Mathematics

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20 pages, 4980 KiB

Open AccessArticle

Improved Swarm Intelligence-Based Logistics Distribution Optimizer: Decision Support for Multimodal Transportation of Cross-Border E-Commerce

by Jiayi Xu, Mario Di Nardo and Shi Yin

Mathematics 2024, 12(5), 763; https://doi.org/10.3390/math12050763 - 4 Mar 2024

Cited by 2 | Viewed by 1925

Abstract

Cross-border e-commerce logistics activities increasingly use multimodal transportation modes. In this transportation mode, the use of high-performance optimizers to provide decision support for multimodal transportation for cross-border e-commerce needs to be given attention. This study constructs a logistics distribution optimization model for cross-border [...] Read more.

Cross-border e-commerce logistics activities increasingly use multimodal transportation modes. In this transportation mode, the use of high-performance optimizers to provide decision support for multimodal transportation for cross-border e-commerce needs to be given attention. This study constructs a logistics distribution optimization model for cross-border e-commerce multimodal transportation. The mathematical model aims to minimize distribution costs, minimize carbon emissions during the distribution process, and maximize customer satisfaction as objective functions. It also considers constraints from multiple dimensions, such as cargo aircraft and vehicle load limitations. Meanwhile, corresponding improvement strategies were designed based on the Sand Cat Swarm Optimization (SCSO) algorithm. An improved swarm intelligence algorithm was proposed to develop an optimizer based on the improved swarm intelligence algorithm for model solving. The effectiveness of the proposed mathematical model and improved swarm intelligence algorithm was verified through a real-world case of cross-border e-commerce logistics transportation. The results indicate that using the proposed solution in this study, the cost of delivery and carbon emissions can be reduced, while customer satisfaction can be improved. Full article

(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)

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24 pages, 3880 KiB

Open AccessArticle

A Multi-Objective Learning Whale Optimization Algorithm for Open Vehicle Routing Problem with Two-Dimensional Loading Constraints

by Yutong Zhang, Hongwei Li, Zhaotu Wang and Huajian Wang

Mathematics 2024, 12(5), 731; https://doi.org/10.3390/math12050731 - 29 Feb 2024

Cited by 2 | Viewed by 1127

Abstract

With the rapid development of the sharing economy, the distribution in third-party logistics (3PL) can be modeled as a variant of the open vehicle routing problem (OVRP). However, very few papers have studied 3PL with loading constraints. In this work, a two-dimensional loading [...] Read more.

With the rapid development of the sharing economy, the distribution in third-party logistics (3PL) can be modeled as a variant of the open vehicle routing problem (OVRP). However, very few papers have studied 3PL with loading constraints. In this work, a two-dimensional loading open vehicle routing problem with time windows (2L-OVRPTW) is described, and a multi-objective learning whale optimization algorithm (MLWOA) is proposed to solve it. As the 2L-OVRPTW is integrated by the routing subproblem and the loading subproblem, the MLWOA is designed as a two-phase algorithm to deal with these subproblems. In the routing phase, the exploration mechanisms and learning strategy in the MLWOA are used to search the population globally. Then, a local search method based on four neighborhood operations is designed for the exploitation of the non-dominant solutions. In the loading phase, in order to avoid discarding non-dominant solutions due to loading failure, a skyline-based loading strategy with a scoring method is designed to reasonably adjust the loading scheme. From the simulation analysis of different instances, it can be seen that the MLWOA algorithm has an absolute advantage in comparison with the standard WOA and other heuristic algorithms, regardless of the running results at the scale of 25, 50, or 100 datasets. Full article

(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)

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20 pages, 3674 KiB

Open AccessArticle

Simulation-Based Analysis for Verifying New Certification Standards of Smart LED Streetlight Systems

by Seung-Wan Cho, Kyung-Min Seo, Jung-Min Yun and Bong-Gu Kang

Mathematics 2024, 12(5), 657; https://doi.org/10.3390/math12050657 - 23 Feb 2024

Viewed by 991

Abstract

The need for certification standards for new convergence products, such as a smart LED streetlight system, has been identified as a critical issue. This study proposes simulation modeling for smart LED streetlight systems and suggests three certification standards: the minimum time to initiate [...] Read more.

