Article

Stochastic modelling of delay propagation in large networks

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Abstract

Using analytical procedures to compute the propagation of delays on major railway networks yields sizeable computing time advantages over Monte Carlo simulations. The key objectives of this paper are to present a formalisation of delay propagation by means of an activity graph, to outline the required mathematical operations to traverse the graph and to elaborate a suitable class of distribution functions to describe the delays as random variables. These cumulative distribution functions allow to be speedily computed but also allows the quality of the computing process to be controlled. Last but not least, issues of procedural theory that arise in the context of networks are elaborated and the translation of the approach to a software tool is presented.

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... However, preparing and evaluating different scenarios can be time/resource-intensive because of the required detailed representation of the system, and usually cannot be run in real-time. Macroscopic models (Wendler, 2007;Hansen and Pachl, 2014;and Büker and Seybold, 2012), in contrast, employ mathematical models based on more aggregate representation of the network and train interactions. They lend themselves for use in optimization models . ...
... This approach is particularly useful for the analysis of a schedule, including stability and impact of delays (Goverde, 2007). Büker and Seybold (2012) enhanced the initial analytical models by employing cumulative density functions to capture the randomness in operations and estimate delay propagation. More recently, this approach has also been applied to real-time control of metro lines (Schanzenbächer et al., 2020;Farhi et al., 2017). ...
... The model can effectively identify critical processes and gauge the stability of rail network performance, but cannot capture details such as trains slowing down due to proximity to the lead train, a major factor affecting delay and line capacity in urban rail transit systems operating close to capacity. Similar to Büker and Seybold (2012), several data-driven methods have also been developed. Huang et al. (2020) present a comprehensive review of data-driven methods for timetable rescheduling under disruptions. ...
... The critical reason why the graph and network models have been widely used in both academic and practice for train operation lies in its high interpretability. The proposed methods include timed event graph, activity graph, and alternative graph [9][10][11][12][13][14]. These models are developed by graphically representing the train events, using the nodes of the graph where the relationships of train events are usually expressed by joint probability tables or density functions. ...
... Other supervised learning methods used for train operation management and control include a support vector machine for train position [48], a decision tree model for delay recovery prediction [49], transfer learning and ensemble learning for delay jumps predictions [50], and a hybrid model (support vector machine and Kalman filter) for train running time prediction [51]. Method Research problem [9][10][11] Timed event graph Delay prediction/propagation [12] Alternative graph Timetable robustness [13] Activity graph Delay propagation [14] Petri net Delay prediction [15][16][17][18] Bayesian networks Delay prediction [19] Bayesian networks Duration of disruptions [20] Bayesian theory Delay propagation [22][23][24][25][26] Markov model Delay prediction [21] Clustering Transport network assignment [28] Clustering Disturbance clustering [29] Clustering Delay pattern discovery A review of the existing literature on graph and clustering models (a summary shown in Table I) reveals that researchers focused on applying a variety of graph and network methods built on Markov property for train operation prediction, or applying the clustering technique on pattern discovery. However, no study focuses on combing the two methods to solve the delay or delay jump prediction problems in train operations. ...
... Therefore, we only use the indicators from the previous section, i.e., 1 a I and 1 d I in Eqs. (13) and (14), as the input of the clustering model. ...
Article
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Train delay evolutions exhibit different patterns (i.e., increasing delays, decreasing delays, or unchanged delays), because of the effects of stochastic disturbances and pre-scheduled supplement/recovery times. The dynamics and uncertainty of the train delay evolution make train delay prediction a challenging task. This study presents a hybrid framework, called context-driven Bayesian network (CDBN), composed of a delay evolution pattern discovery model, i.e., a K-Means clustering approach, and a train delay prediction model, i.e., Bayesian network (BN), to address this problem. The clustering algorithm is used to uncover the delay evolution patterns, and classify the data into different categories, based on the delay jumps, i.e., the change of a delay from one station to a consequent station. The BN model, which considers the delays in previous stations to overcome the Markov property assumption, is used as the predictive model of train delays. The data in each category (classified by the clustering model) are used to train and test the BN model separately. We evaluated the BN model, the clustering algorithm, and the CDBN model, by comparing against their counterparts, respectively. The results show that: (1) the proposed BN structure has advantages over the common delay prediction models built on Markov property; (2) the clustering is effective, and it can extensively improve the accuracy of the predictive model; and (3) the CDBN outperforms the existing delay prediction models in wide usability, because of its more profound understanding of the delay evolution patterns.
... Concerning event-driven approaches, early publications on train delay prediction were based on general graph models (e.g., [2,21,22]) and aimed to describe the uncertainties of future delays by assuming and fitting probability distributions [23][24][25]. An eventactivity graph is used by [23] to stochastically model delay propagation on a network level based on an expansion of exponential polynomials as flexible (i.e., easy to convolute) distribution functions. ...
... Concerning event-driven approaches, early publications on train delay prediction were based on general graph models (e.g., [2,21,22]) and aimed to describe the uncertainties of future delays by assuming and fitting probability distributions [23][24][25]. An eventactivity graph is used by [23] to stochastically model delay propagation on a network level based on an expansion of exponential polynomials as flexible (i.e., easy to convolute) distribution functions. The theory of the max-plus algebra was introduced by [26] to model the train delay propagation for periodical timetables, and extended by [27]. ...
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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.
... The primary delay distributions are simply defined by giving a probability of delay and the average delay in case of delay and are differentiated between stopping, departing, and running delays. A set of input data -a scenario -forms an activity graph [1] for a selected day of operation. Trains accumulate delays incurred from primary delays as well as delays propagated from other trains. ...
... Visualisation of operational data[1]. ...
Conference Paper
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To analyse a rail network’s punctuality and the operational quality of a timetable on a network-wide scale an advanced simulation is needed. Whereas most simulations use a Monte Carlo approach, we calculate delay distributions analytically and thus need only a single calculation run. Previously we used exponential distribution functions as they map the status in railway operations well and are suited for efficient calculation of delays. The resulting delay distributions due to primary delays along a train’s itinerary as well as delay propagation from other trains is handled by convolution of these distribution functions. However, as the resulting distributions become more complex, a simplification step is needed from time to time to keep calculation times reasonable. Increased requirements for the accuracy of the simulation model and improvements in the computational potential led us to remodel the delays with discrete distributions. This has two main advantages. First, restrictions on the possible form of primary delays are much smaller compared to the previous exponential distributions and second, the simplification step is no longer needed, which increases accuracy considerably. We discuss the different options of distribution modelling and their use in railway applications.
