Urban congestions cause inefficient movement of vehicles and exacerbate greenhouse gas emissions and urban air pollution. Macroscopic emission fundamental diagram (eMFD)captures an orderly relationship among emission and aggregated traffic variables at the network level, allowing for real-time monitoring of region-wide emissions and optimal allocation of travel demand to existing networks, reducing urban congestion and associated emissions. However, empirically derived eMFD models are sparse due to historical data limitation. Leveraging a large-scale and granular traffic and emission data derived from probe vehicles, this study is the first to apply machine learning methods to predict the network wide emission rate to traffic relationship in U.S. urban areas at a large scale. The analysis framework and insights developed in this work generate data-driven eMFDs and a deeper understanding of their location dependence on network, infrastructure, land use, and vehicle characteristics, enabling transportation authorities to measure carbon emissions from urban transport of given travel demand and optimize location specific traffic management and planning decisions to mitigate network-wide emissions.

Urban rail transit often operates with high service frequencies to serve heavy passenger demand during rush hours. Such operations can be delayed by two types of congestion: train congestion and passenger congestion, both of which interact with each other. This delay is problematic for many transit systems, since it can be amplified due to the interaction. However, there are no tractable models describing them; and it makes difficult to analyze management strategies of congested transit systems in general and tractable ways. To fill this gap, this article proposes simple yet physical and dynamic model of urban rail transit. First, a fundamental diagram of transit system (i.e., theoretical relation among train-flow, train-density, and passenger-flow) is analytically derived considering the aforementioned physical interaction. Then, a macroscopic model of transit system for dynamic transit assignment is developed based on the fundamental diagram. Finally, accuracy of the macroscopic model is investigated by comparing to microscopic simulation. The proposed models would be useful for mathematical analysis on management strategies of urban rail transit systems, in a similar way that the macroscopic fundamental diagram of urban traffic did.

Trajectory planning is essential for ensuring safe driving in the face of uncertainties related to communication, sensing, and dynamic factors such as weather, road conditions, policies, and other road users. Existing car-following models often lack rigorous safety proofs and the ability to replicate human-like driving behaviors consistently. This article applies multi-phase dynamical systems analysis to well-known car-following models to highlight the characteristics and limitations of existing approaches. We begin by formulating fundamental principles for safe and human-like car-following behaviors, which include zeroth-order principles for comfort and minimum jam spacings, first-order principles for speeds and time gaps, and second-order principles for comfort acceleration/deceleration bounds as well as braking profiles. From a set of these zeroth- and first-order principles, we derive Newell's simplified car-following model. Subsequently, we analyze phases within the speed-spacing plane for the stationary lead-vehicle problem in Newell's model and its extensions, which incorporate both bounded acceleration and deceleration. We then analyze the performance of the Intelligent Driver Model and the Gipps model. Through this analysis, we highlight the limitations of these models with respect to some of the aforementioned principles. Numerical simulations and empirical observations validate the theoretical insights. Finally, we discuss future research directions to further integrate safety, human-like behaviors, and vehicular automation in car-following models, which are addressed in Part 2 of this study \citep{jin2025WA20-02_Part2}, where we develop a novel multi-phase projection-based car-following model that addresses the limitations identified here.

This report examines the effect of mixed traffic, specifically the variation in robot vehicle (RV) penetration rates, on the fundamental diagrams at unsignalized intersections. Through a series of simulations across four distinct intersections, the relationship between traffic flow characteristics were analyzed. The RV penetration rates were varied from 0% to 100% in increments of 25%. The study reveals that while the presence of RVs influences traffic dynamics, the impact on flow and speed is not uniform across different levels of RV penetration. The fundamental diagrams indicate that intersections may experience an increase in capacity with varying levels of RVs, but this trend does not consistently hold as RV penetration approaches 100%. The variability observed across intersections suggests that local factors possibly influence the traffic flow characteristics. These findings highlight the complexity of integrating RVs into the existing traffic system and underscore the need for intersection-specific traffic management strategies to accommodate the transition towards increased RV presence.

Physics-informed deep learning (PIDL)-based models have recently garnered remarkable success in traffic state estimation (TSE). However, the prior knowledge used to guide regularization training in current mainstream architectures is based on deterministic physical models. The drawback is that a solely deterministic model fails to capture the universally observed traffic flow dynamic scattering effect, thereby yielding unreliable outcomes for traffic control. This study, for the first time, proposes stochastic physics-informed deep learning (SPIDL) for traffic state estimation. The idea behind such SPIDL is simple and is based on the fact that a stochastic fundamental diagram provides the entire range of possible speeds for any given density with associated probabilities. Specifically, we select percentile-based fundamental diagram and distribution-based fundamental diagram as stochastic physics knowledge, and design corresponding physics-uninformed neural networks for effective fusion, thereby realizing two specific SPIDL models, namely \text{$\alpha$}-SPIDL and \text{$\cal B$}-SPIDL. The main contribution of SPIDL lies in addressing the "overly centralized guidance" caused by the one-to-one speed-density relationship in deterministic models during neural network training, enabling the network to digest more reliable knowledge-based constraints.Experiments on the real-world dataset indicate that proposed SPIDL models achieve accurate traffic state estimation in sparse data scenarios. More importantly, as expected, SPIDL models reproduce well the scattering effect of field observations, demonstrating the effectiveness of fusing stochastic physics model knowledge with deep learning frameworks.

