This article investigates the distributed consensus filtering problem in sensor networks and proposes the optimal distributed sequential consensus fusion filtering (DSCFF) algorithm. Each sensor node in the network sequentially exchanges information with its neighboring nodes over multiple rounds to obtain global information. The filtering results for all sensor nodes tend to agree, but significant information is repeatedly exchanged between individual nodes, consuming the limited energy in the network. A dynamic event-triggering (DET) mechanism based on the minimum covariance per round is proposed to reduce unnecessary energy loss and decrease the communication bandwidth between sensor nodes. In addition, as the optimal DETDSCFF needs to calculate the cross-covariance matrices (CCMs) between sensor nodes, which increases the calculation complexity, this article provides the suboptimal DETDSCFF algorithm that minimizes the upper bound of the error covariance during fusion to solve the consensus gain. The boundedness of this suboptimal filter is proven, and its effectiveness is proven through simulation experiments.

Temporal dynamic graphs (TDGs), representing the dynamic evolution of entities and their relationships over time with intricate temporal features, are widely used in various real-world domains. Existing methods typically rely on mainstream techniques such as transformers and graph neural networks (GNNs) to capture the spatiotemporal information of TDGs. However, despite their advanced capabilities, these methods often struggle with significant computational complexity and limited ability to capture temporal dynamic contextual relationships. Recently, a new model architecture called mamba has emerged, noted for its capability to capture complex dependencies in sequences while significantly reducing computational complexity. Building on this, we propose a novel method, TDG-mamba, which integrates mamba for TDG learning. TDG-mamba introduces deep semantic spatiotemporal embeddings into the mamba architecture through a specially designed spatiotemporal prior tokenization module (SPTM). Furthermore, to better leverage temporal information differences and enhance the modeling of dynamic changes in graph structures, we separately design a bidirectional mamba and a directed GNN for improved spatiotemporal embedding learning. Link prediction experiments on multiple public datasets demonstrate that our method delivers superior performance, with an average improvement of 5.11% over baseline methods across various settings.

With the development of intelligent connected vehicle technology, human-machine shared control has gained popularity in vehicle following due to its effectiveness in driver assistance. However, traditional vehicle following systems struggle to maintain stability when driver reaction time fluctuates, as these variations require different levels of system intervention. To address this issue, the proposed human-machine shared vehicle following assistance system (HM-VFAS) integrates driver outputs under various states with the assistance system. The system employs an intelligent driver model that accounts for reaction time delays, simulating time-varying driver outputs. Acontrol authority allocation strategy is designed to dynamically adjust the level of intervention based on real-time driver state assessment. To handle instability from driver authority switching, the proposed solution includes a two-layer adaptive finite time sliding mode controller (A-FTSMC). The first layer is an integral sliding mode adaptive controller that ensures robustness by compensating for uncertainties in the driver output. The second layer is a fast non-singular terminal sliding mode controller designed to accelerate convergence for rapid stabilization. Based on the driver-in-the-loop experimental results using the intelligent cockpit system, the performance of the HM-VFAS was evaluated. Results show that the proposed control strategy maintains a safe distance under time-varying driver states, with the actual acceleration error relative to the target acceleration maintained within$\pm 0.6\!\ \text {m/s}^{2}$and the maximum acceleration error reduced by$1.3\!\ \text {m/s}^{2}$. Compared to traditional controllers, the A-FTSMC controller offers faster convergence and less vibration, reducing the stabilization time by 26.8%.

Accurate and refined passenger flow prediction is essential for optimizing the collaborative management of multiple collection and distribution modes in large-scale transportation hubs. Traditional methods often focus only on the overall passenger volume, neglecting the interdependence between different modes within the hub. To address this limitation, we propose MM-STFlowNet, a comprehensive multi-mode prediction framework grounded in dynamic spatial-temporal graph modeling. Initially, an integrated temporal feature processing strategy is implemented using signal decomposition and convolution techniques to address data spikes and high volatility. Subsequently, we introduce the Spatial-Temporal Dynamic Graph Convolutional Recurrent Network (STDGCRN) to capture detailed spatial-temporal dependencies across multiple traffic modes, enhanced by an adaptive channel attention mechanism. Finally, the self-attention mechanism is applied to incorporate various external factors, further enhancing prediction accuracy. Experiments on a real-world dataset from Guangzhounan Railway Station in China demonstrate that MM-STFlowNet achieves state-of-the-art performance, with an average improvement of 52.56% in MSE and 36.38% in MAE. Especially during peak hours, it demonstrates excellent forecasting performance, providing valuable insights for transportation hub management. Our model is also demonstrated strong generalization in low-resource scenarios and different traffic scenarios. Our code is available at https://github.com/BMRETURN/MM-STFlowNet

