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This paper presents a microscopic model for accurate prediction of train event times based on a timed event graph with dynamic arc weights. The process times in the model are obtained dynamically using processed histori-cal track occupation data, thus reflecting all phenomena of railway traffic captured by the train describer systems and preprocess...
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... moving average smoothing method is used to incorpo- rate the prediction error observed during the train run into future predictions until the next stop. A schematic example of adaptive prediction is given in Fig. 5. The running train departed from station A and in the situation from the figure has just cleared the j th out of m blocks to station B where it is scheduled to stop. The gray solid line starting at station A represents the predicted running time of the train based on the actually registered departure delay. For the sake of clarity, for ...
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... l is a parameter l ∈ {1, ..., j−1} that specifies the length of the moving average. Parameters l and m are calibrated separately for each train type. The red dotted line in Fig. 5 denotes the adjusted prediction of running times to station B. By applying this adaptive prediction strategy, the continuous delay sources of the conflict-free run of a single train (e.g. due to particular driving style or defective rolling-stock) as well as temporary speed restrictions (due to infrastructure malfunctions or ...
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... In addition, the BN model was also used to study the influences of interruptions (primary delays, delayed trains, and total delays), where the authors built the BN model based on the inference of the three factors at different stations. Also, the timed event graph with dynamic edge weights can be used to study the delay propagation in time and space (Kecman and Goverde, 2014), where the edge weights were computed separately. The train arrival or departure delays were treated as independent variables to calculate the edge weights, whereas their nearest subsequent running times or dwelling times were addressed as dependent variables. ...
... (2) Incapable of addressing diverse impacts of factors. Only two studies based on traditional methods (e.g., the BN and timed event graphs) considered edge weights, representing the impacts of factors, but the edge weights were roughly determined (Goverde, 2010;Kecman and Goverde, 2014). For example, actual running/dwelling times were exploited as edge weights in (Goverde, 2010); in addition, regression coefficients were used as edge weights in (Kecman and Goverde, 2014); the regression coefficients were obtained by taking rain delays as the independent variables, and actual train running and dwelling times as the dependent variable. ...
... Only two studies based on traditional methods (e.g., the BN and timed event graphs) considered edge weights, representing the impacts of factors, but the edge weights were roughly determined (Goverde, 2010;Kecman and Goverde, 2014). For example, actual running/dwelling times were exploited as edge weights in (Goverde, 2010); in addition, regression coefficients were used as edge weights in (Kecman and Goverde, 2014); the regression coefficients were obtained by taking rain delays as the independent variables, and actual train running and dwelling times as the dependent variable. ...
Explaining train delay propagation using influence factors (to find the determinants) is essential for transport planning and train operation management. Due to high interpretability to train operations, graph/network models, e.g., Bayesian networks and alternative graphs, are extensively used in the train delay propagation/prediction problem. In these graph/network models, nodes represent train arrival/departure/passage events, whereas arcs describe train headway/ running/dwelling processes. However, previously proposed graph/network models do not have edge weights, making them incapable of apperceiving the diverse influences of factors on train delay propagation/prediction. The train dwelling, running, and headway times vary over time, space, and train services. This potentially makes these factors have diverse strengths on train operations. We innovatively use the Graph Attention Network (GAT) to model the train delay propagation. An attention mechanism is used in the GAT model, allowing the GAT model to have arcs with diverse weights (learned from data). This enables the GAT model to discern the nodes' diverse influences; thus, with the learned importance coefficients, the model can be distinctly explained by the influencing factors. Further, the model's accuracy is expected to be improved, because the GAT model (with the attention mechanism) can pay more attention (represented by the learned weights) to the significant factors/nodes. The proposed GAT model was calibrated on operation data from the Dutch railway network. The results show that: (1) the influence factors contribute diversely to the delay propagation, and the train headway is the determinant of train delay propagation; (2) the accuracy of the proposed GAT model is significantly improved (because of the attention mechanism), compared against other state-of-the-art graph/network models. In a word, the proposed GAT method improves the interpretability of delay propagation and the accuracy of delay prediction.
