Railway operations are subject to deviations from the planned schedule, i.e., delays. In those situations, high-quality traffic control actions are needed to reduce the delays. Existing studies mainly used prescriptive techniques (e.g., mathematical programming, heuristics) to identify the best control action. These methods have limitations in the firm reliance on deterministic parameters prescriptively or normatively determined beforehand, and little understandability by the practitioners. These drawbacks hinder their acceptance in practice. This study exploits instead past realization data to provide decision support for traffic control. The realized data describe the traffic control actions taken by human controllers, and their effects; those latter are more complex than a linear sum of predetermined parameters. We use decision graphs to identify which traffic control action leads to the best solution, in terms of reduction of delays, based on the past performance of the same action in similar conditions. We are also able to explain the reasons and the factors that lead to each suggested action. We focus on the relevant case of merging stations, where multiple lines merge as one line, deciding the relative order between two consecutive trains. The method determines the stochastic effects of the two possible decisions at merge points, which allows for choosing the best one. Compared within the framework of realized data, the action suggested is the best out of a series of benchmarks, including simple rules and optimization, improving (reducing delays) approximately 11.7% on the common benchmarks. The variables with the highest impact on the utility are the length of the planned dwell time and the planned presence of an overtaking. The variables influencing the utility most are the actual delays of trains, the train type, and the order actually implemented.

The railway systems are affected by unexpected disturbances on a daily basis causing delays to trains and passengers. Real-time traffic management is necessary and is currently handled by human traffic controllers who mainly focus on minimizing train delays. In the past two decades, extensive research has been done to improve railway traffic management by shifting the focus to passengers (generally called delay management) using optimization or heuristics. The existing optimization-based models are difficult to solve efficiently. The existing heuristics perform well in terms of computational efficiency but are based on simplified passenger behaviours. In this paper, we propose an efficient method including complex passenger behaviours. That is a Reinforcement Learning (RL) framework for delay management (at a network-level for mainline railways) aiming to minimize passenger destination delays. In our method, passengers re-plan their travels when actually miss their transfers (i.e. reactive behaviour) or when they are aware of better path choices than their current planned ones (i.e. proactive behaviour), whichever happens first. The re-plan behaviour is allowed to happen multiple times during a single journey of a passenger as long as it is beneficial. We tested the proposed RL approach on a real-world railway network and compared it to three benchmarks: the first-in-first-out (FIFO) dispatching rule that is widely adopted in practice, and the train-centric and passenger-centric optimization models (TcOM and PcOM) on timetable rescheduling. Results show the ability of our RL approach to obtain better rescheduling solutions (in terms of total passenger delays) than the FIFO and TcOM, and better computational efficiency (43 seconds on average after training) than the PcOM (4572 seconds on average). With sufficient training, 74% of the trained RL agents can solve all other new delay scenarios designed in our case study, implying good generalization performance of the proposed method.

Employing regenerative braking in trains contributes to reducing the amount of energy used, especially when applied to commuter trains and to those used on very dense suburban networks. This paper presents a method to fine-tune the periodic timetable to improve the utilization of regenerative energy and to shave power peaks while maintaining the structure and robustness of the original timetable. First, a mixed-integer linear programming model based on the periodic event scheduling framework is proposed. A set of feasible timetables is determined and optimized with the aim of increasing synchronized acceleration and braking events at the same station, and maintaining the timetable robustness at the specified level. Next, a local search algorithm is developed to optimize the timetable such that the power peak value is minimized. The max-plus system model is adopted to estimate the delay propagation. Monte Carlo simulation is used to evaluate the utilization of regenerative energy and power peaks in random delayed circumstances. The proposed method was adopted to fine-tune the 2019 timetable for a sub-network of the Dutch railway. In the case of on- time scenarios, the optimized timetable increases the regenerative energy usage by almost 290% and decreases the 15-minute power peaks by 8.5%. In the case of delay scenarios, the optimized timetable outperforms the original timetable in terms of using regenerative energy and shaving power peaks.

