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• A probability distribution model of platoon size of connected vehicles is proposed. • A fundamental diagram model of the mixed traffic flow is developed. • An analytical model of the capacity of mixed traffic flow is proposed. • A numerical experiment is designed to discuss the impact of penetration rate and maximum platoon size on road capacity. This paper proposes a capacity analysis model for a mixed traffic flow environment that considers the heterogeneity and maximum platoon size of connected vehicles. Firstly, we explore how the organization mode of platoon affects car-following characteristics in mixed traffic flow with connected and automated vehicles, connected human-driven vehicles, automated vehicles, and human-driven vehicles. Different car-following models are used to describe the car-following characteristics of different types of vehicles. Secondly, the probability distribution model is developed for the size of platoons considering the penetration rate and the maximum platoon size of connected and automated vehicles, connected human-driven vehicles. Thirdly, the fundamental diagram of mixed traffic flow is further derived based on the probability distribution of platoon size and car-following models. Then, the capacity model of mixed traffic flow is proposed. Finally, a numerical experiment is designed to evaluate the impact of different penetration rates and maximum platoon sizes of connected and automated vehicles, connected human-driven vehicles on the capacity of the mixed traffic flow. The results show that (1) with a low penetration rate of connected and automated vehicles, connected human-driven vehicles, the change in the maximum platoon size has no noticeable effect on the distribution of platoon size of connected and automated vehicles, connected human-driven vehicles. (2) Road capacity increases with the maximum platoon size and the penetration rate of connected vehicles. (3) Compared with connected human-driven vehicles, the penetration rate of connected and automated vehicles has a more significant impact on road capacity. [ABSTRACT FROM AUTHOR]

Cycling as a mode of transport is on an upward trend as a low-emission alternative to driving in urbanized areas nowadays. With the increasing number of cyclists, it is of great importance to assess the capacity of cycling infrastructure in practice. Simulation models are useful tools to investigate bicycle flow performance considering cyclists' distinct moving behaviors. However, existing bicycle simulation models are restricted by either space discretization, lane-based setup, adaptation from models for car traffic, or complicated calibration requirement in a force-based environment. In addition, cyclists' decision-making ability in the operational-level cycling behavior are not well-captured in these models. This paper proposes a comprehensible microscopic bicycle simulation model which includes a detailed decision-making process and the ability to simulate continuous-space lateral movement. The model consists of three levels, maneuver decision, movement planning, and physical acceleration. It is able to simulate bicycle flow dynamics in undersaturated traffic conditions on an exclusive bike path. As we do not intend to show the empirical validity of the proposed model, the simulation experiment aims at verifying the model and exploring bicycle flow performance in various scenarios by estimating the fundamental diagrams (FDs). The effect of different path widths on bicycle flow capacity is first explored. Other behavioral factors, including desired speed heterogeneity, overtaking incentive, and safety region size perceived by cyclists, which can potentially influence the shape of the FD are also tested. The model can be further extended to simulate relatively complex cycling behavior with cooperative and anticipative strategies and investigate bicycle flow characteristics in congested traffic conditions. [ABSTRACT FROM AUTHOR]

• Informed fundamental diagram knowledge into a newly proposed data-driven model. • Applied and evaluated the proposed PI-SGTGCN model through real-world dataset. • Investigated the physical interpretation of the dynamic graph adjacency matrix. Accurate and fine-grained traffic state prediction has always been an important research field. For long-term traffic flow prediction, the high-dimensional and coupled traffic feature evolution patterns are deeply recessive, posing challenges in effectively characterizing and modeling them. This paper proposed a novel spatial–temporal graph convolution network model with traffic Fundamental Diagram (FD) information informed. The model decouples the high-dimensional spatiotemporal relationships in the transportation network and fully leverages the physical evolution laws of traffic states. First, the Graph Convolutional Network (GCN) with a spatial attention mechanism was proposed to capture spatial relations of the road network. The mechanism can better represent the spatial dynamics of the graph adjacency matrix in GCN. Second, this study injected prior physical knowledge into the graph adjacency matrix. This process was achieved by embedding characteristics of FDs from historical traffic data on the diagonal of the matrix, by which the propagation pattern of traffic states in road network could be considered. Third, to further catch the time dependence of the road network, the Gated Recurrent Unit (GRU) structure and the Transformer encoding structure were employed to locally and globally reform traffic state time sequences. Finally, experiments on a revised traffic dataset demonstrated that the proposed method consistently outperforms other baselines regarding Mean Absolute Error and Root Mean Square Error across all cases. Moreover, it achieved the optimal Mean Absolute Percentage Error in the 30- and 60-minute prediction tasks. This study shows a novel solution to inform traffic physical laws into data-driven state prediction models, and the reliability of the proposed method in long-term prediction offers valuable support for improving traffic management and alleviating traffic congestion. [ABSTRACT FROM AUTHOR]

We consider situations in which the clustering of some multivariate data is desired, which establishes an ordering of the clusters with respect to an underlying latent variable. As our motivating example for a situation where such a technique is desirable, we consider scatterplots of traffic flow and speed, where a pattern of consecutive clusters can be thought to be linked by a latent variable, which is interpretable as traffic density. We focus on latent structures of linear or quadratic shapes, and present an estimation methodology based on expectation–maximization, which estimates both the latent subspace and the clusters along it. The directed clustering approach is summarized in two algorithms and applied to the traffic example outlined. Connections to related methodology, including principal curves, are briefly drawn. [ABSTRACT FROM AUTHOR]