... Wen and Lessan [19] used multiple linear regression (MLR) and random forest regression (RFR) to predict delay recovery times in high-speed rail using a dataset of over 900 observed primary delays. Kecman [20] utilized a dynamic train event time predicting model using a timed event graph with dynamic arc weights, which has been tested and validated in a real-time environment using train describer log files. Xu [21] proposed a non-homogeneous Markov chain model for the near-future railway delay prediction, which is capable of handling large-scale forecasting problems. ...
Train delays can significantly impact the punctuality and service quality of high‐speed trains, which also play a crucial role in affecting dispatchers with their decision‐making. In this study, a data‐driven train delay prediction framework was proposed and strengthened by considering the impact of dispatching commands and the mechanisms of train delay propagation using XGBoost. Four metaheuristic algorithms were utilized to fine‐tune its hyperparameters. A vast dataset comprising 1.9 million records spanning 38 months of train operation data was utilized for feature extraction and model training. The model's accuracy was evaluated using three statistical metrics, and a comparison of the four tuning frameworks was performed. To emphasize the model's interpretability and its practical guidance for train rescheduling, the relationship of dispatching commands, delay propagation and delay prediction was validated by combining the theory and practical results, and a SHAP (SHapley Additive exPlanations) analysis was used for a clearer model explanation. The results revealed that distinct XGBoost‐Metaheuristic models exhibit unique effects in different criteria, yet they all demonstrated high accuracy and low prediction errors, thereby revealing the potential of using machine learning for train delay prediction, which is valuable for decision‐making and rescheduling.
... The event-driven train delay approach is an iterative process with a chain of prediction steps. Event-driven approaches are primarily based on an equation system (Medeossi et al., 2011) or a graph model such as Bayesian Networks (Corman and Kecman, 2018), Timed event graphs (Kecman and Goverde, 2014), Markov Chains (Schmidt et al., 2019), Petri Nets (Zhuang et al., 2016;Milinković et al., 2013), and Max-plus algebra (Goverde, 2007). On the other hand, data-driven approaches do not explicitly model train-event dependency structures nor intend to explicitly capture traffic flow dynamics. ...
... The implementation of ML and deep learning techniques have shown promise in processing and detecting connections between nonlinear, high-dimensional and sequential/time series data (Bhavsar et al., 2017;Pineda-Jaramillo et al., 2018), being successfully used to find interrelationships in numerous features in rail operations (De Martinis and Corman, 2018;Pineda-Jaramillo et al., 2021). Among different ML approaches applied to predict rail operation delays caused by disruptions and disturbances, Kecman and Goverde (2015b) developed a decision tree model and a least-trimmed squares robust linear regression model for predicting train dwelling and running times. Train dwelling time prediction through the implementation of a linear regression and a K-Nearest Neighbor model was proposed by Li et al. (2016), while other authors have implemented ML models to study the features associated to rail operation disruptions and their associated delays in High-Speed Railway Systems Wen et al., 2017). ...
Intermodal freight rail operations represent a complex stochastic system that is impacted by disruptions and disturbances from diverse causes like extreme weather events, unplanned upstream network delays, equipment failures, labor actions, and intra-railyard inefficiency, which in turn generate delays in travel times. Understanding and predicting the delays caused by the occurrence of these disruptions and disturbances holds the potential to limit their system-wide schedule impact through early-warning prompting mitigating actions. This paper presents the training of a suite of supervised machine learning models using classification algorithms to predict the delay times caused by the occurrence of disruptions and disturbances in intermodal freight rail operations, and the most suitable model in terms of the evaluation metrics (e.g., AUC, recall, and F1-score) was used to explore the major predictors of the delays caused by disturbances and disruptions (using the Morris method). The supporting dataset includes intermodal freight rail operations with origin the central station of the freight rail network of CFL, the National Railway Company of Luxembourg, in the intermodal hub of Bet-tembourg, connecting several EU countries terminals forming a pan-European network. Results reveal that the CatBoost implementation of the gradient boosting machine model outperforms other ML models in terms of the selected metrics. Additionally, results suggest that the train weight, train length, number of TEU, weight per wagon, distance between stations, and the month of operation are key features to predict the delays caused by the occurrence of disruptions and disturbances in the freight operations in the studied rail network. The outcome of the study suggests that longer and more heavily loaded trains are related to the occurrence of trip delays, and this insight can be used to optimize the freight operations of the National Railway Company of Luxembourg.