... Weik, Niebel and Niessen [11] discussed a stochastic model for the capacity analysis of railway lines with applications in long-term planning, and a generalization of an approach widely used in Germany was derived that is valid for a wide range of timetable requirements. The extensions of these approach are given in [12][13][14][15]. ...
... 4: Calculate occupancy time Calculate the occupancy time of all combined trains on the train timetable and add them to obtain the total occupancy time Step 5: Calculate available time Due to the vertical maintenance window, the available time of the train timetable needs to subtract the time occupied by maintenance, maintenance T , and the invalid time caused by the triangle area, triangle T, which can be calculated by Equation(12). ...
Article
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Accurate and convenient assessment of a section’s capacity is an essential problem in the operation of high-speed railway companies. The concept of occupancy time is widely used in the field, but there is still a lack of quantitative analysis to support follow-up studies and application. In this research, the calculation method for one train, two trains and multiple trains is discussed. The occupancy time of the two trains was divided into three cases according to the relationship between them, and the calculation formulas are given. For the calculation of multiple trains, the circumstances were too intricate to be classified. To solve this problem, the concept of a continuous train group was proposed. The three properties of the continuous train group were analyzed and proved by mathematical derivation to provide theoretical support to transform a multi-train problem into many two-train problems. Finally, a combined occupancy method for capacity assessment was formed and applied to the Beijing–Shanghai high-speed railway. A series of numerical cases were designed to evaluate the performance compared with the UIC406 method. The results demonstrate that the combined occupancy method can better assess the capacity and is more convenient to implement.
... Considerable effort has been put into modeling the propagation of delays in transportation systems where analytical 45 , agent-based 46,47 , stochastic [48][49][50][51] , networks 40,52,53 , and purely data-driven models 54 were deployed. Railway networks have been modeled with agent-based simulations (ABS). ...
... Machine learning techniques, especially neural networks, are widely used to model and predict railway outputs (delays). Linear models have been mostly superseded by complex models [2], [8] and [9], including deep neural networks to predict train arrival delay at the next station using Extreme Learning Machine (ELM) with nine characteristics plus the Particle Swarm Optimization (PSO) algorithm to optimize the hyper-parameters of ELM [5], that have greater accuracy and performance, and have the ability to extract valuable insights from unprocessed and unstructured data using gradient boosting (XGBoost) prediction model that captures the relation between the train arrival delays and various railway system characteristics [10]. The latest technological advances allow large volumes of data to be processed and analyzed in real time, thus allowing operators to make knowledgeable rapid decisions. ...
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Predicting delays in metro and tram services is a complex task that requires advanced approaches, such as powerful machine learning tools. This study addresses this topic by applying the XGBoost and Bayesian Optimization (BO) algorithms, which offer a prediction horizon of 15 minutes instead of the next-station prediction, which leaves a very short time for the operator to react if we want to use the prediction for the next station. Our research places a strong emphasis on methodological validation, with daily evaluations against real-time data. This process is reinforced by collaboration with the Operational Control Center (OCC) to ensure robustness. The 15-minute delay strikes a balance, giving control center operators sufficient notice to orchestrate traffic management, mitigate disruption, and take timely action. With an exemplary real-world accuracy of 95%, the results of our model have been validated by the OCC. Future efforts will include the seamless integration of predictive capabilities into real-time display systems for the OCC, providing innovative information to optimize traffic flows and ensure punctuality in urban rail systems.
... Traditional prediction models commonly employ graph and network-based approaches to describe the train operation process, including timed event graphs [9], activity graphs [10], Bayesian networks (BN) [11], [12], and Markov chain models [13], [14], [15]. These models are highly interpretable and effectively illustrate train arrival and departure events. ...
Article
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Train delay prediction is a key technology for intelligent train scheduling and passenger services. We propose a train delay prediction model that takes into account the asynchrony of train events, the dynamics of train operations, and the diversity of influencing factors. Firstly, we consider train operations as discrete sequences of train events and propose a train arrival neural temporal point process (TANTPP) framework focused on predicting train delays that explicitly models the asynchrony of train events. Secondly, we introduce a multi-source dynamic spatiotemporal embedding method for the feature encoder in the TANTPP framework, which enhances the capability to capture the features of train operation networks. Thirdly, to better capture the distribution of train events in the TANTPP framework, we utilize a lognormal mixture hybrid method to learn the probability density distribution of train arrival events. Finally, the experimental result on real-world datasets demonstrates that the TANTPP model outperforms current stateof- the-art models, reducing the MAE by 10.85%, the RMSE by 9.8%, the RRSE by 3.78% and the MAPE by 10.11% on average. To the best of our knowledge, this is the first study to utilize neural temporal point processes to enhance train delay prediction.
... Berger et al. (2011) propose a stochastic model to predict train arrival and departure delays including waiting policies, driving time profiles, and catch-up potential. Büker and Seybold (2012) present a large-scale activity graph model to analytically describe the propagation of train delay on a network level. Their approach is based on an expansion of exponential polynomials as flexible (i.e., easy to convolute) distribution functions to avoid heuristics like the commonly used Monte Carlo sampling. ...
... The problem of train delay propagation/prediction can also be studied from the perspective of railway networks. In this regard, some commonly used methods include graph/network models, e.g., timed event graphs (Goverde, 2010;Hansen et al., 2010), activity graphs (Büker and Seybold, 2012), Petri nets (Milinković et al., 2013), alternative graphs (Meloni et al., 2021), and BN models (Ulak et al., 2020). In these models, a graph model that considers edge weights was proposed by (Goverde, 2010); the authors used the minimum running/dwelling process times to represent the edge weights. ...
Article
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.
... These disturbances can cause deviations from the planned train timetable, resulting in what is known as primary delays [38]. Due to the strong interdependencies within the railway operational processes, initial delays often have adverse effects on subsequent operational activities or trains, leading to delay propagation [39], as discussed in part A and Figure 2. This not only negatively impacts the internal operations of the railway system but also inconveniences passengers in their travel journeys. ...
Article
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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.
... As a way to measure the train interactions from different lines, route conflict is another crucial factor to influence DDOSs (Büker & Seybold, 2012). Although several delay prediction methods relying on different traditional or state-of-the-art techniques have been proposed, most of them only considered the train interaction on the same railway line (Barbour et al., 2018;Huang et al., 2021;Huang et al., 2020b;Oneto et al., 2017). ...
... Model-based approaches have been widely used in the literature for delay prediction in rail networks. They can be found in Berger et al. (2011) as well as Büker and Seybold (2012), for example. However, their disadvantage lies in the complex modeling and the low adaptability to changing operational conditions. ...