The need for certification standards for new convergence products, such as a smart LED streetlight system, has been identified as a critical issue. This study proposes simulation modeling for smart LED streetlight systems and suggests three certification standards: the minimum time to initiate dimming-up, the duration of the dimming-up period, and the number of concurrently controlled streetlights. We utilized Relux to model streetlights and roads in terms of luminance levels, and used analytical formulas to compute the braking distances of oncoming vehicles. The two models were integrated into a smart LED streetlight system model using Simio. Simulation experiments were conducted with two objectives: to provide certification standards, and to apply and verify them in real-world cases. We experimented with 630 scenarios, modeling various dynamic situations involving roads and vehicles, and applied the model to two actual roads in the Republic of Korea to test its validity. The model was subsequently applied to roads for which traffic-volume data were available, to determine potential energy savings. The proposed simulation method can be applied to a smart LED streetlight system and to new products that lack certification standards. Furthermore, the proposed certification standards offer alternative approaches to operating streetlight systems more efficiently. Full article

(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)

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15 pages, 449 KiB

Open AccessArticle

An Automatic Train Operation Based Real-Time Rescheduling Model for High-Speed Railway

by Fan Liu and Jing Xun

Mathematics 2023, 11(21), 4546; https://doi.org/10.3390/math11214546 - 4 Nov 2023

Viewed by 1493

Abstract

With the continuous development of the Automatic Train Operation (ATO) system in high-speed railways, automatic driving is progressively supplanting manual operations, ushering in a new era of predictability and reliability for high-speed railway transport. Concurrently, the advent of the ATO system provides a [...] Read more.

With the continuous development of the Automatic Train Operation (ATO) system in high-speed railways, automatic driving is progressively supplanting manual operations, ushering in a new era of predictability and reliability for high-speed railway transport. Concurrently, the advent of the ATO system provides a notable impact on real-time rescheduling during disruptions, as it equips dispatchers with precise insights into train operation statuses. This paper is dedicated to a thorough analysis of how the transition to automatic driving in train operations influences the real-time rescheduling model. Based on the distinctive impact of the ATO system on real-time rescheduling, we have proposed a mixed-integer linear programming model that combines train re-timing, reordering, and the minimization of passenger delays. To validate the effectiveness of our model, we present several experiments conducted using data from the Beijing–Shanghai high-speed railway line. The results unequivocally demonstrate that our ATO-based model significantly mitigates train delay time, demonstrating its practical value in optimizing high-speed railway operations. Full article

(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)

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18 pages, 1606 KiB

Open AccessEditor’s ChoiceArticle

A Multi-View Approach for Regional Parking Occupancy Prediction with Attention Mechanisms

by Wei Ye, Haoxuan Kuang, Xinjun Lai and Jun Li

Mathematics 2023, 11(21), 4510; https://doi.org/10.3390/math11214510 - 1 Nov 2023

Cited by 3 | Viewed by 1230

Abstract

The near-future parking space availability is informative for the formulation of parking-related policy in urban areas. Plenty of studies have contributed to the spatial–temporal prediction for parking occupancy by considering the adjacency between parking lots. However, their similarities in properties remain unspecific. For [...] Read more.

