated by dynamic traffic models relevant for estimating fuel consumption?

This paper questions the relevance of microscopic traffic models for estimating the impact of traffic strategies on fuel consumption. Urban driving cycles from the ARTEMIS database are simplified into piecewise linear speed profiles to mimic the classical outputs of microscopic traffic flow models. Fuel consumption is estimated for real and simplified trajectories and links between kinematics and the fuel consumption errors are investigated. Simplifying trajectories causes fuel consumption underestimation, from −1.2 to −5.2% on average according to the level of simplification; errors can approach −20% for some cycles. A focus on kinematic phases indicates that the maximum speed reached and the time decelerating are the main influences on fuel consumption. Finally, in the case where maximum speeds are estimated correctly, it is shown that errors committed at each kinematic phase when acceleration distributions are approximated by their mean values, converge towards small errors over complete cycles. A method is developed to quantify and reduce these errors.     

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.     

Accounting for traffic speed dynamics when calculating COPERT and PHEM pollutant emissions at the urban scale

Coupling a traffic microsimulation with an emission model is a means of assessing fuel consumptions and pollutant emissions at the urban scale. Dealing with congested states requires the efficient capture of traffic dynamics and their conditioning for the emission model. Two emission models are investigated here: COPERT IV and PHEM v11. Emission calculations were performed at road segments over 6 min periods for an area of Paris covering 3 km². The resulting network fuel consumption (FC) and nitrogen oxide (NOx) emissions are then compared. This article investigates: (i) the sensitivity of COPERT to the mean speed definition, and (ii) how COPERT emission functions can be adapted to cope with vehicle dynamics related to congestion. In addition, emissions are evaluated using detailed traffic output (vehicle trajectories) paired with the instantaneous emission model, PHEM.COPERT emissions are very sensitive to mean speed definition. Using a degraded speed definition leads to an underestimation ranging from −13% to −25% for fuel consumption during congested periods (from −17% to −36% respectively for NOx emissions). Including speed distribution with COPERT leads to higher emissions, especially under congested conditions (+13% for FC and +16% for NOx). Finally, both these implementations are compared to the instantaneous modeling chain results. Performance indicators are introduced to quantify the sensitivity of the coupling to traffic dynamics. Using speed distributions, performance indicators are more or less doubled compared to traditional implementation, but remain lower than when relying on trajectories paired with the PHEM emission model.     

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.     

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 probabilistic model for vehicle scheduling based on stochastic trip times

Vehicle scheduling plays a profound role in public transit planning. Traditional approaches for the Vehicle Scheduling Problem (VSP) are based on a set of predetermined trips in a given timetable. Each trip contains a departure point/time and an arrival point/time whilst the trip time (i.e. the time duration of a trip) is fixed. Based on fixed durations, the resulting schedule is hard to comply with in practice due to the variability of traffic and driving conditions. To enhance the robustness of the schedule to be compiled, the VSP based on stochastic trip times instead of fixed ones is studied. The trip times follow the probability distributions obtained from the data captured by Automatic Vehicle Locating (AVL) systems. A network flow model featuring the stochastic trips is devised to better represent this problem, meanwhile the compatibility of any pair of trips is redefined based on trip time distributions instead of fixed values as traditionally done. A novel probabilistic model of the VSP is proposed with the objectives of minimizing the total cost and maximizing the on-time performance. Experiments show that the probabilistic model may lead to more robust schedules without increasing fleet size.     

Optimum routing of battery electric vehicles: Insights using empirical data and microsimulation

This study investigates the energy consumption impact of route selection on battery electric vehicles (BEVs) using empirical second-by-second Global Positioning System (GPS) commute data and traffic micro-simulation data. Drivers typically choose routes that reduce travel time and therefore travel cost. However, BEVs’ limited driving range makes energy efficient route selection of particular concern to BEV drivers. In addition, BEVs’ regenerative braking systems allow for the recovery of energy while braking, which is affected by route choices. State-of-the-art BEV energy consumption models consider a simplified constant regenerative braking energy efficiency or average speed dependent regenerative braking factors. To overcome these limitations, this study adopted a microscopic BEV energy consumption model, which captures the effect of transient behavior on BEV energy consumption and recovery while braking in a congested network. The study found that BEVs and conventional internal combustion engine vehicles (ICEVs) had different fuel/energy-optimized traffic assignments, suggesting that different routings be recommended for electric vehicles. For the specific case study, simulation results indicate that a faster route could actually increase BEV energy consumption, and that significant energy savings were observed when BEVs utilized a longer travel time route because energy is regenerated. Finally, the study found that regenerated energy was greatly affected by facility types and congestion levels and also BEVs’ energy efficiency could be significantly influenced by regenerated energy.     

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.     

Conformity: How VMT-speed distributions can affect mobile emission inventories

Transportation conformity is a US regulatory process that requires that transportation modeling be integrated with air quality modeling. Consequently, every change to either modeling process is undertaken with great scrutiny by the regional governments, who have to use the models for demonstrating conformity. This paper explores the "trip versus link debate," which stems from the fact that the standard travel demand models used by most metropolitan planning organizations are primarily link oriented, while the air quality models have been primarily trip oriented. Using the Sacramento region we examine the effects on mobile source emissions inventories when speed-VMT distributions are constructed using the trip and link-based philosophies. The results of our study indicate that trip-based VMT-speed distributions produce consistently lower emissions estimates than the link-based distributions. We use the results to assert that deciding between a trip-based or link-based conformity modeling process involves more than the technical difficulty of changesto the models or the potential political ramifications, it involves assessing which method will provide the most accurate estimates of regional motor vehicle emissions. We also examine ways to think about constructing mobile source emission inventories.     

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.     

Evaluation of vehicle acceleration models for emission estimation at an intersection

We evaluate the constant acceleration, linearly decreasing acceleration, and aaSIDRA models in terms of generating second-by-second speed profiles for emission estimations at an intersection. The models are first calibrated using field data from individual vehicle trajectories. With the calibrated models, second-by-second speed and acceleration data are produced, and emissions are estimated using MOVES. Emission estimations based on the calibrated acceleration models are then compared with those based on field trajectory data. The constant acceleration model tends to overestimate emissions; both the linearly decreasing acceleration model and the aaSIDRA model provide accurate emission estimations.     

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.     

Link travel time inference using entry/exit information of trips on a network

This paper studies link travel time estimation using entry/exit time stamps of trips on a steady-state transportation network. We propose two inference methods based on the likelihood principle, assuming each link associates with a random travel time. The first method considers independent and Gaussian distributed link travel times, using the additive property that trip time has a closed-form distribution as the summation of link travel times. We particularly analyze the mean estimates when the variances of trip time estimates are known with a high degree of precision and examine the uniqueness of solutions. Two cases are discussed in detail: one with known paths of all trips and the other with unknown paths of some trips. We apply the Gaussian mixture model and the Expectation–Maximization (EM) algorithm to deal with the latter. The second method splits trip time proportionally among links traversed to deal with more general link travel time distributions such as log-normal. This approach builds upon an expected log-likelihood function which naturally leads to an iterative procedure analogous to the EM algorithm for solutions. Simulation tests on a simple nine-link network and on the Sioux Falls network respectively indicate that the two methods both perform well. The second method (i.e., trip splitting approximation) generally runs faster but with larger errors of estimated standard deviations of link travel times.     

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.     

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.