This paper focuses on optimizing mixed-fleet bus scheduling (MFBS) with vehicles of different sizes in public transport systems. We develop a novel mixed-integer nonlinear programming (MINLP) model to address the MFBS problem by optimizing vehicle assignment and dispatching programs. The model considers user costs, operator costs, and the crowding inconvenience of standing and sitting passengers. To tackle the complexity of the MFBS problem, we employ Genetic Algorithm (GA) and Grey Wolf Optimizer (GWO). Besides, we develop two hybrid metaheuristics, including GA-SA [a combination of GA and Simulated Annealing (SA)] and GWO-SA (a combination of GWO and SA), to improve optimization capabilities for the MFBS problem. We also employ a Taguchi approach to fine-tune the metaheuristics’ parameters. We widely examine and compare the metaheuristics’ performance across various-sized samples (small, medium, and large), considering solution quality, computational time, and the result stability of each algorithm. We also compare the metaheuristics’ solutions with the optimal solutions acquired by GAMS software in small and medium-scale samples. Our findings show that the GWO-SA outperforms the other metaheuristics. Applying our model to a real bus corridor in Santiago, Chile, we find that precise dispatching plans generated by more sophisticated/advanced algorithms (GA-SA and GWO-SA) lead to larger cost savings and improved performance compared to simpler algorithms (GA and GWO). Interestingly, utilizing more advanced algorithms makes a difference in terms of fleet planning in crowded scenarios, whereas for low and medium-demand cases, simpler dispatching algorithms could be used without a drop in accuracy.

Traffic data imputation plays a crucial role in supporting the development of accurate forecasting models and the provision of reliable real-time information systems. Recent advances in generative modeling, particularly diffusion models, have introduced new solutions to probabilistic traffic data imputation, offering better understanding of imputation uncertainty compared with deterministic models and improved imputation accuracy over previous probabilistic models. Despite the success of these deep imputation models, they may suffer from performance degradation when confronted with complex missing patterns. Additionally, the artificial data corruption used in the prevalent self-supervised learning setting may not align with the missing patterns encountered in unseen test data. To address these challenges, this paper introduces a novel probabilistic approach, Diffusion-based EM framework for traffic data Imputation (DEMI), which integrates the diffusion model into the Expectation-Maximization (EM) algorithm. In contrast to existing methods, DEMI learns the underlying unconditional distribution of traffic data through the iterative EM framework, enabling both accurate imputation without requiring additional corruption of observations. It also allows conditional generation with arbitrary missing patterns, as well as unconditional generation as a data augmentation tool. The framework features a refined posterior sampling method to enhance the quality of conditional reverse sampling and incorporates a transformer-based denoising network to capture spatio-temporal dependencies. Experimental results on real-world traffic datasets demonstrate DEMI’s superior performance over state-of-the-art deterministic and probabilistic imputation models, particularly in scenarios with complicated missing patterns and pattern shifts.

This study investigates the problem of joint optimization of transit network design, timetable, and passenger assignment with exact transfer behavior modeling. The problem is formulated as a bi-level mixed-integer bilinear program to capture passengers’ realistic path choice behavior. The upper-level model aims to minimize the weighted sum of the cost of bus route construction, bus route operation, bus station construction, travel time of passengers, the delay caused by failures in aboarding to the bus trips at the origin, the delay caused by failures in transfer between the bus trips, and the overflow delay when the bus trip operates at capacity. The lower-level model aims to minimize the travel time of passengers. The travel time of passengers is formulated as the sum of the waiting time for boarding, the transfer time, and the in-vehicle travel time. The passenger transfer time and the delay caused by failures in transfer between the bus trips are formulated with exact modeling of passenger transfer behavior. This bi-level mixed-integer bilinear program is transformed into an equivalent mixed-integer bilinear program with equilibrium constraints using Karush-Kuhn-Tucker conditions. To seek a solution of good quality to the proposed model while not requiring a large amount of computer memory, a Benders decomposition algorithm integrated with piecewise linearization is developed. A numerical application demonstrates that the proposed model is able to achieve 3.49% lower total cost than the baseline model assuming passenger transfer time to be half of the headway.