In the context of the current transition in energy structures and the development of renewable energy, optimizing the layout of solar energy systems along highways has become a significant research topic. This study employs five different advanced optimization algorithms, namely NSGA-II, Particle Swarm Optimization (PSO), Simulated Annealing (SA), Differential Evolution (DE), and a combination of NSGA-II and DE (NSGA-II-DE), to minimize total supply cost and maximize energy self-sufficiency. The comparative analysis reveals that the combination of NSGA-II and DE exhibits the best optimization performance. Through detailed experiment and data analysis, the performance and advantages of each algorithm in solving the layout problem of highway solar energy system are demonstrated, and specific implementation strategies are proposed for the optimal solution. In addition, sensitivity analysis is used to understand how changes in parameters such as module efficiency, energy demand fluctuations, and electricity price changes affect the optimization results, adding depth to the findings and making them more applicable to a variety of application scenarios.

Abstract Understanding human mobility in urban areas is important for transportation, from planning to operations and online control. This paper proposes the concept of user-station attention, which describes the user’s (or user group’s) interest in or dependency on specific stations. The concept contributes to a better understanding of human mobility (e.g., travel purposes) and facilitates downstream applications, such as individual mobility prediction and location recommendation. However, intrinsic unsupervised learning characteristics and untrustworthy observation data make it challenging to estimate the real user-station attention. We introduce the user-station attention inference problem using station visit counts data in public transport and develop a matrix decomposition method capturing simultaneously user similarity and station-station relationships using knowledge graphs. Specifically, it captures the user similarity information from the user-station visit counts matrix. It extracts the stations’ latent representation and hidden relations (activities) between stations to construct the mobility knowledge graph (MKG) from smart card data. We develop a neural network (NN)-based nonlinear decomposition approach to extract the MKG relations capturing the latent spatiotemporal travel dependencies. The case study uses both synthetic and real-world data to validate the proposed approach by comparing it with benchmark models. The results illustrate the significant value of the knowledge graph in contributing to the user-station attention inference. The model with MKG improves the estimation accuracy by 35% in MAE and 16% in RMSE. Also, the model is not sensitive to sparse data provided only positive observations are used.

As a primary countermeasure to mitigate traffic congestion and air pollution, promoting public transit has become a global census. Designing a robust and reliable bus timetable is a pivotal step to increase ridership and reduce operating cost for transit authorities. However, most previous studies on bus timetabling rely on historical passenger count and travel time data to generate static schedules, which often yield biased results in these uncertain scenarios, such as demand surge or adverse weather. In addition, acquiring real-time passenger origin/destination from a limited number of running buses is not feasible. This article considers the multiline dynamic bus timetable optimization problem as a Markov decision process model to address the aforementioned issues, and proposes a multiagent deep reinforcement learning framework to ensure effective learning from the imperfect-information game, where the passenger demand and traffic condition are not always known in advance. Moreover, a distributed reinforcement learning algorithm is applied to overcome the limitation of high computational cost and low efficiency. A case study of multiple bus lines in Beijing, China, confirms the effectiveness and efficiency of the proposed model. The results demonstrate that our method outperforms heuristic and state-of-the-art reinforcement learning algorithms by reducing 20.30% of operating and passenger costs compared with actual timetables.

Abstract The (conditional) matching preclusion number of a graph is the minimum number of edges whose deletion leaves the resulting graph (with no isolated vertices) that has neither perfect matchings nor almost perfect matchings. The (conditional) strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion makes the resulting graph (with no isolated vertices) without perfect matching or almost perfect matching. The enhanced hypercube $Q_{n,k}$ $(1\leq k\leq n-1)$ is an extension of hypercube. In this paper, we prove that the matching preclusion number of $Q_{n,k}$ is $n+1$ $(1\leq k\leq n-1)$, the strong matching preclusion number of $Q_{n,k}$ is $n+1$ $(2\leq k\leq n-1)$, the conditional matching preclusion number of $Q_{n,n-1}$ is $2n-1$, the conditional matching preclusion number of $Q_{n,k}$ is $2n$ $(1\leq k\leq n-2)$ and the conditional strong matching preclusion number of $Q_{n,n-2}$ is $2n-3$ $(n\geq 4)$.

