For car traffic it was found that a more crowded area leads to a lower speed and a lower arrival rate. The relation between crowdedness and speed (or arrival rate) can be expressed in a network fundamental diagram, or macroscopic fundamental diagram (MFD). Similar concepts have been shown for pedestrian and train traffic. In this paper, we extend the concept to three spatial dimensions. While simulations have explored some concepts, we present for the first time empirical results of the relation between the crowdedness in the air and the performance of the “network.” We base our results on several months of data of airplanes around Amsterdam Schiphol Airport. Similar to car traffic, we observe a reduction in speeds as the number of airplanes in the area increases. However, even at the highest observed densities, we do not see a reduction in flows. This is because of active and intensive management (based on departure/landing possibilities), comparable to perimeter control in traffic, as well as a minimum airplane speed. This paper introduces an interesting concept of applying a MFD to three-dimensional (3D) spaces. We also show to what extent the performance reduction is caused by speed reduction and to what extent it is caused by less efficient routes. The MFD concept can eventually be used to also manage 3D airspaces for applications with less strict microscopic air traffic management than the current management around airports.@en

Traffic condition forecasting is fundamental for Intelligent Transportation Systems. Besides accuracy, many services require an estimate of uncertainty for each prediction. Uncertainty quantification must consider the inherent randomness in traffic dynamics, the so-called aleatoric uncertainty, and the additional distrust caused by data shortage, the so-called epistemic uncertainty. They together depict how predictable macroscopic traffic is. This study uses deep ensembles of graph neural networks to estimate both types of uncertainty in network-level speed forecasting. Experimental results given by the used model reveal that, although rare congestion patterns arise randomly, the short-term predictability of traffic states is mainly restricted by the irreducible stochasticity in traffic dynamics. The predicted future state bifurcates into congested or free-flowing cases. This study suggests that the potential for improving prediction models through expanding speed and flow data is limited while diversifying data types is crucial.@en

A lane-changing (LC) maneuver may cause the follower in the target lane (new follower) to decelerate and give up space, potentially affecting crash risk and traffic flow efficiency. In congested flow, a more aggressive LC maneuver occurs where the lane changer is partially next to the new follower and creates negative gaps, namely negative gap forced LC (NGFLC). Although NGFLC forms the foundation of sideswipe crashes, little has been done to address its impacts and the contributing factors. To tackle this issue, a total of 15,810 LC trajectory samples are extracted from three drone videos at different locations. These samples are categorized into NGFLC and normal LC groups for comparative analysis. Five commonly used conflict indicators are extended into two-dimensional to evaluate the crash risk of LC maneuver. The change of time gaps during LC maneuver are examined to quantify the impact of LC on traffic flow efficiency. We find that NGFLCs significantly increase crash risk, reflected by the number of hazardous LC events and potential crash areas compared to normal LC. Additionally, results reveal that both the lane changer and the new follower tend to maintain a larger time gap after NGFLCs. Factors including time headway, relative speed, and historical gaps in the target lane significantly affect NGFLC incidence. Once the movement of the leader in the original lane is taken into account, the prediction accuracy improves from 81% to 91%. The transferability tests indicate that the findings about the negative impact of NGFLC and the accuracy of its prediction model are consistent across different locations. These findings hold implications for driving assistance systems to better predict and mitigate NGFLCs.

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Resolving predicted conflicts is vital for safe and efficient autonomous vehicles (AV). In practice, vehicular motion prediction faces inherent uncertainty due to heterogeneous driving behaviours and environments. This spatial uncertainty increases non-linearly with prediction time horizons, leading AVs to perceive more road space occupied by conflicting vehicles. Reacting early to resolve predicted conflicts can ensure safety but may adversely affect traffic efficiency. Therefore, determining how far ahead AVs should start resolving predicted conflicts based on safety and traffic efficiency constraints is crucial. To answer this question, this study proposes a novel approach to explore the trade-off between safety and traffic efficiency considering prediction uncertainty. Firstly, a continuous-time motion prediction framework is proposed for estimating the spatial probability distribution of a vehicle's future position at any moment within the maximum time horizon. Subsequently, average driver space and the corresponding traffic flow are derived from the safety settings of AV and prediction uncertainty. As such, the safety-efficiency trade-off can be quantified. Experiments show that mandatory decision points, high speeds, and traffic state transitions usually cause fast-increasing prediction uncertainty. A case study of Intelligent Driver Models (IDM) shows that traffic efficiency drops rapidly when AVs resolve predicted conflicts longer than 1.5 seconds ahead. AVs can act earlier on motorways for efficiency concerns but must be myopic at urban intersections. Prediction uncertainty fundamentally constrains the safety-efficiency performance of AVs. These findings are instructive for designing traffic-compatible AVs.