Chapter
The aim of the article is to demonstrate the use and benefit of machine learning (ML) in logistics by means of a significant, practice-relevant application: the prediction of estimated times of arrival (ETA) in intermodal transport chains. Based on a real use case, the article first provides an approach for the methodical procedure for the implementation of ETA predictions and a description of essential development phases. Subsequently, a cross-actor prediction approach for the combined road-rail transport of containers in the port hinterland is designed, and ML-based prediction models for specific logistics processes are prototypically implemented and evaluated. Finally, an outlook on future research directions is given.
... Concernant la prévision des retards, les variables ne sont en général pas agrégées, excepté dans le travail de Ulak et al. [2020]. Cependant, ces variables sont généralement représentées par un graphe temps-événement où chaque noeud est un événement horodaté représentant l'heure d'arrivée, de départ ou de passage d'un train à une gare [Büker and Seybold, 2012, Corman and Kecman, 2018. Ce graphe n'est pas adapté à la prévision des montées ou des descentes qui sont observées sur une arrête du graphe. ...
Thesis
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Grâce à ses rames connectées, Transilien mesure en temps réel le nombre de montées et de descentes par porte du train. Nous contribuons à une meilleure synchronisation en phase opérationnelle des flux de trains et de voyageurs à l’aide de ces données uniques. Nous évaluons plusieurs modèles d’apprentissage statistique afin d’estimer les temps de stationnement en fonction des variables d’exploitation ferroviaire et des flux de voyageurs. Ces modèles permettent d’isoler des situations critiques où les flux de voyageurs impactent les temps de stationnement. Nous prévoyons chacune des variables, à l’horizon d’un arrêt, à partir de modèles autorégressifs bidirectionnels exploitant leur passé proche. Ces modèles se simplifient grâce aux motifs issus de la grille horaire. Nous estimons enfin des taux d’occupation par zone des rames traversantes, afin d’informer les voyageurs sur le confort à bord et proposons deux modèles de déplacement des voyageurs à bord.
... graph-based models are widely implemented for predicting train dwelling, running or arrival times, or train delays in rail operations (Berger et al., 2011;Büker and Seybold, 2012;Corman et al., 2014;Milinković et al., 2013). Graph-based models are created by visually depicting the train events, utilizing the graph nodes where the interrelationships of train events are commonly represented using joint probability density functions. ...
Article
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.
... Milinković et al. (2013) proposed a fuzzy Petri net model to estimate train delays with large external disturbances in the system of Serbian Railways. Büker and Seybold (2012) presented a formalisation of delay propagation via stochastic modelling of activity graphs. Meester and Muns (2007) argued that, based on phase-type distributions, it is possible to derive secondary delay distributions from primary delay distributions. ...
Article
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Urban metro systems are often affected by disruptions such as infrastructure malfunctions, rolling stock breakdowns and accidents. The crucial prerequisite of any disruption analytics is to have accurate information about the location, occurrence time, duration and propagation of disruptions. To pursue this goal, we detect the abnormal deviations in trains’ headway relative to their regular services by using Gaussian mixture models. Our method is a unique contribution in the sense that it proposes a novel, probabilistic, unsupervised clustering framework and it can effectively detect any type of service interruptions, including minor delays of just a few minutes. In contrast to traditional manual inspections and other detection methods based on social media data or smart card data, which suffer from human errors, limited monitoring coverage, and potential bias, our approach uses information on train trajectories derived from automated vehicle location (train movement) data. As an important research output, this paper delivers innovative analyses of the propagation progress of disruptions along metro lines, which enables us to distinguish primary and secondary disruptions as well as effective recovery interventions performed by operators.
... It should connect the main scenic spots in the city, and at the same time, it can enable tourists to reach any major scenic spot by one bus. At present, China's urban tourist attractions are relatively scattered, especially a considerable number of tourist attractions are located on the edge of relatively remote cities, so the accessibility of urban attractions on the bus network is very poor [4][5][6][7]. In order to improve urban tourism traffic conditions and provide tourists with comprehensive bus services, it is necessary to set up circular bus routes so that tourists can enjoy one-stop bus services when moving between scenic spots. ...
Article
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Based on vehicle positioning and remote data transmission technology, a quantitative analysis method for the impact of intelligent tour bus loops on the choice of transportation means between tourist attractions is developed. Aiming at the problem of undirected graph path planning where the influence of time series is known and the edge weights are known, Markov chains are introduced on the basis of the “0-1-like planning under time series” model, and a Markov chain-based algorithm is established. In this article, we proposed a model for route planning of a tourist bus. When solving, it is assumed that the weight of the edge changes with time, and random variables are introduced, but the past state will not affect the current state, and other conditions remain unchanged. After the constraint model is established, it is simulated by computer and solved using the stochastic gradient descent algorithm. The model makes the tour bus loop intelligent and has good interpretability and robustness.
... Therefore, macroscopic simulation can be a practical alternative, where fast simulation over large networks can be performed due to less detailed modelling of infrastructure and vehicles. Macroscopic models have been proposed [8], most notably the simulation tool PROTON (previously known as PRISM) [9], [10]. ...
Conference Paper
Railway traffic usually adheres to a timetable, but in Sweden, around two-thirds of the freight trains depart before they are scheduled, often by hours. Even though they occur in real operations, early departures have rarely been included in simulation studies and the effects on punctuality are not fully investigated. With a macroscopic simulation tool such as PROTON, large networks can be simulated in a short time, which makes the simulation process easier. This paper uses the tool PROTON to perform a macroscopic simulation case study on the Swedish Western mainline to investigate how early departures of freight trains affect punctuality. The resulting output is a marginal overall punctuality improvement of about +0.5 percentage points. In addition, different levels of primary run time and dwell time delays have been used as simulation input, based on empirical data. The resulting ratio between primary and secondary delays appear to vary greatly between different train types, but overall about 30% were primary and 70% secondary. Future work includes modelling and calibration of departure deviations, which vary more between different train types, and where it is more difficult to separate between primary and secondary delays. Separating distributions based on train type or location will also be considered.
... To achieve that, simulation-based methods require some huge effort to be configured and maintained and are not easily transferable to other railway systems. RailSys (Radtke and Hauptmann, 2004), OpenTrack (Nash and Huerlimann, 2004), LUKS (Janecek et al., 2010) and OnTime (Büker and Seybold, 2012) are known examples of simulation software for train delay propagation. Additionally, a recent work by Liebchen et al. (2021) points out that simulation tools are still too simple to provide a clearly matching picture of the dynamics withing a railway system. ...
Article
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.
... Macroscopic models, where only the most critical infrastructure elements (such as lines and stations) and the most critical events (such as train departures and arrivals) are represented, can therefore be preferred. A macroscopic model for delay propagation in large networks was presented by Büker and Seybold (2012). Zinser et al. (2018) designed a macroscopic simulation model and performed a case study comparing it to a microscopic simulation approach for infrastructure disruptions, showing promising results for the new model. ...