Traffic forecasting has attracted considerable attention due to its importance in proactive urban traffic control and management. Scholars and engineers have exerted considerable efforts in improving the performance of traffic forecasting algorithms in terms of accuracy, reliability, and efficiency. Spatial feature representation of traffic flow is a core component that greatly influences traffic forecasting performance. In previous studies, several spatial attributes of traffic flow are ignored due to the following issues: a) traffic flow propagation does not comply with the road network, b) the spatial pattern of traffic flow varies over time, and c) single adjacent matrix cannot handle the complex and hierarchical urban traffic flow. To address the abovementioned issues, this study proposes a novel traffic forecasting algorithm called traffic transformer, which achieves great success in natural language processing. The multihead attention mechanism and stacking layers enable the transformer to learn dynamic and hierarchical features in sequential data. Two components, namely, global encoder and global–local decoder, are proposed to extract and fuse the spatial patterns globally and locally. Experimental results indicate that the proposed traffic transformer outperforms state-of-the-art methods. The learned dynamic and hierarchical features of traffic flow can help achieve a better understanding of spatial dependency of traffic flow for effective and efficient traffic control and management strategies.

The customized bus (CB) is an innovative type of transit service that can provide a personalized efficient transit services for passengers and environmental friendliness and congestion alleviation in metropolitan areas. This work develops an integrated optimization method for CB stop deployment, route design, and timetable development optimization problems while meeting travel demands as much as possible to obtain system-optimal CB service plans. Through the perspective of space-time network, the CB service design problem (CBSDP) is formulated as an integrated optimization model with the objectives of maximizing passenger accessibility and minimizing operating cost. An inconvenience index of passengers is introduced in the problem to measure the service quality, and the total number of stops for all involved CB routes is set as one of the objectives to optimize the total cost of the CB system. A heuristic approach is applied to generate efficient solutions for the CBSDP. Two types of instance, namely, a numerical experiment and a real-world instance, are implemented to demonstrate the performance of the proposed method. We also conduct a series of sensitive analyses to explore the influences of various parameters on the CB system for capturing the interaction among stops, routes, and timetables. Final results show that the CB plans obtained by the proposed method can provide efficient services by balancing passenger convenience and operating cost.

The advent of Connected and Autonomous Vehicles (CAVs) and Mobile Internet technologies is reshaping the public transport sector. Autonomous buses are equipped with varying advanced sensors, and hold great promises to enhancing the responsiveness and flexibility of public transit system. In the context of CAVs, transit operators can not only optimize service headway but also adjust bus capacity to meet the time-varying passenger demand. Anticipated benefits of introducing autonomous buses to the existing transit systems include safety improvement, driver cost reduction, and optimal routing. Bus electrification is another global trend to replace traditional diesel buses for energy savings. Electric buses are advantageous to both operators and passengers due to low greenhouse gas emission, maintenance cost, as well as noise pollution. In recent years, demand responsive public transport (DRPT) services (e.g. customized bus, microtransit) receive huge success thanks to the development of Mobile Internet. Unlike traditional bus services or the fixed-route transit service that relies on passive recipients, fixed stops, and schedules, DRPT can provide personalized service for specific clients through interactive information platform (Internet or smartphone). The aforementioned new types of public transit services significantly improve service quality, reduce energy consumption, and ultimately attract more ridership. To fully explore the benefits of personalized, electric and autonomous transit systems, new analytical models and data-driven methods for transit planning and operation are needed. The authors have selected 15 articles for review in this special issue. A summary of these articles is outlined below.

Accurate and reliable traffic forecasting for complicated transportation networks is of vital importance to modern transportation management. The complicated spatial dependencies of roadway links and the dynamic temporal patterns of traffic states make it particularly challenging. To address these challenges, we propose a new capsule network (CapsNet) to extract the spatial features of traffic networks and utilize a nested LSTM (NLSTM) structure to capture the hierarchical temporal dependencies in traffic sequence data. A framework for network-level traffic forecasting is also proposed by sequentially connecting CapsNet and NLSTM. On the basis of literature review, our study is the first to adopt CapsNet and NLSTM in the field of traffic forecasting. An experiment on a Beijing transportation network with 278 links shows that the proposed framework with the capability of capturing complicated spatiotemporal traffic patterns outperforms multiple state-of-the-art traffic forecasting baseline models. The superiority and feasibility of CapsNet and NLSTM are also demonstrated, respectively, by visualizing and quantitatively evaluating the experimental results.

Accurate metro ridership prediction can guide passengers in efficiently selecting their departure time and transferring from station to station. An increasing number of deep learning algorithms are being utilized to forecast metro ridership due to the development of computational intelligence. However, limited efforts have been exerted to consider spatiotemporal features, which are important in forecasting ridership through deep learning methods, in large-scale metro networks. To fill this gap, this paper proposes a parallel architecture comprising convolutional neural network (CNN) and bi-directional long short-term memory network (BLSTM) to extract spatial and temporal features, respectively. Metro ridership data are transformed into ridership images and time series. Spatial features can be learned from ridership image data by using CNN, which demonstrates favorable performance in video detection. Time series data are input into the BLSTM which considers the historical and future impacts of ridership in temporal feature extraction. The two networks are concatenated in parallel and prevented from interfering with each other. Joint spatiotemporal features are fed into a fully connected network for metro ridership prediction. The Beijing metro network is used to demonstrate the efficiency of the proposed algorithm. The proposed model outperforms traditional statistical models, deep learning architectures, and sequential structures, and is suitable for ridership prediction in large-scale metro networks. Metro authorities can thus effectively allocate limited resources to overcrowded areas for service improvement.