We propose and study a data-driven framework for identifying traffic congestion functions (numerical relationships between observations of macroscopic traffic variables) at global scale and segment-level granularity. In contrast to methods that estimate a separate set of parameters for each roadway, ours learns a single black-box function over all roadways in a metropolitan area. First, we pool traffic data from all segments into one dataset, combining static attributes with dynamic time-dependent features. Second, we train a feed-forward neural network on this dataset, which we can then use on any segment in the area. We evaluate how well our framework identifies congestion functions on observed segments and how it generalizes to unobserved segments and predicts segment attributes on a large dataset covering multiple cities worldwide. For identification error on observed segments, our single data-driven congestion function compares favorably to segment-specific model-based functions on highway roads, but has room to improve on arterial roads. For generalization, our approach shows strong performance across cities and road types: both on unobserved segments in the same city and on zero-shot transfer learning between cities. Finally, for predicting segment attributes, we find that our approach can approximate critical densities for individual segments using their static properties.

The macroscopic traffic flow model is widely used for traffic control and management. To incorporate drivers' anticipative behaviors and to remove impractical speed discontinuity inherent in the classic Lighthill-Whitham-Richards (LWR) traffic model, nonlocal partial differential equation (PDE) models with ``look-ahead" dynamics have been proposed, which assume that the speed is a function of weighted downstream traffic density. However, it lacks data validation on two important questions: whether there exist nonlocal dynamics, and how the length and weight of the ``look-ahead" window affect the spatial temporal propagation of traffic densities. In this paper, we adopt traffic trajectory data from a ring-road experiment and design a physics-informed neural network to learn the fundamental diagram and look-ahead kernel that best fit the data, and reinvent a data-enhanced nonlocal LWR model via minimizing the loss function combining the data discrepancy and the nonlocal model discrepancy. Results show that the learned nonlocal LWR yields a more accurate prediction of traffic wave propagation in three different scenarios: stop-and-go oscillations, congested, and free traffic. We first demonstrate the existence of ``look-ahead" effect with real traffic data. The optimal nonlocal kernel is found out to take a length of around 35 to 50 meters, and the kernel weight within 5 meters accounts for the majority of the nonlocal effect. Our results also underscore the importance of choosing a priori physics in machine learning models.

Collisions, crashes, and other incidents on road networks, if left unmitigated, can potentially cause cascading failures that can affect large parts of the system. Timely handling such extreme congestion scenarios is imperative to reduce emissions, enhance productivity, and improve the quality of urban living. In this work, we propose a Deep Reinforcement Learning (DRL) approach to reduce traffic congestion on multi-lane freeways during extreme congestion. The agent is trained to learn adaptive detouring strategies for congested freeway traffic such that the freeway lanes along with the local arterial network in proximity are utilized optimally, with rewards being congestion reduction and traffic speed improvement. The experimental setup is a 2.6-mile-long 4-lane freeway stretch in Shoreline, Washington, USA with two exits and associated arterial roads simulated on a microscopic and continuous multi-modal traffic simulator SUMO (Simulation of Urban MObility) while using parameterized traffic profiles generated using real-world traffic data. Our analysis indicates that DRL-based controllers can improve average traffic speed by 21\% when compared to no-action during steep congestion. The study further discusses the trade-offs involved in the choice of reward functions, the impact of human compliance on agent performance, and the feasibility of knowledge transfer from one agent to other to address data sparsity and scaling issues.

In this paper, we aim at developing new methods to join machine learning techniques and macroscopic differential models for vehicular traffic estimation and forecast. It is well known that data-driven and model-driven approaches have (sometimes complementary) advantages and drawbacks. We consider here a dataset with flux and velocity data of vehicles moving on a highway, collected by fixed sensors and classified by lane and by class of vehicle. By means of a machine learning model based on an LSTM recursive neural network, we extrapolate two important pieces of information: 1) if congestion is appearing under the sensor, and 2) the total amount of vehicles which is going to pass under the sensor in the next future (30 min). These pieces of information are then used to improve the accuracy of an LWR-based first-order multi-class model describing the dynamics of traffic flow between sensors. The first piece of information is used to invert the (concave) fundamental diagram, thus recovering the density of vehicles from the flux data, and then inject directly the density datum in the model. This allows one to better approximate the dynamics between sensors, especially if an accident happens in a not monitored stretch of the road. The second piece of information is used instead as boundary conditions for the equations underlying the traffic model, to better reconstruct the total amount of vehicles on the road at any future time. Some examples motivated by real scenarios will be discussed. Real data are provided by the Italian motorway company Autovie Venete S.p.A.

Existing data-driven and feedback traffic control strategies do not consider the heterogeneity of real-time data measurements. Besides, traditional reinforcement learning (RL) methods for traffic control usually converge slowly for lacking data efficiency. Moreover, conventional optimal perimeter control schemes require exact knowledge of the system dynamics and thus would be fragile to endogenous uncertainties. To handle these challenges, this work proposes an integral reinforcement learning (IRL) based approach to learning the macroscopic traffic dynamics for adaptive optimal perimeter control. This work makes the following primary contributions to the transportation literature: (a) A continuous-time control is developed with discrete gain updates to adapt to the discrete-time sensor data. (b) To reduce the sampling complexity and use the available data more efficiently, the experience replay (ER) technique is introduced to the IRL algorithm. (c) The proposed method relaxes the requirement on model calibration in a "model-free" manner that enables robustness against modeling uncertainty and enhances the real-time performance via a data-driven RL algorithm. (d) The convergence of the IRL-based algorithms and the stability of the controlled traffic dynamics are proven via the Lyapunov theory. The optimal control law is parameterized and then approximated by neural networks (NN), which moderates the computational complexity. Both state and input constraints are considered while no model linearization is required. Numerical examples and simulation experiments are presented to verify the effectiveness and efficiency of the proposed method.