The near-future parking space availability is informative for the formulation of parking-related policy in urban areas. Plenty of studies have contributed to the spatial–temporal prediction for parking occupancy by considering the adjacency between parking lots. However, their similarities in properties remain unspecific. For example, parking lots with similar functions, though not adjacent, usually have similar patterns of occupancy changes, which can help with the prediction as well. To fill the gap, this paper proposes a multi-view and attention-based approach for spatial–temporal parking occupancy prediction, namely hybrid graph convolution network with long short-term memory and temporal pattern attention (HGLT). In addition to the local view of adjacency, we construct a similarity matrix using the Pearson correlation coefficient between parking lots as the global view. Then, we design an integrated neural network focusing on graph structure and temporal pattern to assign proper weights to the different spatial features in both views. Comprehensive evaluations on a real-world dataset show that HGLT reduces prediction error by about 30.14% on average compared to other state-of-the-art models. Moreover, it is demonstrated that the global view is effective in predicting parking occupancy. Full article

(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)

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20 pages, 1897 KiB

Open AccessArticle

An Integrated Method for Reducing Arrival Interval by Optimizing Train Operation and Route Setting

by Wenxing Wu, Jing Xun, Jiateng Yin, Shibo He, Haifeng Song, Zicong Zhao and Shicong Hao

Mathematics 2023, 11(20), 4287; https://doi.org/10.3390/math11204287 - 14 Oct 2023

Viewed by 1851

Abstract

The arrival interval at high-speed railway stations is one of the key factors that restrict the improvement of the train following intervals. In the process of practical railway operation, sudden conflicts occur sometimes. Especially when the conflict arises at the station, because the [...] Read more.

The arrival interval at high-speed railway stations is one of the key factors that restrict the improvement of the train following intervals. In the process of practical railway operation, sudden conflicts occur sometimes. Especially when the conflict arises at the station, because the home signal cannot be opened in time, the emergency may affect the adjustment of the train operation under the scheduled timetable, resulting in a longer train following interval or even delay. With the development of artificial intelligence and the deep integration of big data, the architecture of train operation control and dispatch integration is gradually improving from the theoretical point. Based on this and inspired by the Green Wave policy, we propose an integrated operation method that reduces the arrival interval by avoiding unnecessary stops in front of the home signal and increasing the running speed of trains through the throat area. It is a two-step optimization method combining both intelligent optimization and mathematical–theoretical analysis algorithms. In the first step, the recommended approaching speed and position are obtained by analytical calculation. In the second step, the speed profile from the current position to the position corresponding to the recommended approaching speed is optimized by intelligent optimization algorithms. Finally, the integrated method is verified through the analysis of two distinct case studies. The first case study utilizes data from the Beijing–Shanghai high-speed railway line, while the second one is based on the field test. The numerical result shows that the proposed method could save the entry running time effectively, compared with the normal strategy given by the train driver. The method can mitigate controllable conflict events occurring at the station and provides theoretical support for practical operation. Full article

(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)

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19 pages, 1964 KiB

Open AccessArticle

Proactive Coordination of Traffic Guidance and Signal Control for a Divergent Network

by Yaming Guo, Ke Zhang, Xiqun Chen and Meng Li

Mathematics 2023, 11(20), 4262; https://doi.org/10.3390/math11204262 - 12 Oct 2023

Cited by 1 | Viewed by 1148

Abstract

In the realm of transportation system optimization, enhancing overall performance through the proactive coordination of traffic guidance and signal control in a divergent network can tackle the challenges posed by traffic congestion and inefficiency. Thus, we propose an innovative approach to first allow [...] Read more.