Optimizing the railway timetable to increase synchronous accelerating and braking processes can lead to an improvement in the usage of regenerative energy. However, such a synchronized timetable might result in little or unsuitable transfer connections for the passengers. This paper focuses on the optimization of railway periodic timetables, to increase usage of regenerative energy while ensuring passenger satisfaction. We work by extending the traditional Periodic Event Scheduling Problem (PESP) formulation, to address the problem of synchronization of acceleration and braking phases, (and re-used energy) and including passenger-related events (and their satisfaction). Three objectives are identified, in a resulting Mixed Integer Linear Programming (MILP) model: maximizing the overlapping times of accelerating and braking trains to achieve increased usage of regenerative energy, minimizing the total passengers’ generalized travel times (global passenger dissatisfaction), and minimizing the maximum increase in individual's generalized travel time (local passenger dissatisfaction). A multi-step approach solves the trade-offs among three conflicting objectives. Results on a realistic case study show that the proposed approach can find optimized timetables, which compared to the currently-in-use timetable, can increase the usage of regenerative energy by over 1.5 times, save the average generalized travel time per passenger by 2 min, with only a minor increase on specific individual generalized travel time (up to 4 min). A detailed results analysis imply that to achieve a higher usage of regenerative energy, it is required to have a higher tolerance for the maximum increase in individual generalized travel time, while this is not necessary for the overall passenger generalized travel time, which can even be reduced when the maximum increase in individual generalized travel time becomes larger.

Wheel impact load detectors are widespread railway systems used for measuring the wheel–rail contact force. They usually measure the rail strain and convert it to force in order to detect high impact forces and corresponding detrimental wheels. The measured strain signal can also be used to identify the defect type and its severity. The strain sensors have a limited effective zone that leads to partial observation from the wheels. Therefore, wheel impact load detectors exploit multiple sensors to collect samples from different portions of the wheels. The discrete measurement by multiple sensors provides the magnitude of the force; however, it does not provide the much richer variation pattern of the contact force signal. Therefore, this paper proposes a fusion method to associate the collected samples to their positions over the wheel circumferential coordinate. This process reconstructs an informative signal from the discrete samples collected by multiple sensors. To validate the proposed method, the multiple sensors have been simulated by an ad hoc multibody dynamic software (VI-Rail), and the outputs have been fed to the fusion model. The reconstructed signal represents the contact force and consequently the wheel defect. The obtained results demonstrate considerable similarity between the contact force and the reconstructed defect signal that can be used for further defect identification.

As ports are increasingly confronted with congestion (on the road as well as on rail and on the water), accessibility has become a key port performance indicator. Overall accessibility is related to the ease of realizing a certain transport activity. Policies aimed at guaranteeing accessibility of ports are increasingly focused on management issues (so-called orgware and software), instead of on the building of new infrastructure (hardware). The aim of this chapter is to provide an accessible insight in different perspectives on accessibility and ways in which accessibility can be improved. Hereby, perspectives and measures are motivated with examples from the ports in the Hamburg-Le Havre range.

We introduce a distributed optimization method for improving the computational efficiency of real-time traffic management approaches for large-scale railway networks. We first decompose the whole network into a pre-defined number of regions by using an integer linear optimization approach. For each resulting region, a mixed-integer linear programming approach is used to address the traffic management problem, with micro details of the network and incorporated with the train control problem. For handling the interactions among regions, an alternating direction method of multipliers (ADMM) algorithm based solution approach is developed to solve the subproblem of each region through coordination with the other regions in an iterative manner. A priority rule based solution approach is proposed to generate feasible suboptimal solutions, in case of lack of convergence. Numerical experiments are conducted based on the Dutch railway network to show the performance of the proposed solution approaches, in terms of effectiveness and efficiency. We also show the trade-off between solution quality and computational efficiency.