Article
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In Sweden and other countries it is not an uncommon practice that freight trains depart more or less on-demand instead of strictly following a pre-planned timetable. However, the systematic effects of freight trains departing late or (in particular) early has long been a contested issue. Although some microscopic simulation tools currently have the capability to evaluate the effect of freight trains departing before schedule, it has yet not been established how macroscopic simulation tools, capable of fast simulation of nation-wide networks, can manage such tasks. This paper uses a case study on a line between two large freight yards in Sweden to investigate how the results of microscopic and macroscopic simulation, represented by two modern simulation tools, differ when it comes to this particular problem. The main findings are that both the microscopic and the macroscopic tools replicated the empirical punctuality fairly well. Furthermore, allowing early departures of freight trains increased overall freight train punctuality while the passenger train punctuality decreased slightly, as determined by both tools. The results are encouraging, but further studies are needed to determine if macroscopic simulation is on-par with microscopic simulation.
... Ulak et al. (2020) designed a BN architecture, and used some metrics to quantify the delay dependencies between transit network dwellings, for identifying local network-wide issues sources. Graph-based models also have been proposed, such as the active graph (Büker and Seybold, 2012), the time event graph (Goverde, 2010;Hansen et al., 2010;Kecman and Goverde, 2014), and the alternative graph (Corman et al., 2014). These graph models have considered train arrivals, departures, passages, and dwelling as events and then predicted the detailed time for these events. ...
Article
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Multi-line stations (MLSs) are the intersections of different railway lines; they are crucial for delay propagation in railway networks. Therefore, the precise prediction of train arrival delays at the MLSs can efficiently support train operation rescheduling plans and reduce delay propagation in the railway network. The arrival routes of trains at the MLSs are critical factors for managing train arrival delays, since there may be latent route conflicts with forward arrival/departure trains. However, route conflicts will not occur at single-line stations (SLSs) that are traversed by only one railway line. Existing train delay prediction studies have considered the ways that trains arrive at/depart from stations as black boxes, but have not considered the latent route conflicts from a microscopic view. This study considers the arrival routes of predicted trains and route conflicts with forward trains, for contemplating the gap (not considering the route conflicts from other railway lines) in the existing studies. The influencing factors are separated into three categories according to the data attributes, namely, route-related variables, delay-related variables, and environment-related variables. Then, an architecture called LLCF-net is proposed, with a one-dimensional convolutional neural network (CNN) block for route-related variables, two long short-term memory (LSTM) networks for delay-related variables, and a fully connected neural network (FCNN) block for environment-related variables. Compared with the methods in exiting studies, this architecture showed the best performance for both two MLSs-GuangzhouSouth(GZS) and ChangshaSouth (CSS)-on the Chinese high-speed railway network, regardless of the consideration of route-related variables. In addition, LLCF-net is proven to have a strong predictive effectiveness and a robust performance for different delay lengths.
... As crucial for future exploitation of available railway infrastructure with the variability of operating conditions, railway timetable planning and its robustness have been challenging research areas for many years. Some studies are dedicated to different kinds of disturbances and consequent delays, their characteristics, effects, and transmission among railway operational flow [19][20][21][22][23][24]. Others tend to study robustness indicators and measures, evaluate timetable robustness or explore ways of its improvement concerning one or multiple selected robustness measures and types of the timetable at various levels of detail [25][26][27][28][29][30]. ...
Article
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The robustness of the timetable is a sensitive issue in the daily realization of railway operations. As shown in the paper, robustness is a function of time reserves that helps to prevent unscheduled stops resulting from traffic disruptions and causing a higher energy consumption. The correct handling of time reserves while scheduling is a multidimensional issue, and it has a significant influence on the energy consumption of railway traffic. Therefore, the paper aims to show a simulation-based method, taking into account failure occurring probabilities and their consequences to get an acceptable level of robustness, that can be quantified by the probability of no delay propagation. This paper presents a method for the addition of time margins to the railway timetable. The iterative time buffer adding method is based on operational data as a knowledge source, to achieve the punctuality target. It was verified on a real railway line. An analysis of energy consumption for unscheduled train stops depending on the added buffer time was conducted after the literature review and the presentation of the evaluation model. The paper ends with discussion of the results and conclusions.
... To achieve that, simulation-based methods require some huge effort to be configured and maintained and are not easily transferable to other railway systems. RailSys (Radtke and Hauptmann, 2004), OpenTrack (Nash and Huerlimann, 2004), LUKS (Janecek et al., 2010) and OnTime (Büker and Seybold, 2012) are known examples of simulation software for train delay propagation. Additionally, a recent work by Liebchen et al. (2021) points out that simulation tools are still too simple to provide a clearly matching picture of the dynamics withing a railway system. ...
... La robustesse de la grille est alors évaluée en étudiant la façon dont sont distribués les retards secondaires correspondants pour les différents trains de la grille. Büker et Seybold (2012) proposent une méthode de simulation rapide de la propagation des retards utilisant un modèle de graphes ; la robustesse de la grille est alors évaluée, pour une certaine distribution de retards primaires, à partir de la proportion de retards situés en-dessous d'un certain seuil, l'espérance ainsi que la variance des retards. Certains opérateurs mesurent leur performance en utilisant l'indicateur de régularité à N minutes : il s'agit du pourcentage de circulations étant arrivées au terme de leur mission avec un retard inférieur ou égal à N minutes. ...
Thesis
La concentration de l'activité économique autour des grandes villes y entraîne une augmentation régulière de la demande en transport. Afin de répondre à cette demande, les entreprises de transports en commun tentent de proposer une offre adéquate, mais celles-ci sont contraintes par la saturation progressive des infrastructures. Dans le cas du transport ferroviaire, l'accroissement du nombre de voyageurs et de trains en circulation a pour conséquence une augmentation du nombre de perturbations au cours de l'exploitation, ainsi que de leur tendance à se propager et à s'amplifier. Il en résulte une qualité de service dégradée pour les usagers et des pénalités financières pour les opérateurs. Deux leviers peuvent être actionnés pour atténuer les conséquences de ces perturbations : l'application de mesures de régulation pendant la phase opérationnelle, et la construction en amont de plans de transport robustes face aux petits aléas. C'est principalement sur ce dernier point que porte le travail de la thèse. Après avoir présenté le fonctionnement de l'exploitation ferroviaire en zone dense et donné une définition d'un petit aléa, nous passons en revue les différents travaux ayant été menés sur le sujet. La grande majorité des cadres conceptuels proposés pour la conception d'horaires robustes ne sont pas adaptés au cas spécifique de la zone dense, c'est pourquoi nous proposons un nouveau modèle sous la forme d'un problème d'optimisation stochastique. Une approche de résolution est ensuite détaillée, en trois étapes. La première porte sur l'estimation des distributions de probabilité des aléas de l'exploitation, à partir de données de retour d'expérience. Dans un second temps, nous utilisons ces distributions dans un outil de simulation stochastique permettant d'évaluer la performance d'une grille horaire donnée. Enfin, cet outil est utilisé comme fonction d'évaluation au sein d'une heuristique de recuit simulé visant à générer automatiquement des grilles horaires robustes.