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Predicting the trajectories of road agents is fundamental for self-driving cars. Trajectory prediction contains many sources of uncertainty in data and modelling. A thorough understanding of this uncertainty is crucial in a safety-critical task like auto-piloting a vehicle. In practice, it is necessary to distinguish between the uncertainty caused by partial observability of all factors that may affect a driver's near-future decisions, the so-called aleatoric uncertainty, and the uncertainty of deploying a model in new scenarios that are possibly not present in the training set, the so-called epistemic uncertainty. They reflect the trade-off between data collection and model improvement In this paper, we propose a new framework to systematically quantify both sources of uncertainty. Specifically, to approximate the spatial distribution of an agent's future position, we propose a 2D histogram-based deep learning model combined with deep ensemble techniques for measuring aleatoric and epistemic uncertainty by entropy-based quantities. The proposed Uncertainty Quantification Network (UQnet) employs a causal part to enhance its generalizability so rare driving behaviours can be effectively identified. Experiments on the INTERACTION dataset show that UQnet is able to give more robust predictions in generalizability tests compared to the correlation-based models. Further analysis presents that high aleatoric uncertainty cases are mainly caused by heterogeneous driving behaviours and unknown intended directions. Based on this aleatoric uncertainty component, we estimate the lower bounds of mean-square-error and final-displacement-error as indicators for the predictability of trajectories. Furthermore, the analysis of epistemic uncertainty illustrates that domain knowledge of speed-dependent driving behaviour is essential for adapting a model from low-speed to high-speed situations. Our paper contributes to motion forecasting with a new framework, that recasts the problem of accuracy improvement in a way that focuses on differentiating between unpredictable components and rare cases for which more and different data should be collected.

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The deep understanding of the behaviors of traffic participants is essential to guarantee the safety of automated vehicles (AV) in mixed traffic with vulnerable road users (VRUs). Precise trajectory prediction of traffic participants can provide reasonable solution space for motion planning of AV. Early works mainly focused on handcrafting the feature representation and designing complicated architectures in deep learning-based prediction models. However, these approaches overlooked the fact that different road users perceive the safety of the same interaction differently and also exhibit heterogeneous risk-taking styles. In this paper, we will develop a model for trajectory prediction based on risk-taking styles. The model accounts for the expected positions and occupancy of traffic participants in the surrounding environment. It consists of two sequential steps: risk-taking styles of multi-modal road users under interactive scenes are first clustered, and then reformulated in the heterogeneous graph model for trajectory prediction. The model is validated by the driving data collected on the urban road using a public dataset. Comparative experiments demonstrate that the proposed method can predict the trajectory of traffic participants much more accurately than the state-of-the-art methods.

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A substantial number of vehicles nowadays are equipped with adaptive cruise control (ACC), which adjusts the vehicle speed automatically. However, experiments have found that commercial ACC systems which only detect the direct leader amplify the propagating disturbances in the platoon. This can cause severe traffic congestion when the number of ACC-equipped vehicles increases. Therefore, an ACC system which also considers the second leader further downstream is required. Such a system enables the vehicle to achieve multi-anticipation and hence ensure better platoon stability. Nevertheless, measurements collected from the second leader may be comparatively inaccurate given the limitations of current state-of-the-art sensor technology. This study adopts deep reinforcement learning to develop ACC controllers that besides the input from the first leader exploits the additional information obtained from the second leader, albeit noisy. The simulation experiment demonstrates that even under the influence of noisy measurements, the multi-leader ACC platoon shows smaller disturbance and jerk amplitudes than the one-leader ACC platoon, indicating improved string stability and ride comfort. Practical takeaways are twofold: first, the proposed method can be used to further develop multi-leader ACC systems. Second, even noisy data from the second leader can help stabilize traffic, which makes such systems viable in practice.

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The pre-insertion process called anticipation is an essential component of a lane-changing manoeuvre. There is little empirical research regarding the impact of anticipation. Thus, this paper aims to explore the behaviour of the new follower (NF) in the target lane when it encounters anticipation by using new trajectory datasets. The changing magnitude of the reaction pattern is proposed to identify the NF’s behaviour. We find that the anticipation significantly affects the NF’s movement in terms of gap creation and speed reduction. Then, we conduct a detailed analysis of critical variables to reveal their relationship with the NF’s behaviour. Following this, we develop binary logistic models to predict the NF’s behaviour, resulting in a good performance. It also suggests that the NF’s behaviour is highly related to the anticipation-related variables. The transferability test results show that this model can be directly used in different locations and times with satisfactory accuracy.@en