... In the traditional prediction methods, mathematical statistics, probability models, graph models, network models and simulation techniques are mainly used. Kecman et al. [4] proposed a micro-model to accurately predict train delay events based on a time-event graph and dynamic arc weights. The model considers the impact of the route conflicts caused by braking and re-acceleration on the train running time, which improves the accuracy of the prediction. ...
The delay-causing text data contain valuable information such as the specific reasons for the delay, location and time of the disturbance, which can provide an efficient support for the prediction of train delays and improve the guidance of train control efficiency. Based on the train operation data and delay-causing data of the Wuhan–Guangzhou high-speed railway, the relevant algorithms in the natural language processing field are used to process the delay-causing text data. It also integrates the train operating-environment information and delay-causing text information so as to develop a cause-based train delay propagation prediction model. The Word2vec model is first used to vectorize the delay-causing text description after word segmentation. The mean model or the term frequency-inverse document frequency-weighted model is then used to generate the delay-causing sentence vector based on the original word vector. Afterward, the train operating-environment features and delay-causing sentence vector are input into the extreme gradient boosting (XGBoost) regression algorithm to develop a delay propagation prediction model. In this work, 4 text feature processing methods and 8 regression algorithms are considered. The results demonstrate that the XGBoost regression algorithm has the highest prediction accuracy using the test features processed by the continuous bag of words and the mean models. Compared with the prediction model that only considers the train-operating-environment features, the results show that the prediction accuracy of the model is significantly improved with multiple regression algorithms after integrating the delay-causing feature.
... The proposed method can be easily extended to regular stations, as there are no new constraints compared with merging stations. (Milinković et al., 2013) Petri net Delay prediction Yes, simulated data (Goverde, 2010;Hansen et al., 2010;Kecman and Goverde, 2014) Timed event graph Delay prediction Yes, realized data (Corman and Kecman, 2018;Huang et al., 2020;Huang et al., 2022;Ulak et al., 2020) Bayesian networks Delay prediction Yes, realized data (Zilko et al., 2016) Bayesian networks Duration of disruptions Yes, realized data Bayesian inference Delay propagation Yes, realized data (Artan and Şahin, 2021;Barta et al., 2012;Berger et al., 2011;Gaurav and Srivastava, 2018;Şahin, 2017) Markov chain model Delay prediction Yes, realized data ...
Railway operations are subject to deviations from the planned schedule, i.e., delays. In those situations, timely and high-quality control actions are needed to reduce the impacts of delays on the networks. Existing studies mainly used prescriptive techniques (e.g., mathematical programming, heuristics) to solve the train traffic control problem during interruptions. These methods have limitations in the strong reliance of few deterministic parameters prescriptively or normatively determined beforehand; exponential increase of complexity when considering multiple aspects or larger cases; low transferability because of the assumptions used and unmodeled effects; and little understandability by the practitioners, which hinders their acceptance in practice. Based on decision graphs, this study is able to analyze and exploit past realization data to provide decision support for traffic control, in case of delayed trains in merging-line stations (multiple lines merge as one line). The brand-new perspective is to use realized data, to learn the historical traffic control actions, their resulting effects (i.e., the delay reductions) so that decisions taken by human dispatchers can be explained and proactively suggested, in case of delayed conditions. The model is applied to case studies with train traffic realization data from two stations with multiple lines merging in the Swiss railway network. The method quickly determines the stochastic effects of the two possible decisions at merge points, and is able to identify which factors are most useful, to determine the best outcome. The experimental results show that the traffic control rule obtained from the proposed model is superior to two standard rescheduling methods.