... In addition, some researchers have investigated train delay propagation through a search algorithm based on a probability model, where many results have prove that the search algorithms can solve the specific problems of train delays when the primary delay distributions are known. [20][21][22][23][24][25]. Meester et al . ...
Article
Full-text available
This paper proposes an analytical delay propagation model for single railway lines based on the max-plus algebra theory. The scheduling measures taken by dispatchers, including re-timing and re-ordering, will be incorporated into our delay propagation model using a matrix transformation method. An analysis of delay propagation under some typical emergencies such as segment blockages and train speed limitation is performed. Numerical simulations show that the proposed train delay propagation model can predict emergency-induced train delays under different scheduling strategies, thus may give a guidance to improve the traffic management. In the high-speed railway train system, the scheduling measures taken by dispatchers, such as re-timing and re-ordering, can be formulated as a delay propagation model using a matrix transformation method. © 2021 The Authors. IET Intelligent Transport Systems published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology
... Koutsopoulos et al [111] proposent une méthodologie de calibration automatique d'un simulateur de retards basée sur la minimisation d'une fonction d'erreur entre les mesures observées et simulées. Büker [34] s'intéresseà la distribution des retards primaires puisqu'ils ne sont pas séparés des retards secondaires dans les données. La distribution est obtenue par de la simulation en comparantà la réalité. ...
Thesis
Cette thèse traite de l’incertitude et de la robustesse dans les problèmes de d´décision, avec le cas d’application des affectations de quais en gare en cas de retards. Une m´méthodologie en deux parties est proposée pour aborder ce problème. Dans un premier temps, les archives de données de retards sont utilisées pour construire des modèles de prédiction de distribution de probabilités conditionnellement aux valeurs d’un ensemble de variables explicatives. Une m´méthodologie de validation et d’évaluation de ces prédictions est mise en place afin d’assurer leur fiabilité pour de la prise de d´décision. Le problème d’affectations de quais pouvant être vu comme une recherche de clique de taille maximum, ces distributions prédites sont utilisées dans une seconde partie pour ajouter des pondérations pénalisant les risques de rupture des arêtes en cas de retard. Des algorithmes de recherche locale ont ´été utilisés et les expériences ont montré une importante baisse de conflits.
... ere are many types of failures that cause delays in train operation, and the frequency and duration of their occurrence vary greatly. In order to study the law of its occurrence, a set of calculation methods are based on the original data of the dispatch log, deredundancy, and desensitization, and then the time, space, reason, and other parameters of the fault delay are calculated [11][12][13][14]. Taking the dispatch log of a rail transit network in 2018 as an example, there are a total of 13,423 valid data items, 26 subcategories are processed, and the occurrence frequency and proportion are calculated, and the fault subcategories are merged into major categories to obtain the fault distribution and average processing time as shown in Table 1. ...
Article
Full-text available
With the increase and extension of urban rail transit lines, networked operation has become an inevitable trend of rail transit operations. Once an emergency occurs, it will cause operational delays; in serious cases, it may further lead to group safety incidents. Firstly, the sudden failure of rail transit is defined, statistical calculation is made according to the accumulated failure data, and then the sudden failures and average processing time are quantitatively calculated. Secondly, the time delay and propagation under the state of sudden failure are analyzed, on the basis of which the propagation and dissipation of time delay based on the single station failure cellular automata model and SIR model network based on multistation fault delay propagation are constructed. Finally, the reliability and accuracy of the model are verified by a case of rail transit in a city. The scheme in this paper can be used to estimate the scope of time and space delay under the sudden failure of rail transit and can provide the basis for the adjustment of traffic organization scheme and evacuation of passenger flow under the sudden failure.
... Most models are based on the schedules of the railway system, commonly using trains as agents that have the potential to carry delays. The perspective of delays as a properties of discrete trains or events can be found in many analytical models [15,16,17,18,2], using either deterministic or stochastic techniques to derive future delays from past information. Because of the abundance of this perspective in existing delay propagation models, we refer to the view of delays as properties of discrete trains or events as the 'traditional view'. ...
Preprint
Full-text available
Railway systems form an important means of transport across the world. However, congestions or disruptions may significantly decrease these systems' efficiencies, making predicting and understanding the resulting train delays a priority for railway organisations. Delays are studied in a wide variety of models, which usually simulate trains as discrete agents carrying delays. In contrast, in this paper, we define a novel model for studying delays, where they spread across the railway network via a diffusion-like process. This type of modelling has various advantages such as quick computation and ease of applying various statistical tools like spectral methods, but it also comes with limitations related to the directional and discrete nature of delays and the trains carrying them. We apply the model to the Belgian railways and study its performance in simulating the delay propagation in severely disrupted railway situations. In particular, we discuss the role of spatial aggregation by proposing to cluster the Belgian railway system into sets of stations and adapt the model accordingly. We find that such aggregation significantly increases the model's performance. For some particular situations, a non-trivial optimal level of spatial resolution is found on which the model performs best. Our results show the potential of this type of delay modelling to understand large-scale properties of railway systems.
Article
In this study, train operations were modeled by Bayesian networks (BN), to use the probability essence of the BN to quantify their uncertainty (e.g., the epistemic and aleatoric uncertainty in train operations). To overcome the drawbacks of the existing graph/network-based train delay propagation models, we introduce three timetable-based parameters to enable the proposed BN structure, called context-aware BN (CBN), to recognize the context information in train operations. In addition, the model is established based on updating time horizons (multiple updating time horizons forming the prediction horizon), capable of performing uncertainty quantification and prediction in flexible horizons (i.e., from 5 minutes to 1 hour ahead). The CBN model is calibrated on the train operation data from the Swiss railway network. Experimental results show that the context parameters improve the accuracy and lower the variance of the model, compared to the standard models without considering the timetable parameters. The uncertainties of train operations in a range of prediction horizons were quantified using the CBN model. The results demonstrate that the uncertainty grows near-linearly with the increase of prediction horizon; specifically, long-distance trains exhibit significantly higher uncertainty than short-distance trains. Finally, the CBN was built on a network model, maintaining the interpretability and easy-understanding quality of train delay propagation models.