Identifying and quantifying the influential factors on incident clearance time can benefit incident management for accident causal analysis and prediction, and consequently mitigate the impact of non-recurrent congestion. Traditional incident clearance time studies rely on either statistical models with rigorous assumptions or artificial intelligence (AI) approaches with poor interpretability. This paper proposes a novel method, gradient boosting decision trees (GBDTs), to predict the nonlinear and imbalanced incident clearance time based on different types of explanatory variables. The GBDT inherits both the advantages of statistical models and AI approaches, and can identify the complex and nonlinear relationship while computing the relative importance among variables. One-year crash data from Washington state, USA, incident tracking system are used to demonstrate the effectiveness of GBDT method. Based on the distribution of incident clearance time, two groups are categorized for prediction with a 15-min threshold. A comparative study confirms that the GBDT method is significantly superior to other algorithms for incidents with both short and long clearance times. In addition, incident response time is found to be the greatest contributor to short clearance time with more than 41% relative importance, while traffic volume generates the second greatest impact on incident clearance time with relative importance of 27.34% and 19.56%, respectively.

Bus headway regularity heavily affects transit riders' attitude for choosing public transportation and also serves as an important indicator for transit performance evaluation. Therefore, an accurate estimate of bus headway can benefit both transit riders and transit operators. This paper proposed a relevance vector machine (RVM) algorithm to predict bus headway by incorporating the time series of bus headways, travel time, and passenger demand at previous stops. Different from traditional computational intelligence approaches, RVM can output the probabilistic prediction result, in which the upper and lower bounds of a predicted headway within a certain probability are yielded. An empirical experiment with two bus routes in Beijing, China, is utilized to confirm the high precision and strong robustness of the proposed model. Five algorithms [support vector machine (SVM), genetic algorithm SVM, Kalman filter, k-nearest neighbor, and artificial neural network] are used for comparison with the RVM model and the result indicates that RVM outperforms these algorithms in terms of accuracy and confidence intervals. When the confidence level is set to 95%, more than 95% of actual bus headways fall within the prediction bands. With the probabilistic bus headway prediction information, transit riders can better schedule their trips to avoid late and early arrivals at bus stops, while transit operators can adopt the targeted correction actions to maintain regular headway for bus bunching prevention.

The vehicle routing problem (VRP) is a well-known combinatorial optimization issue in transportation and logistics network systems. There exist several limitations associated with the traditional VRP. Releasing the restricted conditions of traditional VRP has become a research focus in the past few decades. The vehicle routing problem with split deliveries and pickups (VRPSPDP) is particularly proposed to release the constraints on the visiting times per customer and vehicle capacity, that is, to allow the deliveries and pickups for each customer to be simultaneously split more than once. Few studies have focused on the VRPSPDP problem. In this paper we propose a two-stage heuristic method integrating the initial heuristic algorithm and hybrid heuristic algorithm to study the VRPSPDP problem. To validate the proposed algorithm, Solomon benchmark datasets and extended Solomon benchmark datasets were modified to compare with three other popular algorithms. A total of 18 datasets were used to evaluate the effectiveness of the proposed method. The computational results indicated that the proposed algorithm is superior to these three algorithms for VRPSPDP in terms of total travel cost and average loading rate.

In this paper, a self-adaptive tolling strategy (SATS) is developed for dynamically and systematically enhancing highoccupancy toll (HOT) lane system operations. This strategy enhances the overall system performance of both the HOT and general purpose (GP) lanes by better utilizing the HOT lane capacity while maintaining high speed and/or high travel-time reliability for HOT lane traffic when GP lanes are congested. To formulate SATS, the Lighthill-Whitham-Richards kinematic wave model is used to characterize HOT lane traffic flow evolution, and the unilateral Laplace transform is used to convert the system representation from the time domain to the frequency domain. Then, an adaptive tolling controller is designed with both the proportional and integral control components. Real-time traffic measurements, including lane occupancy, average speed, and flow rate, are utilized for toll rate calculations. Following a dual-phase control scheme, the appropriate flow rate for HOT lane utilization is computed, and the corresponding toll is estimated backward. To examine the effectiveness of the proposed tolling strategy, microscopic traffic simulation experiments are conducted using VISSIM. The experiment results demonstrate that the proposed tolling strategy performs reasonably well in improving the overall operations of HOT lane systems under various traffic conditions.