In the realm of transportation system optimization, enhancing overall performance through the proactive coordination of traffic guidance and signal control in a divergent network can tackle the challenges posed by traffic congestion and inefficiency. Thus, we propose an innovative approach to first allow the information on variable message signs (VMS) that deviates from estimated travel times. This proactive approach guides drivers towards optimal routes from a system-wide perspective, such as minimizing vehicle hours traveled. The deviation is constrained both by the lower bound of drivers’ long-term compliance rate and the upper bound of the favored traffic signal operation. The proposed approach coordinates the traffic guidance system with the signal control system. The traffic signal control system sets the upper limit for information deviation in the traffic guidance system, while the traffic guidance system provides demand predictions for the traffic signal control system. Overall, the objective function of the approach is the network-level performance of all users. We gauge traveler satisfaction as a measure of system credibility, using both a route choice module and a satisfaction degree module established through stated preference surveys. Numerical results demonstrate that proactive-coordinated (PC) strategies outperform reactive-coordinated (RC), proactive-independent (PI), and reactive-independent (RI) strategies by improving the system performance, meanwhile keeping the system trustworthy. Under the normal traffic scenario, the PC strategy reduces total travel time by approximately 10%. Driver satisfaction with the PC strategy increases from a baseline of 76% to 95%. Moreover, in scenarios with sudden changes in either traffic demand or supply, e.g., accidents or large events, the proactive guidance strategy is more flexible and can potentially improve more from the system perspective. Full article

(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)

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23 pages, 915 KiB

Open AccessArticle

A Min-Plus Algebra System Theory for Traffic Networks

by Nadir Farhi

Mathematics 2023, 11(19), 4028; https://doi.org/10.3390/math11194028 - 22 Sep 2023

Viewed by 1120

Abstract

In this article, we introduce a comprehensive system theory based on the min-plus algebra of

2 \times 2

matrices of functions. This novel approach enables the algebraic construction of traffic networks and the analytical derivation of performance bounds for such networks. We use [...] Read more.

In this article, we introduce a comprehensive system theory based on the min-plus algebra of

2 \times 2

matrices of functions. This novel approach enables the algebraic construction of traffic networks and the analytical derivation of performance bounds for such networks. We use the term “traffic networks” or “congestion networks” to refer to networks where high densities of transported particles lead to flow drops, as commonly observed in road networks. Initially, we present a model for a segment or section of a link within the network and demonstrate that the dynamics can be expressed linearly within the min-plus algebra. Subsequently, we formulate the linear system using the min-plus algebra of

2 \times 2

matrices of functions. By deriving the impulse response of the system, we establish its interpretation as a service guarantee, considering the traffic system as a server. Furthermore, we define a concatenation operator that allows for the combination of two segment systems, demonstrating that multiple segments can be algebraically linked to form a larger network. We also introduce a feedback operator within this system theory, enabling the modeling of closed systems. Lastly, we extend this theoretical framework to encompass two-dimensional systems, where nodes within the network are also taken into account in addition to the links. We present a model for a controlled node and provide insights into other potential two-dimensional models, along with directions for further extensions and research. Full article

(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)

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16 pages, 5565 KiB

Open AccessArticle

A Study on Cognitive Error Validation for LED In-Ground Traffic Lights Using a Digital Twin and Virtual Environment

by Bong Gu Kang and Byeong Soo Kim

Mathematics 2023, 11(17), 3780; https://doi.org/10.3390/math11173780 - 3 Sep 2023

Cited by 1 | Viewed by 2325

Abstract

Traffic accident prevention is considered one of the most crucial public safety issues due to the ongoing rise in traffic accidents. The installation of LED in-ground traffic lights is one strategy that has proven to be quite effective in preventing numerous traffic accidents, [...] Read more.

Traffic accident prevention is considered one of the most crucial public safety issues due to the ongoing rise in traffic accidents. The installation of LED in-ground traffic lights is one strategy that has proven to be quite effective in preventing numerous traffic accidents, notably pedestrian accidents. The traffic signal helps reduce accidents for pedestrians, but there is a drawback in that such installations may lead to cognitive errors, such as the driver making a mistaken start or stop. Therefore, it is crucial to validate cognitive errors in advance of the widespread adoption of LED in-ground traffic signals. To this end, in this study, we (i) built an experimental environment that can be employed for various traffic tests using digital twins and virtual simulators; (ii) designed test scenarios and measurement plans for validation to conduct a validation test, and (iii) demonstrated cognitive errors through data from various experiments. As a result, it was proven that there is a possibility that the LED in-ground traffic lights may cause cognitive errors for drivers, and the causes of this were analyzed. In the future, this framework can be used to demonstrate various transportation problems and can contribute to improving the quality of public safety. Full article