Article
Full-text available
It is evident that the telecommunications industry in Accra, Ghana, has experienced significant growth, aligning with the influx in mobile devices and internet usage. However, the widespread issue of network latency tends to jeopardize and obstruct the overall user experience. This project focuses on assessing the impact of network latency on user experience in telecommunications industries in Accra, Ghana. The aim of this research was to investigate the causes and effects of network latency on user experience and also, evaluate strategies adopted by telecommunications industries to tackle network latency challenges to aid in the improvement of services in the telecommunications industries in Accra, Ghana. The study employs both qualitative and quantitative methods to conduct a survey where data on user experience and network latency statistics, alongside, interviews with industry experts were acquired. By employing descriptive and inferential statistics, including regression analysis, the study used textual analysis to gain insight from the industry experts. The expected outcome is a comprehensive report that will spotlight the underlying causes, examine the impacts and suggest remedial measures, resulting in implementable steps for enhancement in telecommunications industries. The significance of this project is found in making contribution to the intellectual resource surrounding network latency and its effects on user experience in telecommunications industries in Accra, Ghana. The findings impart understanding to telecommunications industries in Accra, Ghana, facilitating their ability to enhance overall network performance and user experience. In summary, the study pledges a beneficial influence on users, establishing an atmosphere where telecommunications industries in Accra, Ghana provide an ideal and satisfying experiences.
Article
Incidents pose challenges to the reliable operation of urban rail transit systems. Given the high frequency of subway services, even minor incidents can cause cascading delays across multiple trains. Understanding incident effects is crucial for improving response time and enabling efficient recovery strategies. This study uses operational records from the Montreal subway system to quantify the overall impact of incidents including the number of affected trains and total delay time. The proposed approach involves integrating operational records with incident data to identify the source of delays and subsequent knock-on effects. To recognize distinct propagation patterns among various incident types, K-means clustering is applied to categorize incidents into three clusters. Cluster 1 represents incidents with the lowest impacts, affecting only one direction of a subway line and imposing an average total delay time of 16 min. Cluster 2, which comprises most incidents, causing moderate operational impacts with an average total delay time of 52 min. Cluster 3 includes severe incidents, affecting an average of 26 trains and causing a total delay time of 273 min. Peak hour analysis indicates that morning and evening peak hours have the highest average number of affected trains, emphasizing the impact of peak hours on incident severity. Investigation into the causes of incidents highlights that the most frequent incidents fall into Cluster 2, implying moderate impacts on subway operations. This research provides valuable insights into subway incident management, laying the groundwork for further studies aimed at enhancing the performance of urban rail transit systems during service disruptions.
Article
China’s high-speed railway (HSR) has entered the era of networked operation. Any internal disturbance or eternal disturbance may result in delays of some trains and even cascading delays, which will not only reduce the traffic efficiency of HSR, but also break passengers’ travel and lower their satisfaction. Studying the delay propagation mechanism could assist the dispatcher in suppressing the negative effect of disturbances. However, current studies seldom consider the withholding strategy’s impact on delay propagation. Inspired by this, this article proposes a novel bi-directional delay propagation model combined with the trains’ operation trajectory and stations’ withholding strategy. Moreover, the operation constraint, station capacity constraint, and interlocking constraint are also considered. Then, the primary delay under section disruption (SD) and section temporary speed limit (STSL) are derived based on the location of the disturbance, duration time of the disturbance, and the operation strategy. Then, a max-plus algebra-based delay propagation model is established to compute the corresponding secondary delays. Also, the All Pair Critical Path algorithm is modified to incorporate the station capacity constraint in the searching process. Simulations based on the real China HSR subnetwork are implemented to verify the proposed model. Compared with the current study, the proposed model could accurately unfold the delay propagation in the opposite train heading direction. Besides, the relationship among disturbance duration, primary delay, and accumulative delay for the SD scenario and the relationship among temporarily limited velocity, primary delay, and accumulative delay for the STSL scenario are revealed.
Article
Accurately predicting delays for high-speed railways (HSRs) is a challenging yet significant task. The historical operation data of the HSRs, implicating delay derivation rules under the dispatchers’ rescheduling strategies, have sparsity characteristics, resulting in heterogeneous prediction performances under different scenarios. This article proposes a Gaussian noise data augmentation-based delay prediction method to cope with the sparsity. Specifically, the Gaussian noise is added to the original data based on the train operation data characteristics. Then, the delay data rather than the full-state dataset are selected as the training data for different designed machine learning prediction models. Numerous studies based on real HSR operational data from the Beijing Railway Bureau show that the proposed method could significantly improve the prediction accuracy under different scenarios with different machine learning models, verifying the effectiveness of the performance improvement. The relevant results could be significantly helpful for real-time train rescheduling and passenger management, thus improving the emergency response capabilities of HSRs.
Article
Based on train operation data, Bayesian networks (BN) are used to model the cascading effects of traffic control actions and their influences (such as changes in train delays) for two and three consecutive trains. Influence factors are first determined to describe the interactions between train delays and control actions, i.e. the delay changes due to control actions over time and space. Considering the interdependence of these factors, their causal relationships are obtained, and the BN model’s connection paradigm is determined based on these causal ties. The BN structures are then proposed by combining domain knowledge and a data-driven method. The proposed models are tested on the train operation data from the Chinese high-speed railways. The results show that the proposed method exhibits a good fit for the train operation data and outperforms other conventional train operation models in terms of various evaluation metrics. Besides, the strength of train control actions’ cascading effects is investigated. It shows that section train control actions are stronger than those in stations, and both are considerably correlated with train delays and recovery times in sections and stations. Finally, a macroscopic model for control actions between several trains (more than three) is obtained based on the learned paradigm of the presented models and the cascading effects between two and three trains, demonstrating the model’s extensibility. The proposed models are intended to support traffic controllers with the estimation of future train delay change patterns, the expected control actions, and the cascading effects of control actions, and they are imperative for aiding the decision-making of controllers to manage high-speed railway traffic.
Chapter
Supply chains are complex and continuously evolving to become more complex. With globalization of supply chains and ever-increasing customer demands for better service, planning is very important. The vulnerabilities in the supply chain were exposed with COVID-19, and transportation, a key supply chain element, was impacted significantly. Transportation connects various nodes in the supply chain network. There are several nodes, numerous links between nodes, various modes of transportation in addition to people and systems in the network. Ensuring better service for customers is of paramount importance for companies. With disparate systems involved, collecting and harnessing this data can identify problems in the network. Data science techniques, machine learning, and artificial intelligence can help identify service failures in planning even before they happen. Predicting service failures in planning can ensure better service and reduce costs. In this article, the authors use machine learning to predict service failures in domestic transportation planning.