We study the integration of real-time traffic management and train control by using mixed-integer nonlinear programming (MINLP) and mixed-integer linear programming (MILP) approaches. In Part 1 of the paper (Luan et al., 2018), three integrated optimization problems, namely the P_NLP problem (NLP: nonlinear programming), the P_PWA problem (PWA: piecewise affine), and the P_TSPO problem (TSPO: train speed profile option), have been developed for real-time traffic management that inherently include train control. A two-level approach and a custom-designed two-step approach have been proposed to solve these optimization problems. In Part 2 of the paper, aiming at energy-efficient train operation, we extend the three proposed optimization problems by introducing energy-related formulations. We first evaluate the energy consumption of a train motion. A set of nonlinear constraints is first proposed to calculate the energy consumption, which is further reformulated as a set of linear constraints for the P_TSPO problem and approximated by using a piecewise constant function for the P_NLP and P_PWA problems. Moreover, we consider the option of regenerative braking and present linear formulations to calculate the utilization of the regenerative energy obtained through braking trains. We focus on two objectives, i.e., delay recovery and energy efficiency, through using a weighted-sum formulation and an ε-constraint formulation. With these energy-related extensions, the nature of the three optimization problems remains same to Part 1. In numerical experiments conducted based on the Dutch test case, we consider the P_NLP approach and the P_TSPO approach only and compare their performance with the inclusion of the energy-related aspects; the P_PWA approach is neglected due to its bad performance, as evaluated in Part 1. According to the experimental results, the P_TSPO approach still yields a better performance within the required computation time. The trade-off between train delay and energy consumption is investigated. The results show the possibility of reducing train delay and saving energy at the same time through managing train speed, by up to 4.0% and 5.6% respectively. In our case study, applying regenerative braking leads to a 22.9% reduction of the total energy consumption.

We study the integration of real-time traffic management and train control by using mixed-integer nonlinear programming (MINLP) and mixed-integer linear programming (MILP) approaches. Three innovative integrated optimization approaches for real-time traffic management that inherently include train control are developed to deliver both a train dispatching solution (including train routes, orders, departure and arrival times at passing stations) and a train control solution (i.e., train speed trajectories). Train speed is considered variable, and the blocking time of a train on a block section dynamically depends on its real speed. To formulate the integrated problem, we first propose an MINLP problem (P_NLP), which is solved by a two-level approach. This MINLP problem is then reformulated by approximating the nonlinear terms with piecewise affine functions, resulting in an MILP problem (P_PWA). Moreover, we consider a preprocessing method to generate the possible speed profile options for each train on each block section, one of which is further selected by a proposed MILP problem (P_TSPO) with respect to safety, capacity, and speed consistency constraints. This problem is solved by means of a custom-designed two-step approach, in order to speed up the solving procedure. Numerical experiments are conducted using data from the Dutch railway network to comparatively evaluate the effectiveness and efficiency of the three proposed approaches with heterogeneous traffic. According to the experimental results, the MILP approach (P_TSPO) yields the best overall performance within the required computation time. The experimental results demonstrate the benefits of the integration, i.e., train delays can be reduced by managing train speed.

In the Netherlands, the main port Rotterdam, is confronted with a steady growth in total volume, mostly resulting in a direct increase of the road transport; the resulting road congestion led to various initiatives increasing the share of transport over water and rail. Overall, this intermodal situation is vulnerable to many sources of uncertainty, ranging from relatively common, low impact events, to relatively rare, high impact events.

Transport demand for containers has been increasing for decades, which places pressure on road transport. As a result, rail transport is stimulated to provide better intermodal freight transport services. This paper investigates mathematical models for the planning of container movements in a port area, integrating the inter-terminal transport of containers (ITT, within the port area) with the rail freight formation and transport process (towards the hinterland). An integer linear programming model is used to formulate the container transport across operations at container terminals, the network interconnecting them, railway yards and the railway networks towards the hinterland. A tabu search algorithm is proposed to solve the problem. The practical applicability of the algorithm is tested in a realistic infrastructure case and different demand scenarios. Our results show the degree by which internal (ITT) and external (hinterland) transport processes interact, and the potential for improvement of overall operations when the integrated optimization proposed is used. Instead, if the planning of containers in the ITT system is optimized as a stand-alone problem, the railway terminals may suffer from longer delay times or additional train cancellations. When planning the transport of 4060 TEU containers within one day, the benefits of the ITT planning without considering railway operations account for 17% ITT cost reduction but 93% railway operational cost growth, while the benefits of integrating ITT and railway account for a reduction of 20% in ITT cost and 44% in railway operational costs.