(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)

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16 pages, 4121 KiB

Open AccessArticle

Short-Term Prediction of Time-Varying Passenger Flow for Intercity High-Speed Railways: A Neural Network Model Based on Multi-Source Data

by Huanyin Su, Shanglin Mo and Shuting Peng

Mathematics 2023, 11(16), 3446; https://doi.org/10.3390/math11163446 - 8 Aug 2023

Cited by 1 | Viewed by 1301

Abstract

The accurate prediction of passenger flow is crucial in improving the quality of the service of intercity high-speed railways. At present, there are a few studies on such predictions for railway origin–destination (O-D) pairs, and usually only a single factor is considered, yielding [...] Read more.

The accurate prediction of passenger flow is crucial in improving the quality of the service of intercity high-speed railways. At present, there are a few studies on such predictions for railway origin–destination (O-D) pairs, and usually only a single factor is considered, yielding a low prediction accuracy. In this paper, we propose a neural network model based on multi-source data (NN-MSD) to predict the O-D passenger flow of intercity high-speed railways at different times in one day in the short term, considering the factors of time, space, and weather. Firstly, the factors that influence time-varying passenger flow are analyzed based on multi-source data. The cyclical characteristics, spatial and temporal fusion characteristics, and weather characteristics are extracted. Secondly, a neural network model including three modules is designed based on the characteristics. A fully connected network (FCN) model is used in the first module to process the classification data. A bi-directional Long Short-Term Memory (Bi-LSTM) model is used in the second module to process the time series data. The results of the first module and the second module are spliced and fused in the third module using an FCN model. Finally, an experimental analysis is performed for the Guangzhou–Zhuhai intercity high-speed railway in China, in which three groups of comparison experiments are designed. The results show that the proposed NN-MSD model can predict many O-D pairs with a high and stable accuracy, which outperforms the baseline models, and multi-source data are very helpful in improving the prediction accuracy. Full article

(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)

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15 pages, 747 KiB

Open AccessArticle

A Deep Reinforcement Learning Scheme for Spectrum Sensing and Resource Allocation in ITS

by Huang Wei, Yuyang Peng, Ming Yue, Jiale Long, Fawaz AL-Hazemi and Mohammad Meraj Mirza

Mathematics 2023, 11(16), 3437; https://doi.org/10.3390/math11163437 - 8 Aug 2023

Viewed by 1407

Abstract

In recent years, the Internet of Vehicles (IoV) has been found to be of huge potential value in the promotion of the development of intelligent transportation systems (ITSs) and smart cities. However, the traditional scheme in IoV has difficulty in dealing with an [...] Read more.

In recent years, the Internet of Vehicles (IoV) has been found to be of huge potential value in the promotion of the development of intelligent transportation systems (ITSs) and smart cities. However, the traditional scheme in IoV has difficulty in dealing with an uncertain environment, while reinforcement learning has the advantage of being able to deal with an uncertain environment. Spectrum resource allocation in IoV faces the uncertain environment in most cases. Therefore, this paper investigates the spectrum resource allocation problem by deep reinforcement learning after using spectrum sensing technology in the ITS, including the vehicle-to-infrastructure (V2I) link and the vehicle-to-vehicle (V2V) link. The spectrum resource allocation is modeled as a reinforcement learning-based multi-agent problem which is solved by using the soft actor critic (SAC) algorithm. Considered an agent, each V2V link interacts with the vehicle environment and makes a joint action. After that, each agent receives different observations as well as the same reward, and updates networks through the experiences from the memory. Therefore, during a certain time, each V2V link can optimize its spectrum allocation scheme to maximize the V2I capacity as well as increase the V2V payload delivery transmission rate. However, the number of SAC networks increases linearly as the number of V2V links increases, which means that the networks may have a problem in terms of convergence when there are an excessive number of V2V links. Consequently, a new algorithm, namely parameter sharing soft actor critic (PSSAC), is proposed to reduce the complexity for which the model is easier to converge. The simulation results show that both SAC and PSSAC can improve the V2I capacity and increase the V2V payload transmission success probability within a certain time. Specifically, these novel schemes have a 10 percent performance improvement compared with the existing scheme in the vehicular environment. Additionally, PSSAC has a lower complexity. Full article