Chapter
The article discusses the main parameters and test results of a innovative freight electric locomotive with rotary-field traction motors on Artyshta II—Altayskaya section of West Siberian Railway. The paper presents the results of the analysis of the technical equipment of the mainline asynchronous traction motor electric locomotive of innovative series. The paper focuses on traction electrical devices as well as the technical characteristics of the traction rolling stock under consideration. The article presents a comparative analysis of the main parameters of asynchronous traction motor electric freight locomotives with moving trains of estimated weight in nominal traction mode on the limiting upward journey of the serviced section of the railway operating domain per hour. The paper presents the results of experimental tests conducted by the authors of the article. The methodology for processing the results obtained based on the results of experimental trips is given. Conclusions are drawn and discussion questions are proposed.
Preprint
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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.
Article
Full-text available
Railway systems form an important means of transport across the world. However, congestions or disruptions may significantly decrease these systems’ efficiencies, making predicting and understanding the resulting train delays a priority for railway organisations. Delays are studied in a wide variety of models, which usually simulate trains as discrete agents carrying delays. In contrast, in this paper, we define a novel model for studying delays, where they spread across the railway network via a diffusion-like process. This type of modelling has various advantages such as quick computation and ease of applying various statistical tools like spectral methods, but it also comes with limitations related to the directional and discrete nature of delays and the trains carrying them. We apply the model to the Belgian railways and study its performance in simulating the delay propagation in severely disrupted railway situations. In particular, we discuss the role of spatial aggregation by proposing to cluster the Belgian railway system into sets of stations and adapt the model accordingly. We find that such aggregation significantly increases the model’s performance. For some particular situations, non-trivial optimal levels of spatial resolution are found on which the model performs best. Our results show the potential of this type of delay modelling to understand large-scale properties of railway systems.
Chapter
In this paper, we improve the scalability of an exact symbolic simulation method to compute the impact of stochastic delays in railway systems. We present transformation rules that allow minimizing the size of the system state representation (which train is where with which probability), without losing exactness. Based on these transformation rules, we propose two different approaches to decrease the simulation effort and thus the running time of the symbolic simulation method. One approach iteratively applies our transformation rules to the state representation, while the other encodes transformation steps logically and uses satisfiability checking tools to determine which rule combination leads to the strongest possible reduction. We evaluate the proposed improvements on realistic case studies and discuss further possible speed-up techniques that approximate the results.
Article
High-speed rail (HSR) has formed a networked operational scale in China. Any internal or external disturbance may deviate trains' operation from the planned schedules, resulting in primary delays or even cascading delays on a network scale. Studying the delay propagation mechanism could help to improve the timetable resilience in the planning stage and realize cooperative rescheduling for dispatchers. To quickly and effectively predict the spatial-temporal range of cascading delays, this paper proposes a max-plus algebra based delay propagation model considering trains' operation strategy and the systems' constraints. A double-layer network based breadth-first search algorithm based on the constraint network and the timetable network is further proposed to solve the delay propagation process for different kinds of emergencies. The proposed model could deal with the delay propagation problem when emergencies occur in sections or stations and is suitable for static emergencies and dynamic emergencies. Case studies show that the proposed algorithm can significantly improve the computational efficiency of the large-scale HSR network. Moreover, the real operational data of China HSR is adopted to verify the proposed model, and the results show that the cascading delays can be timely and accurately inferred, and the delay propagation characteristics under three kinds of emergencies are unfolded.
Chapter
Full-text available
Trajectory elements of train movement, such as departure and running times, are subject to random influences, which can lead to disruption of the arrivals. Analysis of the corresponding probability distributions and their changes, which arise depending on intermediate stations, makes it possible to identify the degree of influence of various factors on the movement process, as well as to assess the quality of train traffic control. This article provides an approach for calculating the distribution of the arrival time deviations and investigates the evolution of this distribution when trains travel on an extended section of a main railway line. Historical data on the scheduled freight train traffic at the Russian Railways are used to verify the proposed model.
Chapter
In this paper we propose an exact symbolic simulation method to compute the impact of delays in railway systems. We use macroscopic railway infrastructure models and model primary delays of trains in a timetable by discrete probability distributions. Our method is capable of computing exact probabilistic quantities like delay probability distributions and expected delays for timetable trains, or expected capacity usage of infrastructure elements within a given finite time window. In turn, these quantities allow us to examine timetable robustness and to identify problematic infrastructure elements. We evaluate our approach on realistic case studies and discuss possible further improvements.
Article
Full-text available
Switching max-plus-linear (SMPL) systems are discrete-event systems that can switch between different modes of operation. In each mode the system is described by a max-plus-linear state equation and a max-plus-linear output equation, with different system matrices for each mode. The switching may depend on the inputs and the states, or it may be a stochastic process. In this paper two equivalent descriptions for switching max-plus-linear systems will be discussed. We will also show that a switching max-plus-linear system can be written as a piecewise affine system or as a constrained max-min-plus-scaling system. The last translation can be established under (rather mild) additional assumptions on the boundedness of the states and the inputs. We also develop a stabilizing model predictive controller for SMPL systems with deterministic and/or stochastic switching. In general, the optimization in the model predictive control approach then boils down to a nonlinear nonconvex optimization problem, where the cost criterion is piecewise polynomial on polyhedral sets and the inequality constraints are linear. However, in the case of stochastic switching that depends on the previous mode only, the resulting optimization problem can be solved using linear programming algorithms.
Conference Paper
Swiss Federal Railways plan and operate one of the densest rail networks in the world. Over the last 8 years, punctuality on the network has been steadily increasing. Figures comparing train traffic density and showing the punctuality of Swiss trains over the last 8 years will be presented and briefly discussed. Then the process of collecting the train traffic data at SBB will be explained and discussed. The main points of this paper will be the mathematical methods and the graphical data visualisation method developed by SBB to continually optimise the timetable with extensive use of historical train traffic data. Based on quite simple collected data – actual arrival and arrival delay, actual departure and departure delay – for each train at about 1000 stations, the paper will define and review the different types of analysis that the method facilities: arrival punctuality, departure punctuality, dwelling time, journey time, dwelling time deviation and journey time deviation. The paper will also discuss the type of distribution function which can be observed and explain why the original statistical definition of boxplots by John Wilder Tukey (Exploratory Data Analysis, Addison-Wesley) has been adapted for rail-related use. Subsequently, the strength of this new defined boxplot is demonstrated with a top-down delay cause analysis starting with punctuality in Switzerland, then comparing the major Swiss stations and the train family, and finally identifying the problems on the corridors. We then show how the usage of median insights into the dynamics of the railway system helps us to identify potential stability problems. To conclude, the identification and visualisation of knock-on delay between trains based on actual train traffic data is addressed as an interesting open issue. Keywords: timetable stability, traffic data, statistic, boxplot, punctuality, cyclic timetable, data mining.