In railway operations, when a disruption occurs, train dispatchers aim to adjust the affected schedule and to minimize negative consequences during and after the disruption. As one of the most important components of the railway system, railway signals are used to guarantee the safety of train services. We study the train dispatching problem with consideration of railway signaling commands under the fixed-block signaling system. In such a system, signaling commands dynamically depend on the movement of the preceding trains in the network. We clarify the impact of the signaling commands on train schedules, which has so far been neglected in the literature on railway train dispatching, and we propose an innovative set of signaling constraints to describe the impact. The determination of the signal indicators is presented using “if-then” constraints, which are further transformed into linear inequalities by applying two transformation properties. Activation of the train speed limits that result from the signaling commands is the core purpose of the signaling constraints, and this is implemented by using the signal indicators. Moreover, we formulate the Greenwave (GW) policy, which requires that trains always proceed under green signals, and we further investigate the impact of the GW policy on delays. In numerical experiments, the proposed signaling constraints are employed within a time-instant optimization problem, which is a mixed-integer linear programming (MILP) problem. The experimental results demonstrate the effectiveness of the proposed signaling constraints and show the impact of the signaling commands and GW policy on the train dispatching solution.

Research focused on the real-time rescheduling of high-speed railway traffic with a quasi-moving blocking system and transition process affected by the entrance delays and disruptions determining speed limitation. A mixed-integer linear program model related to a job shop model of operations is formulated to reduce the final delay (tardiness) of trains, where three objective functions combine different manners related to traffic control and speed management. The dynamic interaction between train speed and distance headway is considered in the model. Through experiments on a real-world high-speed line in China, the solution quality of the model is assessed by the delay distribution of trains or the smooth degree of train speed profile. The model manages to optimize traffic in the transition from a disordered condition (when disruptions appear) to a normal condition (after disruptions) for real-time operations. In conclusion, there are two and three transition phases for the cases without and with entrance delays, respectively, seen by analyzing the deviation between the rescheduled and planned timetables.

Wheel Impact Load Detectors are common devices that measure the rail response made by the wheel-rail contact to estimate the condition of the in-service wheels. The data collected by the multiple sensors can be fused to reconstruct a wheel-rail contact pattern over the circumferential coordinate that provides some description of the wheel condition. Moving of a defective wheel with different velocities and axle loads influence the wheel-rail interaction and the pattern reconstructed. As a result, there is a range of variation in the pattern reconstructed for each defect. Therefore, this paper aims to tackle this challenge and to classify the railway wheel defects using pattern recognition tools. Due to the lack of real data, ADAMS/Rail is used to model the wheel-rail contact and to simulate the data collected by the sensors. Then, based on the fusion algorithm, the condition state signals are reconstructed for different wheel defects with different velocities, and axle loads. Then a dataset based on these patterns is generated that is used for training, and testing the classifiers. In this paper, the magnitude of the signal is directly used as the features. The results of the classification show that the wheel defects including a minor defect can be correctly classified with zero error.

This paper addresses the real-time problem of coordinating aircraft ground and air operations in an airport area. At a congested airport, airborne decisions are related to take-off and landing operations, while ground (taxiway) decisions consist of scheduling aircraft movements between the gates and the runways. Since the runways are the initial/terminal points of both decisions, coordinated actions have a great potential to improve the overall performance. However, in the traffic control practice the different decisions are taken by different controllers, at least in large airports. Weak coordination may result in long queues at the runways, with increasing aircraft delays and energy consumption. This paper investigates models, methods and policies for improving the coordination between taxiway scheduling and airborne scheduling. The performance of a solution is measured in terms of delay and travel time, the latter being related to the energy consumption of an aircraft. A microscopic mathematical formulation is adopted to achieve reliable solutions. Exact and heuristic methods have been analysed in combination with the different policies, based on practical-size instances from Amsterdam Schiphol airport, in the Netherlands. Computational experience shows that good quality solutions can be found within limited time, compatible with real-time operations.