(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)

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19 pages, 3698 KiB

Open AccessArticle

Optimal Train Platforming with Shunting Operations for Multidirectional Passenger Stations: A Case Study of Guangzhou Station

by Yinggui Zhang, Ruihua Hu, Qiongfang Zeng, Yuhang Wang, Ya Liu and Shan Huang

Mathematics 2023, 11(14), 3136; https://doi.org/10.3390/math11143136 - 16 Jul 2023

Viewed by 1646

Abstract

Busy, complex railway stations that serve as origin and termination points for a significant proportion of trains are essential to regional railway networks. Resolving conflicts between arrival–departure operations and shunting operations of cross-line trains and originating or terminating passenger trains in the throat [...] Read more.

Busy, complex railway stations that serve as origin and termination points for a significant proportion of trains are essential to regional railway networks. Resolving conflicts between arrival–departure operations and shunting operations of cross-line trains and originating or terminating passenger trains in the throat area is important for safety in these multidirectional stations. The main task of this paper is to study the train platforming problem, and we consider the integration of track and route allocation with shunting route allocation on the basis of the traditional TTP problem, so as to formulate a strong anti-interference track allocation plan for busy, complex railway stations. Therefore, in view of the complex characteristics of train operation in busy, complex railway stations, we extensively examine the technical operational characteristics of various trains in multidirectional stations, which are the key constraints of the model, and establish a mixed-integer linear programming model. This model aims to balance the buffer time for track occupation and optimize the routing and scheduling of trains in stations. Furthermore, an improved genetic algorithm is proposed to effectively implement the developed model. In the case study of Guangzhou Station, the occupation analysis after the optimization of the method in this paper indicates that the shunting operations significantly interfere with arrival–departure operations in throat areas. The optimization of buffer times and track utilization times resulted in notable reductions of 30.55% and 77.82%, respectively, in quadratic differences. These outcomes provide empirical evidence supporting the feasibility of the proposed model and algorithm for addressing train platforming problems, particularly in complex, multidirectional, and heavily trafficked railway stations. Full article

(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)

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24 pages, 5569 KiB

Open AccessArticle

A Novel Explanatory Tabular Neural Network to Predicting Traffic Incident Duration Using Traffic Safety Big Data

by Huiping Li and Yunxuan Li

Mathematics 2023, 11(13), 2915; https://doi.org/10.3390/math11132915 - 29 Jun 2023

Cited by 1 | Viewed by 1387

Abstract

Traffic incidents pose substantial hazards to public safety and wellbeing, and accurately estimating their duration is pivotal for efficient resource allocation, emergency response, and traffic management. However, existing research often faces limitations in terms of limited datasets, and struggles to achieve satisfactory results [...] Read more.

Traffic incidents pose substantial hazards to public safety and wellbeing, and accurately estimating their duration is pivotal for efficient resource allocation, emergency response, and traffic management. However, existing research often faces limitations in terms of limited datasets, and struggles to achieve satisfactory results in both prediction accuracy and interpretability. This paper established a novel prediction model of traffic incident duration by utilizing a tabular network-TabNet model, while also investigating its interpretability. The study incorporates various novel aspects. It encompasses an extensive temporal and spatial scope by incorporating six years of traffic safety big data from Tianjin, China. The TabNet model aligns well with the tabular incident data, and exhibits a robust predictive performance. The model achieves a mean absolute error (MAE) of 17.04 min and root mean squared error (RMSE) of 22.01 min, which outperforms other alternative models. Furthermore, by leveraging the interpretability of TabNet, the paper ranks the key factors that significantly influence incident duration and conducts further analysis. The findings emphasize that road type, casualties, weather conditions (particularly overcast), and the number of motor and non-motor vehicles are the most influential factors. The result provides valuable insights for traffic authorities, thus improving the efficiency and effectiveness of traffic management strategies. Full article

