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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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

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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With the increased deployment of autonomous vehicles (AVs) in mixed traffic flow, ensuring safe and efficient interactions between AVs and human road users is important. In urban environments, intersections have various conflicts that can greatly affect driving safety and traffic efficiency. This study uses road test data to examine the possible safety and efficiency impacts of intersection conflict resolution involving AVs. The contribution comprises two main aspects. Firstly. we prepare and open a high-quality lateral conflict resolution dataset derived from the Argoverse-2 data, specifically targeting urban intersections. A rigorous data processing pipeline is applied to extract pertinent scenarios, rectify anomalies, enhance data quality, and annotate conflict regimes. This effort yields 5000+ AV-involved and 16000 AV-free cases, covering rich conflict regimes and balanced traffic states. Secondly, we employ surrogate safety measures to assess the safety impact of AVs on human-driven vehicles (HVs) and pedestrians. In addition, a novel concept of Minimum Recurrent Clearance Time (MRCT) is proposed to quantify the traffic efficiency impacts of AVs during conflict resolution. The results show that, for AV–HV and HV–HV conflict resolution processes, the differences in selected safety and efficiency measures for human drivers are statistically insignificant. In contrast, pedestrians demonstrate diverse behaviour adjustments. Some pedestrians behave more conservatively when interacting with AVs than with HVs. Notably, the efficiency of AV-involved conflict resolution is significantly lower than in AV-free instances due to the conservative driving style of AVs. This efficiency gap is particularly large when AVs pass through the conflict point after human drivers in unprotected left turns. These observations offer a perspective on how AVs potentially affect the safety and efficiency of mixed traffic. The processed dataset is openly available via https://github.com/RomainLITUD/conflict_resolution_dataset.

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Integrating Automated Vehicles (AVs) into existing traffic systems holds the promise of enhanced road safety, reduced congestion, and more sustainable travel. Effective integration of AVs requires understanding the interactions between AVs and Human-driving Vehicles (HVs), especially during the transition period in which AVs and HVs coexist in a mixed traffic environment. Numerous recent empirical studies find reduced headways of human drivers following an AV compared to following an HV, and attribute this reduction to behavioural changes of drivers when they follow AVs. However, more factors may be at play due to the inherent inconsistencies between the comparison conditions of HV-following-AV and HV-following-HV. This study scrutinises three alternative explanations for the observed reduction in headways: (1) systematic differences in car-following states during data collection, (2) systematic differences in driving variability between leading AVs and HVs, and (3) systematic differences in driving characteristics of leading AVs versus HVs. We use a large-scale dataset extracted from Lyft AV motion data and examine each of these explanations through data stratification and simulation. Our results show that all three mechanisms contribute to the observed reduction in headways of human drivers following AVs. In addition, our findings highlight the importance of driving homogeneity and stability in achieving reliably shorter headways. Thereby, this study offers a more comprehensive understanding on the difference between HV–AV and HV–HV interactions in mixed traffic, and is expected to promote more effective integration of AVs into human traffic.

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Observing, modelling, predicting, and understanding the dynamics of traffic systems on different levels is one of the most critical topics in the transport and planning domain. At the macroscopic scale, traffic congestion is the central problem that impacts all aspects of society. Traffic congestion costs valuable travel time, extra fuel consumption, and frustration in daily life. Traffic congestion is not always avoidable but accurate predictions of traffic conditions in a road network are useful for road users. For example, drivers can make faster and safer route choices based on the estimated time of arrival and the predicted congestion evolution. Reliable traffic forecasting also provides essential information for real-time traffic control systems and the development of long-term sustainable mobility systems. On the other hand, on the microscopic level, modelling the interaction between road users and predicting their behaviours is drawing more and more attention due to the increasing popularity of autonomous driving. Accurately anticipating other agents’ decisions is indispensable for a safe and smooth autopilot system. This actively-studied domain has become the focus of many scholars from academia and engineers from industry.@en

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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Modelling, predicting and analysing driver behaviours are essential to advanced driver assistance systems (ADAS) and the comprehensive understanding of complex driving scenarios. Recently, with the development of deep learning (DL), numerous driver behaviour learning (DBL) methods have been proposed and applied in connected vehicles (CV) and intelligent transportation systems (ITS). This study provides a review of DBL, which mainly focuses on typical applications in CV and ITS. First, a comprehensive review of the state-of-the-art DBL is presented. Next, Given the constantly changing nature of real driving scenarios, most existing learning-based models may suffer from the so-called “catastrophic forgetting,” which refers to their inability to perform well in previously learned scenarios after acquiring new ones. As a solution to the aforementioned issue, this paper presents a framework for continual driver behaviour learning (CDBL) by leveraging continual learning technology. The proposed CDBL framework is demonstrated to outperform existing methods in behaviour prediction through a case study. Finally, future works, potential challenges and emerging trends in this area are highlighted.

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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

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

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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Accurate and explainable short-term traffic forecasting is pivotal for making trustworthy decisions in advanced traffic control and guidance systems. Recently, deep learning approach, as a data-driven alternative to traffic flow model-based data assimilation and prediction methods, has become popular in this domain. Many of these deep learning models show promising predictive performance, but inherently suffer from a lack of interpretability. This difficulty largely originates from the inconsistency between the static input–output mappings encoded in deep neural networks and the dynamic nature of traffic phenomena. Under different traffic conditions, such as freely-flowing versus heavily congested traffic, different mappings are needed to predict the propagation of congestion and the resulting speeds over the network more accurately. In this study, we design a novel variant of the graph attention mechanism. The major innovation of this so-called dynamic graph convolution (DGC) module is that local area-wide graph convolutional kernels are dynamically generated from evolving traffic states to capture real-time spatial dependencies. When traffic conditions change, the spatial correlation encoded by DGC module changes as well. Using the DGC, we propose a multistep traffic forecasting model, the Dynamic Graph Convolutional Network (DGCN). Experiments using real freeway data show that the DGCN has a competitive predictive performance compared to other state-of-the-art models. Equally importantly, the prediction process in the DGCN and the trained parameters are indeed explainable. It turns out that the DGCN learns to mimic the upstream–downstream asymmetric information flow of typical road traffic operations. Specifically, there exists a speed-dependent optimal receptive field – which governs what information the DGC kernels assimilate – that is consistent with the back-propagation speed of stop-and-go waves in traffic streams. This implies that the learnt parameters are consistent with traffic flow theory. We believe that this research paves a path to more transparent deep learning models applied for short-term traffic forecasting.@en

Short-term traffic forecasting is one of the key functions in Intelligent Transportation System (ITS). Recently, deep learning is drawing more attention in this field. However, how to develop a deep learning based traffic forecasting model that can dynamically extract explainable spatial correlations from traffic data is still a challenging issue. The difficulty mainly comes from the inconsistency between static model structures and the dynamic evolution of traffic conditions. To overcome this difficulty, we proposed a novel multistep speed forecasting model, Dynamic Graph Filters Networks (DGFN). The major contribution is that the regular pixel-wise dynamic convolution is extended to graph topology. DGFN has a simple recurrent cell structure where local area-wide graph convolutional kernels are dynamically computed from varying inputs. Experiments on ring freeways show that DGFN is able to precisely predict short-term evolution of traffic speed. Furthermore, we theoretically explain why DGFN is not a pure “black-box”, but a “gray-box” model that actually reduces entangled spatial and temporal features into one component representing dynamic spatial correlations. It permits tracking real-time interactions among adjacent links. DGFN has the potential to relate trained parameters in deep learning models with physical traffic variables.@en