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.

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.

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.

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.

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.

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.

Chinese high-speed railways faced a fast development in recent years. Their performances are still confronted with disruptions unavoidably, which impact on the reliability of the traffic and passenger satisfaction. This paper presents a rescheduling model which is able to solve the critical problem of effective disruption management (namely, fast and dynamic train speed adaptation, supervision of braking and changing train sequence due to incidents, warnings or alarms), and consider in detail the signalling and safety systems based on a quasi-moving block system with variable headways. We integrate the modelling of efficient traffic management measures and the supervision of speed, braking and headway in one general job-shop model. We use a commercial solver with a custom-designed two-step method to speed up the procedure in order to solve instances from real-world high-speed networks in China quickly. Overall, the approach guarantees the resolution of the traffic control and speed management within few minutes of computation time. The output demonstrates that the proposed approach can achieve a reduction of train delays by 70% compared to the solution determined by keeping the order of the original timetable, and get the optimality for more than 90% of instances with a realistic case.

Optimization models for railway traffic rescheduling tackle the problem of determining, in real-time, control actions to reducing the effect of disturbances in railway systems. In this field, mainly two research streams can be identified. On the one hand, train scheduling models are designed to include all conditions relevant to feasible and efficient operation of rail services, from the viewpoint of operations managers. On the other hand, delay management models focus on the impact of rescheduling decisions on the quality of service perceived by the passengers. Models in the first stream are mainly microscopic, while models in the second stream are mainly macroscopic. This paper aims at merging these two streams of research by developing microscopic passenger-centric models, solution algorithms and lower bounds. Several fast heuristic methods are proposed, based on alternative decompositions of the model. A lower bound is proposed, consisting of the resolution of a set of min-cost flow problems with activation constraints. Computational experiments, based on multiple test cases of the real-world Dutch railway network, show that good quality solutions and lower bounds can be found within a limited computation time.