(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)

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20 pages, 5607 KiB

Open AccessEditor’s ChoiceArticle

Machine Learning Techniques Applied to the Harmonic Analysis of Railway Power Supply

by Manuela Panoiu, Caius Panoiu, Sergiu Mezinescu, Gabriel Militaru and Ioan Baciu

Mathematics 2023, 11(6), 1381; https://doi.org/10.3390/math11061381 - 12 Mar 2023

Cited by 8 | Viewed by 3861

Abstract

Harmonic generation in power system networks presents significant issues that arise in power utilities. This paper describes a machine learning technique that was used to conduct a research study on the harmonic analysis of railway power stations. The research was an investigation of [...] Read more.

Harmonic generation in power system networks presents significant issues that arise in power utilities. This paper describes a machine learning technique that was used to conduct a research study on the harmonic analysis of railway power stations. The research was an investigation of a time series whose values represented the total harmonic distortion (THD) for the electric current. This study was based on information collected at a railway power station. In an electrified substation, measurements of currents and voltages were made during a certain interval of time. From electric current values, the THD was calculated using a fast Fourier transform analysis (FFT) and the results were used to train an adaptive ANN—GMDH (artificial neural network–group method of data handling) algorithm. Following the training, a prediction model was created, the performance of which was investigated in this study. The model was based on the ANN—GMDH method and was developed for the prediction of the THD. The performance of this model was studied based on its parameters. The model’s performance was evaluated using the regression coefficient (R), root-mean-square error (RMSE), and mean absolute error (MAE). The model’s performance was very good, with an RMSE (root-mean-square error) value of less than 0.01 and a regression coefficient value higher than 0.99. Another conclusion from our research was that the model also performed very well in terms of the training time (calculation speed). Full article

(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)

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23 pages, 1258 KiB

Open AccessEditor’s ChoiceArticle

Train Delay Predictions Using Markov Chains Based on Process Time Deviations and Elastic State Boundaries

by Thomas Spanninger, Beda Büchel and Francesco Corman

Mathematics 2023, 11(4), 839; https://doi.org/10.3390/math11040839 - 7 Feb 2023

Cited by 3 | Viewed by 2860

Abstract

Train delays are inconvenient for passengers and major problems in railway operations. When delays occur, it is vital to provide timely information to passengers regarding delays at their departing, interchanging, and final stations. Furthermore, real-time traffic control requires information on how delays propagate [...] Read more.

Train delays are inconvenient for passengers and major problems in railway operations. When delays occur, it is vital to provide timely information to passengers regarding delays at their departing, interchanging, and final stations. Furthermore, real-time traffic control requires information on how delays propagate throughout the network. Among a multitude of applied models to predict train delays, Markov chains have proven to be stochastic benchmark approaches due to their simplicity, interpretability, and solid performances. In this study, we introduce an advanced Markov chain setting to predict train delays using historical train operation data. Therefore, we applied Markov chains based on process time deviations instead of absolute delays and we relaxed commonly used stationarity assumptions for transition probabilities in terms of direction, train line, and location. Additionally, we defined the state space elastically and analyzed the benefit of an increasing state space dimension. We show (via a test case in the Swiss railway network) that our proposed advanced Markov chain model achieves a prediction accuracy gain of 56% in terms of mean absolute error (MAE) compared to state-of-the-art Markov chain models based on absolute delays. We also illustrate the prediction performance advantages of our proposed model in the case of training data sparsity. Full article

(This article belongs to the Special Issue Advanced Methods in Intelligent Transportation Systems)

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