The traffic density of small aerial vehicles operating within urban environments is expected to increase significantly in the near future. This urban environment is highly constrained due to being limited to the low-altitude airspace directly above the existing road network. Multiple studies have addressed factors influencing the capacity of urban airspace. These have used simulations of aircraft, yet the empirical nature of these simulations limits their use beyond the specific conditions that have been tested. Analytical models would not have this limitation, but they are only developed for general airspace, while the emergent patterns in constrained urban airspace are different than in general, unconstrained conditions. For instance, queuing and local congestion are patterns that are unique to the heavily-constrained environment. Therefore, in this paper, we derive an analytical model for air traffic in a confined airspace to find the influencing factors for its capacity. By means of a simulation of aerial vehicles, we verify the analytical model and show a relationship between the mean flow rate and mean density in a two-dimensional orthogonal grid network airspace. Results show that the entire airspace can become unstable when the maximum capacity of just one intersection is reached. Furthermore, the maximum airspace density is found to be unaffected by cruise speed. The results demonstrate how the derived analytical model provides an effective tool to predict the effect of several design parameters on the capacity of constrained urban airspace. Moreover, this model can form the basis for further extensions, including the altitude dimension and non-orthogonal or non-four-way intersections.

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The macroscopic fundamental diagram (MFD) is developed to describe traffic operations aggregated over an area. The MFD is defined by network traffic states as a relationship between the accumulation of vehicles and flow or speed of vehicles. The concept of the MFD has been applied to model traffic dynamics and to design control strategies. For various applications (e.g., routing and departure time choices), the MFD is often assumed to be of a particular shape, consisting of two branches—a free-flow branch and a congestion branch. However, empirical observations show some inconsistencies between the theoretical and the empirical MFD. First, the empirical MFD only presents free-flow branch, i.e., the congestion branch is missing. Second, the MFD presents as hysteresis loop(s). This paper explores these differences, providing insights into urban network traffic dynamics. This work takes the travelers’ departure time choices and user equilibrium (UE) as starting points. We consider demand to be in UE in terms of departure time choices. Using this property of the demand profile, the paper proposes a closed-form expression for average density and outflow. Finally, we show some insights in the urban traffic dynamics: (i) an explanation of the hysteresis phenomenon solely from the perspective of departure time choices and UE and (ii) an explanation of why we hardly observe the MFD congestion branch in real life even in heavily congested networks. Our study shows that, for management purposes, the missing of congestion branch is a result of UE, rather than an indicator of congestion severity.

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Path dispersion (the spatial distribution of vehicular paths) is an important feature of traffic flow inside intersections and differs from traffic flow running along traffic lanes at road segment, especially under conflicting movements. The path dispersion reflects the operational features of traffic flow and is related to driving behaviour, arrival flow patterns, layout design, and the traffic control and management scheme. This study aims to improve the understanding of the overall path dispersion of unprotected left-turns and the opposing through movement. A behavioural simulation model was established to represent the overall path dispersion. Human behaviours regarding vehicle trajectory planning with and without conflicting vehicles were modelled based on optimal control and integrated into the proposed discrete event simulation framework. The descriptive power and accuracy of the proposed simulation model were validated using empirical data. The effects of the spatial size of the intersection, crossing angle, and traffic volume on the path dispersion of the left-turn and through movement were explored based on numerical experiments. The results show that the proposed simulation model can represent the path dispersion of left-turn and opposing through movement well for both the calibrated intersections and newly added intersections without model parameter recalibration with an average error of 8.92%.@en

Lane-changing (LC) in congested traffic has been identified as a trigger for the sudden deceleration behavior of the new follower in the target lane, leading to severe traffic disturbances. Thus, investigating the response of the new follower to an LC maneuver is an important research topic in the literature. To date, numerous efforts have been devoted to understanding the impact of the lane changer on the new follower after the insertion, while less attention has been given to this influence during the pre-insertion stage (anticipation). Therefore, this paper aims to establish a new car-following (CF) model to capture the new follower's driving behavior during anticipation. Specifically, we introduce an attention mechanism deviating from Newell's CF rules to quantify the impact of anticipation. Then, we apply a neural network with an attention layer to estimate the attention mechanism and incorporate it into the Newell CF model, which yields a new CF model, denoted as CF_Attention. Using real-world trajectory data, we design three experiments and select three representative CF models to validate the CF_Attention. The results indicate that the CF_Attention outperforms the other models in predicting the new follower's trajectory, which is not affected by the heterogeneous behavior of the new follower and the anticipation duration. Additionally, the CF_Attention is proven effective in capturing the speed-space relationship and the formation of oscillation. Finally, our transferability test suggests that the CF_Attention is promising for different locations and times without requiring retraining. The results of this study could advance the integration of the LC impact and CF behavior, and could be implemented into commercial traffic simulation programs to describe vehicle movements in traffic flow more accurately.

