Search

The dynamics of a moving train are usually described by means of a motion model based on Newton's second law. This model uses as input track geometry data and train characteristics like mass, the parameters that model the running resistance, the maximum tractive effort and power, and the brake rates to be applied. It can reproduce and predict train dynamics accurately if the mentioned train characteristics are carefully calibrated. The model constitutes the core element of a broad variety of railway applications, from timetabling tools to Driver Advisory Systems and Automatic Train Operation. Among the existing train motion model calibration techniques, those that use operational data are of particular interest, as they benefit from on- board recorded data, capturing the train dynamics during operation. In this literature review article we provide an overview of the train motion model calibration techniques that have been published in the scientific literature between January 2000 and December 2021 and either use operational data or can be minimally adapted to use it. To this end, we present a critical overview of the existing train motion model calibration approaches, distinguishing online calibration that analyzes data on- the-go and offline calibration that analyzes historical data batchwise. We propose a research agenda and highlight some potential goals to be tackled in the near future: from devising accurate online calibrators for eco-driving applications to quantitizing the physical sources of parameter variation. Last, we discuss practical recommendations for practitioners and scholars inferred from the current state of the art.

Train movement dynamics are usually modelled by means of Newton's second law. The resulting dynamic equation can be very precise if the parameters that it depends on are determined accurately. However, these parameters may vary in time and show wide variations, making the calibration task nontrivial and jeopardizing the performance of a broad variety of applications in the railway industry: from timetable planning and railway traffic simulation to Driver Advisory Systems and Automatic Train Operation. In this article, the online train motion model calibration problem is addressed with a special focus on energy-efficient on-board applications. To this end, location and speed measurements are assumed to be available for a train running under normal operation conditions. A well-known real-time parameter estimation algorithm, the Unscented Kalman Filter, is combined with a driving regime calculator and a post-processing module in order to obtain bounds and statistics of parameters such as the maximum applied tractive effort and power, the applied brake rates, the cruise speed and the length of the final coasting and braking. The proposed framework is tested in a case study with real data from trains operating on the Eindhoven-’s-Hertogenbosch corridor in the Netherlands. Results obtained show that UKF is able to track the speed and location measurements and to estimate the parameters that model the running resistance in the dynamic equation. The proposed driving regime and the post-processing modules can determine the current regime accurately and give a deeper insight into the variations of the driving style, respectively.

Trains consist of one or more railway vehicles called rolling stock, which need interior and exterior cleaning and small technical checks on a daily basis. These services are executed at service locations (SLs). Scheduling rolling stock servicing tasks during an operational day is important to guarantee the fulfilment of servicing deadlines. Public transport companies face large scheduling problems, especially those with 24-hour-a-day operation. The expected increase in transport frequencies enhances the need for improving scheduling servicing tasks during an operational day. Therefore, the Rolling Stock Servicing Scheduling Problem (RS-SSP) is modelled comprising a MILP model. Complying with the planned timetable, the RS-SSP maximises the RS units being serviced during daytime. The RS-SSP allows RS exchanges between RS units having completed servicing and operating RS units requiring servicing. Due to this RS Exchange Concept, the number of RS units visiting the SL during daytime can be increased. The proposed RS-SSP model has been tested on a real-life case from the Dutch railways. For multiple scenarios, the model was able to exchange all running RS. Consequently, the capacity usage at SLs can be increased by the RS-SSP by shifting some of the excessive workload to daytime, and thus solving the capacity shortages.

During railways operations, unplanned events might occur which can result in rail traffic being heavily impacted. The paper proposes a passenger-centred resilience assessment for disruption scenarios which consist of multiple simultaneous disruptions. It combines train traffic operations, passenger flows and network restoration. To evaluate resilience, an optimization-based approach has been developed for solving the new infrastructure restoration and transport management (IRTM) problem. Additionally, this approach develops mitigation plans for the best infrastructure restoration and traffic recovery and it captures the time-dependent transport network performance during disruptions. The approach is general with respect to types of disruptions, and can be applied for evaluation against short disruptions (1–2 h) as well as more substantial ones (multiple days or weeks). The performance of the proposed approach has been demonstrated on a Dutch railway network. Furthermore, the resilience of the system is assessed against the critical infrastructure disruption scenarios in the network. This optimization-based approach shall enable decision makers to quantify accurately impacts of multiple disruptions by considering the created inconveniences to passengers in the railway operation due to these disruptions.