Demand variations throughout the day and area popularity differences across the city result in spatiotemporal changes in traffic flow. One of the well-known phenomena arising from these changes is tidal traffic, characterized by an imbalance between inbound and outbound traffic on a given road. It reflects the fluctuation in the alignment between transportation system supply and demand. Lane reversal control has been a common supply-side measure for dealing with this urban traffic “sickness” by adapting road capacity allocation to the demand imbalance between two directions of a road. This study investigates the dynamic network capacity allocation control problem in the era of connected and autonomous vehicles (CAVs), which integrates dynamic traffic signal splits and lane reversal controls. Considering the high dimensionality and non-linearity of urban transportation systems, we apply the sparse identification of nonlinear dynamics (SINDy) technique to construct a sparse yet sufficiently accurate surrogate model. This model estimates the forthcoming network traffic state based on the current state and implemented control decisions. The surrogate model is integrated into a model predictive control (MPC) method, forming a SINDy-MPC framework to assist in optimal decision-making in real time. The experiments show that the system identified by SINDy exhibits stability in the presence of Gaussian noise disturbances. The proposed dynamic network allocation control scheme can effectively reduce traffic imbalance, improve traffic efficiency, and enhance traffic resilience against cyberattacks.

This study investigates the problem of road side unit (RSU) location optimization considering vehicle-to-RSU (V2R) communication channel competition. To hedge against the uncertainty of vehicle density, the problem is formulated as a stochastic mixed-integer nonlinear program with equilibrium constraints. This program aims to minimize the expectation of weighted sum of V2R communication delay, packet loss rate and packet collision rate and age of information in V2R communication over all scenarios given RSU location budget limit. Decision variables are RSU locations and the number of connected autonomous vehicles (CAVs) communicating with each located RSU. Equilibrium constraints in the program model V2R communication channel competition among CAVs and ensures the choice of CAVs on RSUs to satisfy user equilibrium principle. The V2R communication is calculated under 6G technology. The program is linearized by using piecewise linearization method. To enhance the solution efficiency, a progressive hedging algorithm is developed to decompose the relaxed linearized model into several subproblems. The optimal solution to the relaxed linearized model is found by iteratively formulating and the solving subproblems. A branch and bound algorithm is introduced to obtain the optimal integer solution to the linearized model. The numerical results show that the proposed model can achieve 20.55% lower total communication delay than the state-of-the-art model only optimizing total V2R information propagation delay, when CAVs choose RSUs for communication in a competitive manner.

Predicting the trajectories of multiple agents in dynamic driving scenarios such as intersections and roundabouts remains challenging due to dense agent interactions, varying speeds, and complex environmental constraints. While previous studies have proposed interaction-aware models, they often neglect the combined effects of traffic states and individual driving behaviors. This study presents a personalized motion prediction framework based on Vehicle-to-Vehicle (V2V) communication to support decision-making in complex environments. An unsupervised method is proposed to recognize driving styles by analyzing features derived from V2V communication, which are then encoded and incorporated into the prediction models, with feature importance analyzed via a random forest algorithm. Traffic states are modeled using relative spatial relationships and captured through spatiotemporal encoding. To explore different prediction paradigms, three architectures, GAN-based, CVAE-based, and Transformer-based, are designed and comparatively evaluated, each incorporating driving style and traffic state information as categorical encodings. Among these, the Transformer-based model demonstrates superior performance across multiple prediction horizons and metrics due to its effective integration of behavioral and contextual features in both encoder and decoder. The proposed framework is evaluated on two public interactive driving datasets, rounD and INTERACTION, where it achieves state-of-the-art accuracy. Results show that incorporating personalized driving styles and traffic context significantly enhances trajectory prediction, making it more suitable for real-time decision support in connected and autonomous vehicles.