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Microscopic traffic flow models enable predictions of traffic operations, which allows traffic engineers to assess the efficiency and safety effects of roadway designs. Modeling vehicle trajectories inside intersections is challenging because there is an infinite number of possible paths in a two-dimensional space, and drivers can simultaneously adapt their speeds as well. To date, human driver models for simultaneous longitudinal and lateral vehicle control based on the infrastructure characteristics and interactions with other drivers inside an intersection are still lacking. The contribution of this paper is threefold. First, it proposes an integrated microscopic traffic flow model to describe human-driven vehicle maneuvers under interactions. Drivers plan their heading and acceleration in the predicted future to minimize costs representing undesirable situations. The model works with a joint optimization for an interaction cost term. The weights associated with the interaction cost reflect how selfish or altruistic drivers are. Second, the proposed model endogenously gives the order of vehicles in case of crossing paths. Third, the paper develops a clustered validation method for microscopic traffic flow models with interacting vehicles, which account for interdriver variations. Results show that the model can accurately describe vehicle passing orders of interacting maneuvers, paths, and speeds against empirical data. The model can be applied to assess various intersection designs.

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Traffic dynamics on freeways are stochastic in nature because of errors in perception and operation of drivers as well as the heterogeneity between and within drivers. This stochasticity is often represented in car-following models by a stochastic term, which is assumed to follow a normal distribution for the convenience of mathematical processing. However, the validity of this assumption has not been studied yet. In this study, we focused on the shape of the distribution of a stochastic term in the car-following model that predicts an acceleration after a time step. Based on vehicle trajectory data on a freeway in Japan, a car-following model is first developed by using data-driven methodology in which long short-term memory (LSTM) network is applied. In this LSTM network, the acceleration value is discretized and the model parameters are trained with the focal loss function. The relationship between the predicted distributions’ modality, standard deviation (SD), and (Formula presented.) with respect to traffic states is then examined. The findings demonstrate that: 1) the developed model can accurately predict the accelerations; 2) a probabilistic distribution tends to have a large SD and multimodality around a merging point and at the beginning of and along stop-and-go waves; and 3) driving behavior can be classed in one of four clusters based on the variation of the percentile value that a driver takes within the probability distribution. The proposed model and the insights are helpful for improving microscopic simulation models when considering new traffic management measures.

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Car-Following (CF), as a fundamental driving behaviour, has significant influences on the safety and efficiency of traffic flow. Investigating how human drivers react differently when following autonomous vs. human-driven vehicles (HV) is thus critical for mixed traffic flow. Research in this field can be expedited with trajectory datasets collected by Autonomous Vehicles (AVs). However, trajectories collected by AVs are noisy and not readily applicable for studying CF behaviour. This paper extracts and enhances two categories of CF data, HV-following-AV (H-A) and HV-following-HV (H-H), from the open Lyft level-5 dataset. First, CF pairs are selected based on specific rules. Next, the quality of raw data is assessed by anomaly analysis. Then, the raw CF data is corrected and enhanced via motion planning, Kalman filtering, and wavelet denoising. As a result, 29k+ H-A and 42k+ H-H car-following segments are obtained, with a total driving distance of 150k+ km. A diversity assessment shows that the processed data cover complete CF regimes for calibrating CF models. This open and ready-to-use dataset provides the opportunity to investigate the CF behaviours of following AVs vs. HVs from real-world data. It can further facilitate studies on exploring the impact of AVs on mixed urban traffic.@en

When do traffic jams emerge? Can we predict, given certain demand levels, when queuing will occur, how long the queues will be, how they will propagate in space and time, and how long it takes for the congestion to resolve? Why does an overloaded traffic network underperform? This chapter gives a basic introduction in traffic flow theory which can help to answer these kinds of questions.@en