Critical infrastructure networks, such as transport and power networks, are essential for the functioning of a society and economy. The rising transport demand increases the congestion in railway networks and thus they become more interdependent and more complex to operate. Also, an increasing number of disruptions due to system failures as well as climate changes can be expected in the future. As a consequence, many trains are cancelled and excessively delayed, and thus, many passengers are not reaching their destinations which compromises customers need for mobility. Currently, there is a rising need to quantify impacts of disruptions and the evolution of system performance. This review paper aims to set-up a field-specific definition of resilience in railway transport and gives a comprehensive, up-to-date review of railway resilience papers. The focus is on quantitative approaches. The review analyses peer-reviewed papers in Web of Science and Scopus from January 2008 to August 2019. The results show a steady increase of the number of published papers in recent years. The review classifies resilience metrics and approaches. It has been recognised that system-based metrics tend to better capture effects on transport services and transport demand. Also, mathematical optimization shows a great potential to assess and improve resilience of railway systems. Alternatively, data-driven approaches could be potentially used for detailed ex-post analysis of past disruptions. Finally, several rising future scientific topics are identified, spanning from learning from historical data, to considering interdependent critical systems and community resilience. Practitioners can also benefit from the review to understand a common terminology, recognise possible applications for assessing and designing resilient railway transport systems.

A significant growth of the railway transportation demand is forecasted in the next decades which needs an increase of network capacity. Where possible, infrastructure upgrading can provide extra capacity; although in some cases, this is not enough to satisfy the entire transportation demand even if optimised timetabling is performed. We propose a heuristic model to develop a stable timetable which maximises the satisfaction of transportation demand in situations where network capacity is limited. In case the demand cannot be fully satisfied, the model relaxes the given line plan and timetable design parameters. The aim is to keep as many train services as possible and reduce the level of service minimally. We develop a mixed integer linear programming (MILP) model for minimising the cycle time to find an optimised stable timetable for the given line plan. The heuristic iteratively solves the MILP model and applies relaxation measures. We tested the model on the Dutch network. The results showed that the model can generate stable timetables by removing train services from the critical circuit, and also, higher transportation demand can be satisfied by additionally relaxing timetable design parameters.

In big cities, the metro lines usually face great pressure caused by huge passengers demand, especially during peak hours. When disruptions occur, passengers accumulate quickly at stations. It is of great importance for dispatchers to take passenger flow control into consideration for the traffic management to ensure passengers' safety and to maintain their satisfaction. This paper proposes an integrated disruption management model, which incorporates train rescheduling and passenger flow control. In this model, the train services can be short-turned, cancelled and rerouted, while the number of passengers entering a station is managed by controlling the station gates with consideration of the capacities of platforms and trains. Moreover, the number of passengers arriving at a station is calculated according to the origin-destination matrices. The objectives are to recover the train operation to the original timetable as soon as possible and to minimize the waiting time of passengers outside the stations. With the interaction between train services, passengers and station gates, an iterative metaheuristic approach is proposed to solve the integrated disruption management problem. Based on the data of a Beijing metro line, numerical experiments are conducted to test the proposed algorithm. The results demonstrate the importance of integrated disruption management and the effectiveness of our solution method.

Highly utilized railway networks require regular infrastructure maintenance. Different track sections often need to be closed for entire days to carry out engineering works, which makes the regular timetables no longer feasible and thus adjusted railway services and temporary alternative services need to be planned. We introduce the Multimodal Alternative Services for Possessions (MASP) problem to support the planning of alternative services, from the passenger and transport operator points of view, including an adjusted train timetable, bus-bridging services and extra train services. The MASP problem is formulated based on the Service Network Design Problem and the Vehicle Routing Problem. To solve it efficiently, we develop a solution framework that incorporates heuristics based on the column and row generation with mixed-integer linear programming. The developed framework provides the optimized alternative service routes, schedules and passenger flows routing. We demonstrated the performance of the MASP solution framework on the real-life Dutch railway network. The results show that the MASP framework is capable of efficiently generating alternative services to route passenger flows affected by possessions with a very limited increase in the total passenger costs compared to a scenario with no link closures. High computational efficiency is observed even for highly disrupted networks., Transportation Research Part B: Methodological, 154, ISSN:0191-2615, ISSN:1879-2367