Article
For scheduled train services, a trade-off exists between efficiently utilizing the capacity of railway networks and improving the reliability and punctuality of train operations. This paper proposes a new analytical stochastic model of train delay propagation in stations, which estimates the knock-on delays of trains caused by route conflicts and late transfer connections realistically. The proposed model reflects the constraints of signalling system and train protection operations rules. The stochastic variations of track occupancy times due to the fluctuations of train speed in case of different signal aspects are modelled with conditional probability distributions. The model is solved on the basis of a numerical approximation of the Stieltjes convolution of individual independent distributions and can be integrated into a larger computerized decision support tool for timetable design and train dispatching. Having been validated successfully with empirical data, the model is applied for optimizing the station capacity utilization in a case study of the Dutch railway station The Hague Holland Spoor. The model can determine the maximal frequency of trains passing the critical level crossing with a given maximum knock-on delay at a certain confidence level. It is found that when the scheduled buffer time between train paths at the level crossing decreases, the mean knock-on delay of all passing trains increases exponentially.
Article
In highly-interconnected timetables or dense railway traffic, a single delayed train may cause a domino effect of secondary delays over the entire network, which is a main concern to planners and dispatchers. This paper describes a stability theory to analyse timetables on sensitivity and robustness to delays based on a linear system description of a railway timetable in max-plus algebra. The max-plus model includes train interdependencies resulting from the timetable, logistics, and the shared infrastructure. Stability is the self-regulatory behaviour of the railway system to return to the steady state of the railway timetable after disruptions. The proposed approach evaluates timetable realizability and stability using max-plus spectral analysis and quantifies robustness using critical path algorithms. Moreover, delay propagation of initial delay scenarios over time and space is effectively computed by explicit recursive equations taking into account zero-order dynamics. The max-plus approach enables a real-time analysis of large-scale periodic railway timetables. A case-study of the Dutch national railway timetable illustrates the potential of the developed methodology to support the design of reliable railway timetables in dense railway traffic networks.
Article
It is difficult to analyse stochastic models for the propagation of delays in railway networks. It seems that the choice is between very global mathematical (queueing) models at one extreme and simulation models at the other. In this paper we discuss a (fairly general but not too detailed) model for delay propagation and show that in a world of so-called phase-type distributions it is possible to derive secondary delay distributions from primary delay distributions. We shall explain why phase-type distributions and the delay propagation model are suited for each other and show by an example that it is possible to develop algorithms that analyse such networks.
Article
A trade-off exists between efficiently utilizing the capacity of railway networks and improving the reliability and punctuality of train operations. This dissertation presents a new analytical probability model based on blocking time theory which estimates the knock-on delays of trains caused by route conflicts and late transfer connections in stations. The model estimates the propagation of train delays with a higher accuracy than existing analytical models by taking into account the interdependences of the arrival and departure times of different train lines and the dependences of the dwell times of trains on arrival delays. A detailed statistical analysis of real-world traffic data reveals that the variations of train events and process times can be well approximated by either the lognormal distribution or the Weibull distribution. Given the mean and standard deviation of input delays at the boundary of a station and those of primary delays within the area, the knock-on and exit delay distributions are estimated by means of the stochastic models. Consequently, the maximal traffic capacity utilization of complex stations and interlocking areas can be estimated according to a desired level of train punctuality. The research results support railway infrastructure managers, timetable designers, and train operators in optimizing the network capacity utilization and train scheduling.
Conference Paper
This paper describes the architecture and potentials of Simone. Simone is a simulation environment to generate, simulate and analyze complex and large scale train networks. The purpose of Simone is to (1) assess the robustness of timetables; (2) determine the stability of the network; analyze causes and effects of delays; (3) improve timetables, by determining the relations between design standards and robustness of the timetable; (4) detect and quantify bottlenecks in a train network and (5) quantify delays for different lay-outs of railway infrastructures A strong feature of Simone is the ability to automatically generate ready-to-use network simulation models from databases. First, the concepts are described, then two case studies are presented. Last, the paper ends with a short evaluation of the use up till now and forthcoming developments for Simone
Ausgewählte Aspekte der Verspätungsfortpflanzung in Netzen Efficient modelling of delay distribution functions Simulating delays for realistic time-table optimization
  • Büker
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  • E Wendler
Büker, Th., 2010. Ausgewählte Aspekte der Verspätungsfortpflanzung in Netzen, PhD thesis submitted at RWTH Aachen University. Büker, Th., Wendler, E., 2009. Efficient modelling of delay distribution functions, Proceedings RailZurich2009. Engelhardt-Funke, O., Kolonko, M., 2001. Simulating delays for realistic time-table optimization, in: Proceedings Symposium on Operations Research 2001, Duisburg.
OnTime – Netzweite Analyse der Fahrplanstabilität
  • B Franke
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Franke, B., Graffagnino, Th., Labermeier, H., Büker, Th., 2012. OnTime – Netzweite Analyse der Fahrplanstabilität. Eisenbahntechnische Rundschau (6), 36–40.
Modellierung und Simulation von Verspütungen für die Fahrplanoptimierung, presentation at ''Automatic Timetable Generation colloquium Stochastic delay propagation in railway networks and phase-type distribution
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Kolonko, M., 2007. Modellierung und Simulation von Verspütungen für die Fahrplanoptimierung, presentation at ''Automatic Timetable Generation colloquium, Dresden. Meester, L.E., Muns, S., 2007. Stochastic delay propagation in railway networks and phase-type distribution. Transportation Research Part B: Methodological 41 (2), 218–230.
Railroad simulation using open track
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Nash, A., Hürlimann, D., 2004. Railroad simulation using open track, In: Ninth International Conference on Computer in Railways (Comprail IX), Dresden.
Matrix-geometric Solutions in Stochasitc Models: An Algorithmic Approach Publications by the Transport Science Institute at RWTH Aachen Combining microscopic and macroscopic infrastructure planning models
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Neuts, M., 1981. Matrix-geometric Solutions in Stochasitc Models: An Algorithmic Approach. Johns Hopkins University Press. Schwanhäußer, W., 1974. Die Bemessung der Pufferzeiten im Fahrplangefüge der Eisenbahn, vol. 20, Publications by the Transport Science Institute at RWTH Aachen. Sewcyk, B., Radtke, A., Wilfinger, G., 2007. Combining microscopic and macroscopic infrastructure planning models, In: Proceedings RailHannover 2007.