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| Writer | Objective | Methods | Results |
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| Schön and König (2018) [10] | Solving the Bellman equations recursively to minimize the total delay passengers experience at their final stations | We offer stochastic dynamic programming (SDP) | SDP approach outperforms other approaches for a reasonable time resolution to delay. |
| Rückert et al. (2017) [11] | Time delay information and passenger flow estimates, evaluating impacts of waiting decisions on passenger arrival delays at their final destination | Introduce a web-based simulation tool for dispatchers, called PANDA | Waiting or not waiting at a critical transfer station is based on a majority rule that considers 8 criteria defined as the delay distribution at the passenger’s final destination. |
| Zhu (2011) [12] | To minimize train delays | Scenario-based route choice model | The model was built mainly to deal with predictably large passenger flow events but failed to forecast the network passenger flow distribution under unexpected events. |
| Berger et al. (2011) [13] | Proposed a delay propagation in large transportation networks, suited to process massive streams of real-time data | Stochastic model | A stochastic model was used for delay. |
| Corman et al. (2012) [14] | To minimize train delays and missed connections due to disturbances | Applied two heuristic algorithms to select the connections to be enforced | Study shows that good coordination of connected train services is important to achieve real-time efficiency of railway services since the management of connections can heavily affect train punctuality. The two algorithms accurately approximate the Pareto front in a limited computation time. |
| Krasemann (2012) [15] | Proposed a greedy algorithm that effectively delivers good solutions within the permitted time | Branch-and-cut approach | Detects that for certain scenarios, it is difficult to find good solutions within seconds using a branch-and-cut approach. |
| Almodovar and Ródenas (2013) [16] | Proposed a model for timetable rescheduling in emergency cases, reallocating trains/buses in real time to other service lines | An optimization approach | This model assumes passengers use travel strategies and waiting passengers are loaded at trains/buses on a first-come-first-served basis. The infrastructure restrictions are not considered by the model. |
| Milinkovic et al. (2010) [17] | Calculate train delay | Simulation model | Results of simulation are exported to a database for additional data mining and comparative analysis. Model is tested on a part of Belgrade Railway Node. Train delays are calculated in a simulation model using a Fuzzy Petri Net subsystem. |
| Markovic et al. (2015) [18] | This paper proposed machine-learning models that capture the relationship between passenger train-arrival delays and various characteristics of a railway system | Support vector regression and artificial neural network | Statistical comparison of the two models indicates that the support vector regression outperforms the artificial neural network. |
| Wang et al. (2021) [19] | The purpose of this study was to investigate how the winter weather precipitation affect the occurrence of primary delays and the transitions between delayed and nondelayed states. | Cox proportional hazard model and Markov chain model | Markov chain model to the train operation data is more reasonable, since it is strict to assume the transition intensity does not change over time in reality |
| Hou et al. (2020) [20] | This paper proposed to determine the effects of two train operation adjustment actions on train delay recovery were explored using train operation records from scheduled and actual train timetables. | Gradient-boosted regression tree (GBRT) machine-learning model | A comparison of the prediction results of the GBRT model with those of a random forest model confirmed the better performance of the GBRT prediction model. |
| Jiang et al. (2019) [21] | This paper aimed to develop primary delay recovery (PDR) predictor model using train operation records from Wuhan-Guangzhou (W-G) high-speed railway. | Random forest regression (RFR) model, multiple linear regression (MLR), support vector machine (SVM), and artificial neural networks (ANN) | RFR model can achieve up to 80.4% of prediction accuracy, while the accuracy level is 44.4%, 78.5%, and 78.5% for MLR, SVM, and ANN models, respectively. |
| Wang and Zang (2019) [22] | The aim of study to determine patterns of train delays and to predict train delay time | Machine-learning model | The prediction model is useful not only for passengers wishing to plan their journeys more reliably, but also for railway operators developing more efficient train schedules and more reasonable pricing plans. |
| Corman and Kecman (2018) [23] | This paper aimed to present a stochastic model for predicting the propagation of train delays based on Bayesian networks. | Bayesian networks | The presented method is important for making better predictions for train traffic that are not only based on static, offline collected data, but are able to positively include the dynamic characteristics of the continuously changing delays. |
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