This paper tackles railway timetabling with infrastructure work possessions. It introduces the integrated Passenger and Freight Train Timetable Adjustment Problem (PF-TTAP) which handles both passenger as well as freight trains. To deal with possessions, passenger trains are typically retimed, reordered or partially cancelled, while for freight trains it is important to reach their destination, possibly using an alternative path. Alternative paths for freight trains are generated using the k-shortest path algorithm. To solve the PFTTAP, a mixed integer linear programming (MILP) problem is developed to simultaneously retime, reroute and cancel trains in the network. The model aims at minimizing deviations from the original timetable and in particular selecting alternative freight paths with the least turning activities and noncommercial stops. The model was tested on the Dutch national railway network. The PF-TTAP model successfully created an alternative hour pattern satisfying all the railway stakeholders.

Due to increasing railway use, the capacity at railway yards and maintenance locations is becoming limiting to accommodate existing rolling stock. To reduce capacity issues at maintenance locations during nighttime, railway undertakings consider performing more daytime maintenance, but the choice at which locations personnel needs to be stationed for daytime maintenance is not straightforward. Among other things, it depends on the planned rolling stock circulation and the maintenance activities that need to be performed. This paper presents the Maintenance Location Choice Problem (MLCP) and provides a Mixed Integer Linear Programming model for this problem. The model demonstrates that for a representative rolling stock circulation from the Dutch railways a substantial amount of maintenance activities can be performed during daytime. Also, it is shown that the location choice delivered by the model is robust under various time horizons and rolling stock circulations. Moreover, the running time for optimizing the model is considered acceptable for planning purposes., 16 pages, 5 figures

Increasing supply in railway networks comes at the cost of an increased need for infrastructure maintenance. This also means adjusting the timetable due to long maintenance or constructions’ possessions. In this article, we introduce the Train Timetable Adjustment Problem (TTAP), which for given station and open-track possessions, finds an alternative timetable that minimizes the deviation from the original timetable. We propose a mixed integer linear programming (MILP) model for solving TTAP, and apply retiming, reordering, short-turning and cancellation to generate alternative timetables. The model represents an extended periodic event scheduling problem (PESP) formulation and introduces new constraints for cancelling and retiming train lines, while short-turning is being applied in a preprocessing step. In order to solve larger and more complex instances, we use a row generation approach to add station capacity constraints. The model solves real-life instances with multiple possessions for a large area of the Dutch railway network in reasonable time, and could be up-scaled to the complete Dutch network. Additionally, it may be applicable for disruption management after some modifications. Operators and infrastructure managers could use it to automatically generate optimal alternative timetables on the macroscopic level in case of maintenance or construction works and thus, coordinate traffic for the complete network.

The performance and behaviour of critical infrastructure in case of disruptions is an important topic and we are still lacking of insights. Due to disruptions, infrastructure becomes unavailable and may force the trains and passengers to adapt. In this paper, we introduce a problem of railway network vulnerability from the perspective of passenger flows and train operations. We propose a new Railway Network Vulnerability Model (RNVM) to assess the vulnerability of the system by finding the critical combination of links, which cause the most adverse consequences to passengers and trains. To solve this challenging problem, we present a RNVM framework, which combines two heuristics based on column and row generation with mixed integer linear programming, to efficiently model alternative passenger flows and infrastructure constraints. The developed framework provides the critical combination of links, the corresponding passenger flows, train routes and timetables. We demonstrate the performance of the RNVM framework on the real-world instance of a part of the Dutch railway network. The results show that the RNVM framework can efficiently reassign passenger flows and reroute trains during disruptions. The results also reveal that the critical links are highly demand dependent rather than a static feature of the networks topology. Finally, the computation times remain small when increasing the number of disrupted links as well as the size of the passenger demand, which allows fast and efficient network vulnerability assessment.