Accurate short-term traffic forecasting is the cornerstone for Intelligent Transportation Systems. In the past several decades, many models have been proposed to continuously improve the predictive accuracy. A key but unsolved question is whether there is a theoretical bound to the accuracy with which traffic can be predicted and whether that limit can be directly estimated from data. To answer this question, we use core concepts in information theory to derive the limit of predictability in short-term traffic forecasting. Theoretical analysis proves that conditional differential entropy poses a rigorous lower bound of negative-log-likelihood (NLL) for probabilistic models. And the continuous form of Fano's theorem further gives a loose lower bound of mean-square-error (MSE) for deterministic models. Based on the special properties of traffic dynamics, two assumptions are made in the estimate of entropy metrics: cyclostationarity (traffic phenomena show strong periodicity) and localized spatial correlation (due to kinematic wave propagation). They allow formulating the limit of predictability as a function of longitudinal space and time-of-day which finds the most uncertain locations and periods solely from data. Experiments on univariate traffic accumulation forecasting and network-level speed forecasting show that the selected models, including some state-of-the-art deep learning models, indeed cannot outperform the estimated lower bounds but just approach them. The limit of predictability depends on time-of-day, network locations, observation range, and prediction horizon. The results reveal that the stochastic nature of traffic dynamics and improper assumptions on the prior distribution of output are two major factors that restrict the predictive performance. In summary, the proposed method estimates a trustworthy performance boundary for most traffic forecasting models. These conclusions are helpful for further studies in this domain.

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Predicting the trajectories of road agents is fundamental for self-driving cars. Trajectory prediction contains many sources of uncertainty in data and modeling. A thorough understanding of this uncertainty is crucial in a safety-critical task like auto-piloting a vehicle. We need to distinguish between the uncertainty caused by partial observability of all factors that may affect a drivers’ nearfuture decisions, the so-called aleatoric uncertainty, and the uncertainty of deploying a model in new scenarios that are possibly not present in the training set, the so-called epistemic uncertainty. In this paper we propose a new framework to systematically quantify both sources of uncertainty. Specifically, to approximate the spatial distribution of an agent’s future position, we propose a 2D histogram-based deep learning model combined with deep ensemble techniques for measuring both aleatoric and epistemic uncertainty by entropy-based quantities. The proposed Uncertainty Quantification Network (UQnet) employs a causal part to enhance its generalizability. Experiments on the INTERACTION dataset show that UQnet significantly improves the generalizability of the missing rate compared to the previous state-of-the-art. Further analysis shows that high aleatoric uncertainty cases are mainly caused by heterogeneous driving behaviors and unknown intended directions. Based on this aleatoric uncertainty component, we estimate the lower bounds of mean-square-error and final-displacementerror as indicators for the predictability of trajectories. Furthermore, we use the epistemic uncertainty to identify rare cases in the test set. Our results illustrate that domain knowledge on speed-dependent driving behavior is essential for adapting a model from low-speed to high-speed situations. Our paper contributes to motion forecasting with a new framework, that recasts this problem in terms of model generalisation, and puts forward methods to quantify the resulting uncertainty. @en

Pedestrians are among the travelers most vulnerable to collisions that are associated with high fatality and injury rates. The increasing rate of urbanization and mixed land-use construction make walking (along with other non-motorized travel) a predominant transportation mode with a wide variety of behaviors expected. Because of the inherent safety concerns seen in pedestrian transportation infrastructures, especially those with conflicting multimodal movements expected (crosswalks, transit platforms, etc.), it is important that pedestrian behavior is modeled as a risk-taking stochastic behavior that may lead to errors and thus collision formation. In previous work, the complexity and cost associated with building pedestrian models in a cognitive-based environment weighted down the construction of simulation tools that can capture pedestrian-involved collisions, including those seen in shared space environments. In this paper, a tool that will help evaluate the safety of pedestrian traffic is initiated: an extended modeling framework of pedestrian walking behavior is adopted while incorporating different physiological, physical, and decision-making elements. The focus is on operational decisions (i.e., path choices defined by longitudinal and lateral trajectories) with a pre-specified set of origins and destinations. The model relies on the prospect theory paradigm where pedestrians evaluate their acceleration and directional alternatives while considering the possibility of colliding with other ‘‘particles.’’ Using a genetic algorithm method, the new model is calibrated using detailed trajectory data. This model can be extended to model the interactions between a variety of different modes that are present in different mixed land-use environments.

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Traffic jams are caused by a traffic demand that exceeds road capacity. Road capacity, therefore, is an important road feature. This capacity might change as function of time, even for the same road stretch, owing to changing driving behaviors or vehicle characteristics. In this study, we empirically analyzed the changes in road capacity over a 5- to 10-year period. The study differentiated between free flow capacity and queue discharge rate. We used three road stretches that remained unchanged to study free flow capacity. For 143 other locations that experienced changing properties over time, we analyzed queue discharge rates and corrected for external changes. We found that free flow capacity decreased, and queue discharge rates (slightly) increased over time. It is remarkable that one decreased, whereas the other increased. These results could be used in policies for road planning and design. Moreover, they provide an interesting background for further studies analyzing the effects of particular behavioral changes or driver assistance systems.@en