Platooning of connected automated vehicles (CAVs) on highways has attracted the interest of researchers, companies and administrations for years. This interest has yielded a vast literature on CAV platooning, which generally describes its benefits in terms of traffic efficiency, safety and environmental impacts, among others. However, the boundary conditions of these studies and the reported magnitude of these benefits vary greatly among the different contributions. In this context, this paper presents the result of a comprehensive literature review on CAV platooning on highways, organizing the existing research and establishing links between the different strategies proposed and their expected impacts. Starting points for future investigations are suggested, and the research gaps to be addressed are identified. The analysis performed shows that the current state-of-the-art has two major limitations. First, few CAV platooning strategies have been proven to be asymptotically stable, which should be a requirement for any feasible solution. Second, in most cases, the CAV platooning algorithms are simplistic adaptations from existing car-following models proposed for human driving that, therefore, unnecessarily transfer current traffic-related problems to future cooperative environments.

In today’s automotive industry, modern vehicles are equipped with numerous sensors to monitor the vehicle’s state. Accurate prediction of component wear-and-tear requires the identification and alignment of the appropriate sensors. However, this task is complicated by the sheer number of sensor features, their intermittent logging activity, and non-uniform data. Furthermore, the number of vehicles deemed suitable for analysis is exceedingly limited. In this paper, we address the prevalent challenge of sparse, irregular, and multivariate time series data encountered in various domains, with a particular focus on the automotive industry. Conventional methods like imputation or interpolation, which attempt to estimate data points, are inapplicable when the dataset is limited in size, consists of highly irregular time spans, a large feature space, and data sparsity. To tackle these issues, we introduce a novel subsampling methodology for VEhicle MUltivariate Irregular Time series data (VEMUT). Utilizing VEMUT, multiple sub-samples generate an increased dataset size, allowing machine learning models to learn high-performing and generalizable models, even when the dataset is limited in size. We examine the performance of the resulting dataset from VEMUT’s sub-sampling across three simple network architectures: a fully convolutional network, a fully convolutional network with attention, and a convolutional network with pooling. Our findings reveal over 99% accuracy for all architectures on the validation data, leading to a correct prediction of the wear-and-tear of a Porsche Taycan’s air suspension module. These results highlight the potential of our approach to significantly enhance models capable of recognizing patterns in data and predicting future developments. Such advancements are especially vital for prognosing wear-and-tear of various components in modern vehicles, ultimately contributing to improved maintenance and cost efficiency.

Unmanned aerial systems, known as “drones,” are relatively new in collecting traffic data. Data from drone videography can have potential applications for traffic research. Drones can record the vehicles from their aerial point-of-view and provide their naturalistic driving behavior. Processing raw data from drones to remove noise and anomalies is crucial to ensure that the data are fit for subsequent applications, e.g., the development of traffic flow or crash risk models. This study uses a part of the pNEUMA dataset, a large dataset with almost half a million trajectories captured by a swarm of drones over Athens, Greece. This novel dataset offers an opportunity to analyze the data attributes and treat the noise and outliers in the data. We use a combination of smoothing filters and Extreme Gradient Boosting with adaptive regularization to process the speed and acceleration profiles of the vehicle trajectories in the dataset. Our approach can help prospective data users treat this or similar trajectory datasets alternatively to applying manual thresholds and assist in accelerating research in microscopic traffic analysis.