Urban railway transit systems in big cities operate at high capacity and represent the main arteries of city transport networks. In current operations, infrastructure failures occur occasionally causing severe disruptions. In this research, we propose a novel integrated disruption management methodology for automatically rescheduling trains and controlling passenger flows for a given disruption. Our framework incorporates a train traffic management model together with a model for adjusting flows of passengers and aims to minimize the total delay of passengers, the number of denied passengers, adjustments to train services, and recover time. On the train side, we short-turn, cancel and reroute train services. On the passenger side, we reflow passengers according to a disrupted timetable and control station gates. We test our integrated disruption management approach on real-life cases and discover dependencies between delayed/denied passengers and traffic management. Our goal is developing practical solutions to this critical transportation problem that will lead to establishing advanced decision support systems to assist metro dispatchers.

Routing trains through busy railway station layouts is an important part of the timetabling process. For each train, a feasible route has to be determined to provide reliable operations, given the arrival and departure times at stations. In this paper, we propose a model for stable and robust train routing with the goal to minimize capacity occupation and maximize robustness. We define a multi-objective optimization problem and provide the heuristic RouteCare based on a max-plus automata model and a delay propagation model. We consider microscopic infrastructure to guarantee practical feasibility. The performance of the proposed algorithm is demonstrated on real-life instances of the Dutch railway network. The generated solutions outperformed the variants of RouteCare that independently maximize stability or robustness by 10.4% and 9.5%, respectively. In addition, RouteCare showed that even for the same number of resources used, a more robust route plan can be found that uses the station capacity more efficiently.

This article tackles the real-world planning problem of railway operations. Improving the timetable planning process will result in more reliable product plans and a higher quality of service for passengers and freight operators. We focus on the microscopic models for computing accurate track blocking times for guaranteeing feasibility and stability of railway timetables. A conflict detection and resolution model manages feasibility by identifying conflicts and computing minimum headway times that provide conflict-free services. The timetable compression method is used for computing capacity consumption and verifying the stability according to the UIC Capacity Code 406. Furthermore, the microscopic models have been incorporated in a multilevel timetabling framework for completely automated generation of timetables. The approach is demonstrated in a real-world case study from the Dutch railway network. Practitioners can use these microscopic timetabling models as an important component in the timetabling process to improve the general quality of timetables.

This paper proposes a new multi-objective periodic railway timetabling (MOPRT) problem with four objectives to be minimized: train journey time, timetable regularity deviation, timetable vulnerability and the number of overtakings. The aim is to find an efficient, regular and robust timetable that utilizes the infrastructure capacity as good as possible. Based on the Periodic Event Scheduling Problem, we formulate the MOPRT problem as a Mixed Integer Linear Program (MILP). The e-constraint method is applied to deal with the multi-objective property, and algorithms are designed to efficiently create the Pareto frontier. By solving the problem for different values of e, the four-dimensional Pareto frontier is explored to uncover the trade-offs among the four objectives. The optimal solution is obtained from the Pareto-optimal set by using standardized Euclidean distance, while capacity utilization is used as an additional indicator to chose between close solutions. Computational experiments are performed on a theoretical instance and a real instance in one direction of a Dutch railway corridor, demonstrating the efficiency of the model and approach.

With the increasing demand for railway transportation infrastructure managers need improved automatic timetabling tools that provide feasible timetables with enhanced performance in short computation times. This paper proposes a hierarchical framework for timetable design which combines a microscopic and a macroscopic model of the network. The framework performs an iterative adjustment of train running and minimum headway times until a feasible and stable timetable has been generated at the microscopic level. The macroscopic model optimizes a trade-off between minimal travel times and maximal robustness using an Integer Linear Programming formulation which includes a measure for delay recovery computed by an integrated delay propagation model in a Monte Carlo setting. The application to an area of the Dutch railway network shows the ability of the approach to automatically compute a feasible, stable and robust timetable. Practitioners can use this approach both for effective timetabling and post-evaluation of existing timetables.

This book promotes the use of mathematical optimization and operations research methods in rail transportation. The editors assembled thirteen contributions from leading scholars to present a unified voice, standardize terminology, and assess the state-of-the-art. There are three main clusters of articles, corresponding to the classical stages of the planning process: strategic, tactical, and operational. These three clusters are further subdivided into five parts which correspond to the main phases of the railway network planning process: network assessment, capacity planning, timetabling, resource planning, and operational planning. Individual chapters cover: Simulation Capacity Assessment Network Design Train Routing Robust Timetabling Event Scheduling Track Allocation Blocking Shunting Rolling Stock Crew Scheduling Dispatching Delay Propagation

Capacity assessment is essential for densely utilized railway networks. To guarantee stable operations, it is necessary to evaluate the capacity occupation and determine possible infrastructure bottlenecks. This requires accurate microscopic models that incorporate detailed infrastructure characteristics, signalling and interlocking logic, train characteristics, and driver behaviour. This chapter presents capacity assessment models based on a novel algebraic approach that builds on accurate running and blocking time computations. The capacity assessment should be undertaken on corridors, station areas, and networks, and as such, support a better understanding of the existing timetable constraints and possible infrastructure investments.