This paper proposes the fundamental diagram model for a mixed traffic flow environment that considers different car-following modes under various levels of automation and connectivity. First, the SAE classification of vehicle automation levels, from L 0 to L 5 , has been further divided into connectivity and automation levels. Second, the car-following modes that affect car-following characteristics are analyzed in mixed traffic flow with different levels of connectivity and automation. Different car-following models are used to describe the car-following characteristics of different types of modes. Third, the fundamental diagram model of mixed traffic flow is further derived based on the different levels of automation and connectivity. Finally, a numerical experiment is designed to evaluate the impact of different penetration rates (PRs) of the car-following modes on the traffic capacity of the mixed traffic flow. The results show that (1) with a higher PR of the automation level of the vehicle, the greater the traffic capacity. At the same time, as the automation levels increase, the change in the penetration rate of high automation levels has a more and more significant impact on traffic capacity. (2) Traffic capacity increases with increased PR of higher automation levels, representing an increase of approximately 11.1 % (3) Compared with connectivity, the PR of automation levels significantly impacts traffic capacity, which is approximately 52.6 %. [ABSTRACT FROM AUTHOR]

Accurate traffic congestion estimation and prediction are critical building blocks for smart trip planning and rerouting decisions in transportation systems. Over the decades, there have been many studies focusing on traffic congestion estimation and prediction with different statistical approaches (e.g., Markov chain) and machine learning models (e.g., clustering, Bayesian networks, and artificial neural networks). However, there is a lack of a unified framework to address the mechanisms of different models and integrate the advantages of different methods through combinations. This paper introduces the FD-Markov-LSTM model, a hybrid interpretable approach that combines the fundamental diagram (FD), Markov chain, and long short-term memory (LSTM). The aim is to estimate and predict traffic states by integrating statistical data in both congested and uncongested scenarios. The FD-Markov-LSTM model leverages the FD to identify hierarchical traffic states and utilizes the Markov process to capture the probabilistic transitions between these states. We employ the LSTM model to further capture the residual time series produced by the Markov chain model (assuming a memoryless property) to enhance the estimation and prediction performance. The proposed model's accuracy in estimating and predicting traffic flow is evaluated using empirical data from three case studies conducted in Beijing and Los Angeles. The results highlight a significant improvement in accuracy compared to classical benchmark models such as the Markov model, ARIMA model, k-Nearest Neighbor model, Random Forest model, and LSTM. Specifically, the FD-Markov-LSTM model achieves reductions of over 39% in mean absolute error, 35% in root mean squared error, and 7.4% in mean absolute percentage error. These results clearly demonstrate that the FD-Markov-LSTM model outperforms the benchmark models, enabling more precise predictions of traffic flow. [ABSTRACT FROM AUTHOR]

• We introduce the PIDL method to traffic state estimation, enabling accurate estimation results even with sparse data. • The computational graph method is applied to determine the key parameters of the fundamental diagram of traffic flow. • PIDLʹs versatility is showcased through two different traffic data scenarios: loop detectors and probe vehicles. • The research highlights the significance of integrating the physical models into the deep learning framework. Traffic state estimation (TSE) is a critical task for intelligent transportation systems. However, it is extremely challenging because the traffic data quality is often affected by the installation position of devices, data collection frequency, interference during the transmission process, etc., thus causing the problem of data sparsity or data missing. To address the issue of traffic state estimation under the scenario of data sparsity, we propose a TSE model that combines the computational graph with physics-informed deep learning (PIDL) methods. Firstly, we apply the computational graph method to determine the parameters of the traffic fundamental diagram. These parameters are embedded into the computational graph framework, and their values are determined through the forward propagation of variables and the backward propagation of errors. Next, we employ the PIDL method to realize TSE (taking the LWR model based on the Greenshields fundamental diagram as an example). The PIDL leverages the advantages of data-driven and model-driven approaches to achieve accurate traffic state estimation. Case studies are conducted using the NGSIM dataset under two sparse data scenarios: loop detectors and probe vehicles. Experimental results demonstrate that PIDL can accurately reconstruct the traffic state of the entire road segment based on partially observed data. Furthermore, compared to pure deep learning methods and other baseline models, PIDL performs better in situations with sparse data, thereby proving the feasibility of integrating domain knowledge with deep learning frameworks. This paper fully acknowledges the issue of data sparsity in TSE and effectively addresses it by applying the PIDL method to achieve precise TSE, which holds significant implications for the control and management of real traffic flow. [ABSTRACT FROM AUTHOR]

The Totally Asymmetric Simple Exclusion Process (TASEP) is a paradigm of out-of-equilibrium Statistical Physics that serves as a simplistic model for one-way vehicular traffic. Since traffic is perturbed by cars cruising for parking in many metropolises, we introduce a variant of TASEP, dubbed SFP, in which particles are initially cruising at a slower speed and aiming to park on one of the sites adjacent to the main road, described by a unidimensional lattice. After parking, they pull out at a finite rate and move at a normal speed. We show that this stylized model, which breaks many of the conservation rules applicable in other TASEP variants, exhibits singular features, in particular non-monotonic variations of the steady-state current with the injection rate and re-entrant transitions in the phase diagram, for some range of parameters. These features are robust to variations in the update rule and the boundary conditions. Neither the slow speed of cruising cars nor the perturbation of the flow due to pull-out maneuvers, taken in isolation, can rationalize these observations. Instead, they originate in a cramming (or ‘paper jam’) effect which results from the coupling of these mechanisms: injecting too many cars into the system saturates the first sites of the road, which prevents parked cars from pulling out, thus forcing cruising cars to travel farther along the road. These strong discrepancies with even the qualitative trends of the baseline TASEP model highlight the importance of considering the effect of perturbations on traffic.