Though timetabling can account for some possible delays, in practice, external events still regularly lead to delays. Once trains are deviating from their schedule, conflicts can occur. A conflict implies that (at least) two trains require the same part of the infrastructure at the same time. Conflicts need to be resolved quickly in a way that disturbs the system as little as possible. Therefore, the impact on the whole network should be taken into account when solving conflicts. This paper discusses a heuristic conflict prevention technique capable of solving multiple conflicts together by reordering, retiming and locally rerouting trains. Based on a close-to-practice simulation tool where a simplified prediction horizon up to 10 minutes is considered, this technique is compared to FCFS. Results show significant improvements when comparing to FCFS.

Train dispatching is vital for the punctuality of train services, which is critical for a train operating company (TOC) to maintain its competitiveness. Due to the introduction of competition in the railway transport market, the issue of discrimination is attracting more and more attention. This paper focuses on delivering non-discriminatory train dispatching solutions while multiple TOCs are competing in a rail transport market, and investigating impacting factors of the inequity of train dispatching solutions. A mixed integer linear programming (MILP) model is first proposed, in which the inequity of competitors (i.e., trains and TOCs) is formalized by a set of constraints. In order to provide a more flexible framework, a model is further reformulated where the inequity of competitors is formalized as the maximum individual deviation of competitors’ delay cost from average delay cost in the objective function. Complex infrastructure capacity constraints are considered and modelled through a big M-based approach. The proposed models are solved by a standard MILP solver. A set of comprehensive experiments is conducted on a real-world dataset adapted from the Dutch railway network to test the efficiency, effectiveness, and applicability of the proposed models, as well as determine the trade-off between train delays and delay equity.

Delays and disruptions reduce the reliability and stability of the rail operations. Railway traffic rescheduling includes ways to manage the operations during and after the occurrences of such disturbances. In this study, we consider the simultaneous presence of large disruptions (temporary full or partial blockage of tracks) as well as stochastic variation of operations, as a source of disturbance. The occurrence time of blockage and its recovery time are given. We designed a simulation-based optimization model that incorporates dynamic dispatch priority rules with the objective of minimizing the total delay time of trains. We moreover design a variable neighborhood search meta-heuristic scheme for handling traffic under the limited capacity close to the blockage. The new plan includes a set of new departure times; dwell times, train running times. We evaluate the proposed model on a set of disruption scenarios covering a large part of the Iranian rail network. The result indicates that the developed simulation-based optimization approach has substantial advantages in producing practical solution quickly, when compared to commercial optimization software. In addition, the solutions have a lower average and smaller standard deviation than currently accepted solutions, determined by human dispatcher or by standard software packages.

We address the problem of simultaneously scheduling trains and planning preventive maintenance time slots (PMTSs) on a general railway network. Based on network cumulative flow variables, a novel integrated mixed-integer linear programming (MILP) model is proposed to simultaneously optimize train routes, orders and passing times at each station, as well as work-time of preventive maintenance tasks (PMTSs). In order to provide an easy decomposition mechanism, the limited capacity of complex tracks is modelled as side constraints and a PMTS is modelled as a virtual train. A Lagrangian relaxation solution framework is proposed, in which the difficult track capacity constraints are relaxed, to decompose the original complex integrated train scheduling and PMTSs planning problem into a sequence of single train-based sub-problems. For each sub-problem, a standard label correcting algorithm is employed for finding the time-dependent least cost path on a time-space network. The resulting dual solutions can be transformed to feasible solutions through priority rules. Numerical experiments are conducted on a small artificial network and a real-world network adapted from a Chinese railway network, to evaluate the effectiveness and computational efficiency of the integrated optimization model and the proposed Lagrangian relaxation solution framework. The benefits of simultaneously scheduling trains and planning PMTSs are demonstrated, compared with a commonly-used sequential scheduling method.