Road crashes are one of the critical issues in the transportation sector. Crash studies aim to establish the relationship of crash occurrences with driver, environment and traffic factors. Lack of a large disaggregate driving or accident data constrains the study of driver factors and driving maneuvers. Moreover, the usual outcome of these studies is the crash likelihood without accounting for the impact of a potential crash, thus leading to an incomplete interpretation of crash risk. New and innovative ways of data collection, such as drone videography and floating car data, are a promising candidate for a disaggregated analysis. Our study proposes a method for estimation of rear-end crash risk during a specific traffic state, using separate formulations of likelihood and severity. We quantify rear-end crash risk by weighing the likelihood by the potential severity of a collision, wherein we introduce a severity indicator for the rear-end crash. The methodology is applied to the highD dataset, a large naturalistic traffic dataset collected on German freeways. The proposed methodology allows for the analysis of risk with traffic state and lane-changing maneuver. The findings show that speed-drop is associated with increased crash risk. Also, lane changing is associated with higher rear-end crash risk, as compared to lane-keeping, during the free-flow as well as congestion traffic. The understanding of the evolution of the crash risk, due to the driving maneuvers under different traffic conditions, can be useful for real-time crash prediction and for devising traffic management strategies.

Calibration and validation have long been a significant topic in traffic model development. In fact, when moving to dynamic traffic assignment (DTA) models, the need to dynamically update the demand and supply components creates a considerable burden on the existing calibration algorithms, often rendering them impractical. These calibration approaches are mostly restricted either due to non-linearity or increasing problem dimensionality. Simultaneous perturbation stochastic approximation (SPSA) has been proposed for the DTA model calibration, with encouraging results, for more than a decade. However, it often fails to converge reasonably with the increase in problem size and complexity. In this paper, we combine SPSA with principal components analysis (PCA) to form a new algorithm, we call, PC–SPSA. The PCA limits the search area of SPSA within the structural relationships captured from historical estimates in lower dimensions, reducing the problem size and complexity. We formulate the algorithm, demonstrate its operation, and explore its performance using an urban network of Vitoria, Spain. The practical issues that emerge from the scale of different variables and bounding their values are also analyzed through a sensitivity analysis using a non-linear synthetic function.

This paper presents a methodology for estimating the upper and lower bounds of a real-time traffic prediction system, i.e., its prediction interval. Without a very complex implementation work, our model is able to complement any preexisting prediction system with extra uncertainty information such as the 5% and 95% quantiles. We treat the traffic prediction system as a black box that provides a feed of predictions. Having this feed together with observed values, we then train conditional quantile regression methods that estimate the upper and lower quantiles of the error. The goal of conditional quantile regression is to determine a function, i.e., dτ(x), that returns the specific quantile r of a target variable d, given an input vector x. Following Koenker, we implement two functional forms of dτ(x): locally weighted linear, which relies on value on the neighborhood of x, and splines, a piecewise defined smooth polynomial function. We demonstrate this methodology with three different traffic prediction models applied to two freeway data sets from Irvine, CA, and Tel Aviv, Israel. We contrast the results with a traditional confidence intervals approach that assumes that the error is normally distributed with constant (homoscedastic) variance. We apply several evaluation measures based on earlier literature and contribute two new measures that focus on relative interval length and balance between accuracy and interval length. For the available data set, we verified that conditional quantile regression outperforms the homoscedastic baseline in the vast majority of the indicators.

The eight articles in this special section focus on techniques devised for the management of uncertainty in computational traffic models.

An online calibration approach that jointly estimates demand and supply parameters of dynamic traffic assignment (DTA) systems is presented and empirically validated through an extensive application. The problem can be formulated as a nonlinear state-space model. Because of its nonlinear nature, the resulting model cannot be solved by the Kalman filter, and therefore, nonlinear extensions need to be considered. The following three extensions to the Kalman filtering algorithm are presented: 1) the extended Kalman filter (EKF); 2) the limiting EKF (LimEKF); and 3) the unscented Kalman filter. The solution algorithms are applied to the on-line calibration of the state-of-the-art DynaMIT DTA model, and their use is demonstrated in a freeway network in Southampton, U.K. The LimEKF shows accuracy that is comparable to that of thebestalgorithm but with vastly superior computational performance. The robustness of the approach to varying weather conditions is demonstrated, and practical aspects are discussed.