... Methodologies based on Bayesian network were proposed to update predictions of train delays [8], [9]. In [10], train delays predictions are updated using timed event graph with dynamic arc weights. In the context of individual charging behaviour we have not identified any paper exploring updates of predictions. ...
... Keyhani et al. (2012) and Lemnian et al. (2014) present stochastic graph approaches to predict the expected reliability of a scheduled train connection. Kecman and Goverde (2015b) use a microscopic TEG model to predict train events with dynamic edge weights. ...
Railway operations are vulnerable to delays. Accurate predictions of train arrival and departure delays improve the passenger service quality and are essential for real-time railway traffic management to minimise their further spreading. This review provides a synoptic overview and discussion covering the breadth of diverse approaches to predict train delays. We first categorise research contributions based on their underlying modelling paradigm (data-driven and event-driven) and their mathematical model. We then distinguish between very short to long-term predictions and classify different input data sources that have been considered in the literature. We further discuss advantages and disadvantages of producing deterministic versus stochastic predictions, the applicability of different approaches during disruptions and their interpretability. By comparing the results of the included contributions, we can indicate that the prediction error generally increases when broadening the prediction horizon. We find that data-driven approaches might have the edge on event-driven approaches in terms of prediction accuracy, whereas event-driven approaches that explicitly model the dynamics and dependencies of railway traffic have their strength in providing interpretable predictions, and are more robust concerning disruption scenarios. The growing availability of railway operations data is expected to increase the appeal of big-data and machine learning methods.
... Moreover, the number of factors considered in the regression is significantly smaller, since data on passenger trail is significantly more limited compared to data available (internally) to the freight railroad. Kecman and Goverde [34] offer a microscopic model for railroad networks to forecast train travel time and delay. To predict train delays, historical track occupancy data is utilized to train the parameters in the microscopic model. ...
In today’s world, data has become an asset for businesses. Many sectors use data technology to advance their businesses. Building management is one of the processes on which numerous studies have been conducted to assist building users. Thailand has progressed in terms of transportation infrastructure and public transportation. The Metropolitan Rapid Transit (MRT) system has more than one hundred million users per year. However, crowding is a concern in the present since crowding creates a problem and reduces customer pleasure. The goal of this research is to create a machine learning model for forecasting passenger demand over time. In addition, standard data collecting equipment was used to collect data from the Metropolitan Rapid Transit (MRT) Purple Line. This line has a total of 16 stations. Station name, date, day, month, period, number of passengers, holidays, weekends, and weather are among the nine factors. Analysis approaches included the analysis phase, classification, and regression algorithm. However, the regression algorithm’s accuracy is poor and therefore cannot be used. Before using machine learning classification methods, the K-means was used to cluster the types of passengers. In addition, for this investigation, three classification methods were used: artificial neural network, random forest, and decision tree. Furthermore, the findings revealed that the artificial neural network has a high predicting accuracy. The accuracy value stated is more than 0.85 for demand over time.
... Two reviews of models and algorithms for real-time train rescheduling and railway traffic management can be found in Cacchiani et al. [5] and Corman and Meng [6]. Kecman and Goverde [7] developed a data-driven method to predict train event times at control points by repeatedly adjusting predictions, considering route conflicts at microscopic level. Historical track occupation data together with acceleration and deceleration times are used in a timed event graph model by dynamically adjusting arc weights. ...
A homogeneous Markov chain model is proposed to make delay analysis and prediction for near future train movements in a non-periodic single-track railway timetable setting. The prediction model constitutes two principal processes, namely sectional running and conflict resolution, which are represented by the stochastic recovery and deterioration matrices, respectively. The matrices are developed using a data-driven approach. Given the initial delay of a train at the beginning of the prediction horizon, its delay within the horizon can be estimated by vector and matrix operations, which are performed for individual processes separately or in combination of the processes. A baseline linear model has also been developed for comparison. The numerical tests conducted give consistent and stable predictions for train delays made by the Markov model. This is mainly because of that the Markov model can capture uncertainties deep in the horizon and respond to variations in train movements.