During infrastructure maintenance possessions, commonly not all trains can operate, and the original timetable may have to be adjusted accordingly. To deliver the best service to passengers, operators have to coordinate adjustment measures dealing with multiple possessions at the network level. In this paper, we consider the Train Timetable Adjustment Problem (TTAP) and present a mixed integer programming (MIP) model for solving TTAP. In order to solve large-scale problems, such as national Dutch network, and design high-quality solutions, modelling extensions are needed. First, we apply three network aggregation techniques to decrease the problem size, which enables to solve instances on the complete Dutch network within satisfactory computation times. Second, we model turnaround activities for short-turned trains and test different strategies. Third, we introduce flexible short-turning possibilities to the MIP to possibly reduce the number of cancelled train lines. We test the proposed model on real-life cases of Netherlands Railways (NS) and assess the effect on computation times and solution quality. Also, we identify differences with current planners’ practice. Planners were positive about the quality of generated solutions and the computation speed. The current model can also be used to decide on combinations of time windows for possessions.

The performance of railway operations depends highly on the quality of the railway timetable. In particular for dense railway networks it can be challenging to obtain a stable robust conflict-free and energy-efficient timetable with acceptable infrastructure occupation and short journey times. This paper presents a performance-based railway timetabling framework integrating timetable construction and evaluation on three levels: microscopic, macroscopic, and a corridor fine-tuning level, where each performance indicator is optimized or evaluated at the appropriate level. A modular implementation of the three-level framework is presented and demonstrated on a case study on the Dutch railway network illustrating the feasibility of this approach to achieve the highest timetabling design level.

Predictions of railway traffic are needed by planners and dispatchers for the design of robust timetables and real-time traffic management of perturbed conditions. These tasks can be effectively performed only when using train running time models which reliably describe actual speed profiles. To this purpose calibration of model parameters against field data is a necessity. In this paper a simulation-based optimization approach is introduced to calibrate the parameters of the train dynamics equations against field data collected at the level of track sections. A genetic algorithm is used to minimize the error between simulated and observed speed profiles. Furthermore, a procedure for the estimation of train lengths has been developed. This method has been applied to trains with different rolling stock running on the Rotterdam-Delft corridor in the Netherlands. The model parameters were calibrated for a significant number of trains of different compositions. We also derived probability distributions for each parameter which can be usefully employed for simulations. The results show that the train length estimation model obtained good computation accuracy. The effectiveness of the calibration method in giving a reliable estimation of the real train path trajectories is shown. It has been observed that some of the parameters of tractive effort and resistance do not affect the train behaviour significantly. Also, the braking rate is significantly smoother than the default value used by the railway undertaking while calibrated resistance parameters tend to have lower mean than defaults. Finally, the computational efficiency of the approach is suitable for real-time applications.

In the last decades advanced simulation models have been more and more used by railway timetable designers and dispatchers to support both the off-line planning and the real-time management of traffic. Fundamental requirements for these models are the accuracy and reliability of describing real train dynamics. To this aim it is necessary to calibrate train running time models against real data collected from the field. In this paper a simulation-based calibration approach is proposed to fine-tune the parameters of the different phases of train motion (acceleration, deceleration, coasting and cruising) against track occupation data. A customized genetic algorithm is developed to minimize the error between observed and simulated data. The model has been calibrated for different classes of trains against a significant number of observed trains running on the Dutch corridor Rotterdam-Delft. A probability distribution is then estimated for each parameter to understand how driver behavior affects their variations and to identify the most probable value for each of the parameters. The results show the ability of the proposed model to calibrate train parameters robustly and reproduce observed train trajectories accurately. It is observed that the coasting phase is not applied frequently on the case corridor. Also, drivers adopt a braking rate that is significantly smoother than the default value used by the railway undertaking.