Performance aspects such as travel time, punctuality and robustness are conflicting goals of utmost importance for railway transports. To successfully plan railway traffic, it is therefore important to strike a balance between planned travel times and expected delays. In railway operations research, a lot of attention has been given to construct models and methods to generate robust timetables—that is, timetables with the potential to withstand design errors, incorrect data, and minor everyday disturbances. Despite this, the current state-of-practice in railway planning is to construct timetables manually, possibly with support of microsimulation for robustness evaluation. This paper aims to narrow the gap between the state-of-the-art optimization-based research approaches, and the current state-of-practice to construct timetables by combining simulation and optimization. The paper proposes a combined simulation-optimization approach for double-track lines, which generalizes previous work to allow full flexibility in the order of trains by including a new and more generic model to predict delays. By utilizing delay data from simulation, the approach can make socio-economically optimal modifications of a given timetable by minimizing predicted disutility—the weighted sum of scheduled travel time and total predicted delay.  In a large simulation experiment on the heavily congested Swedish Western Main Line, it is demonstrated that compared with a real-life, manually constructed, timetable large reductions of delays as well as improvements in punctuality could be obtained to a small cost of marginally longer travel times. The cost of scheduled in-vehicle travel time and mean delay was reduced by 5% on average, representing a large improvement for a highly utilized railway line. Furthermore, a separate scaling experiment indicate that the approach can be suitable also for larger problems. 

Punctuality is commonly recognized as one of the most important quality indicators for passenger traffic. Despite this, surprisingly few methods for explicitly maximizing punctuality by optimizing the timetable exists in the literature. We study how late-stage adjustments during the capacity allocation can improve punctuality of the traffic. In this paper, we therefore extend a combined simulation-optimization method so it can be used to explicitly maximize the predicted punctuality of a given nonperiodic timetable on a double-track line. The method is evaluated in two microsimulation experiments in the southbound direction of the Swedish Western Main Line using Railsys. We compare the method in simulation with our previous method for minimizing total disutility, two methods from the scientific literature (light robustness, and robustness in critical points) and two naïve strategies. The methods’ effectiveness is assessed in a detailed statistical analysis considering end-station punctuality, total punctuality, and the robustness measure total disutility. Only light robustness results in timetables that in simulation performs better or equally well as the given timetable (based on the national timetable) with respect to all performance measures and evaluated scenarios. The method for maximizing punctuality performs best with respect to total punctuality.

Railway timetables have an important role in efficient and punctual railway operations. In particular, the robustness of the timetable has a direct impact on the traffic's punctuality. To evaluate the robustness of a timetable, simulation is commonly used. A simulation study may indicate that some trains are too sensitive against minor delays, which may lead to that they fall out of their planned channel of operations (defined by their surrounding trains). We define this as robustness vulnerabilities of the timetable. The work explores reinforcement learning (RL) as a method to resolve timetable robustness vulnerabilities. We formulate a RL-based model for the robust railway timetabling problem and will explore different RL algorithms and compare with timetables generated using optimization-based methods from our previous work [1, 2]. The models are evaluated using microscopic RailSys simulation for the traffic in the westbound direction of the Swedish Western Main Line. The results are expected to provide better support for robust railway timetabling in practice.

The execution of scheduled railway operations is characterized by continuous monitoring and systematic adjustment of the existing schedule to the occurrence of stochastic events. The adjustment of the schedule can be referred to as the “Conflict Detection & Conflict Resolution” (CDCR) process. Caused by propagating conflicts between plan adjustments and the initially planned schedule, CDCR is a highly complex process. Due to complexity, a series of decision-support tools mostly relying on heuristic methods have been developed to assist dispatchers in real-time. This article aims to identify strategic enhancement potentials for improving existing schedule adjustment approaches by integrating different methods (e.g., machine learning methods). A decomposition method is utilized to identify the processes during schedule adjustment that could benefit from applying hybrid methodologies, resulting in a much more efficient and effective search space exploration. At the outset the processes of generating a set of conflict resolution alternatives and selecting the best-fitting alternative to the actual operating situation have been early identified as potential processes that would benefit from incorporating hybrid methods (e.g., machine learning and heuristic methods). This study utilizes an actual decision-support tool applied within a real scenario to derive concrete evidence regarding the extent to which hybrid methods can be integrated and used to solve complex problems within the real-time adjustment of railway schedules by means of their actual implementation in an existing process. The knowledge and experience gained from the experimental research, acting as a proof of concept, are then translated into general guidelines for further use in improving existing approaches used in decision-support tools for the CDCR.

Minimal travel time and maximal reliability are two of the most important properties of a railway transportation service. This paper considers the problem of finding a timetable for a given set of departures that minimizes the weighted sum of scheduled travel time and expected delay, thereby capturing these two important socio-economic properties of a timetable. To accurately represent the complex secondary delays in operational railway traffic, an approach combining microscopic simulation and macroscopic timetable optimization is proposed. To predict the expected delay in the macroscopic timetable, a surrogate function is formulated, as well as a subproblem to calibrate the parameters in the model. In a set of computational experiments, the approach increased the socio-economic benefit by 2-5% and improved the punctuality by 8-25%.

This paper considers the problem of minimizing travel times and maximizing travel time reliability, which are important socio-economic properties of a railway transport service, for a given set of departures on a double-track line. In this paper travel time reliability is measured as the average delay, and a delay prediction model for MILP timetable optimization is presented. The average delay prediction model takes into consideration time supplements, buffer times and propagation of delays in the railway network and is not restricted to a fixed order of the trains. Validation of the average delay prediction model, and an evaluation of the approach with combined simulation-optimization for improving railway timetables, are conducted by a simulation study on a part of the Swedish Southern Main Line. Results from the simulation study show that the average delays are reduced by up to approximately 40% and that the punctuality is improved by up to approximately 8%.

The Train Timetabling Problem (TTP) is the problem of finding the timetable that utilizes the infrastructure as efficient as possible, while satisfying market demands and operational constraints. As reliability is important to passengers it is important that timetables are robust. In this paper we propose a method that combines optimization and simulation to find the timetable that minimizes the travel times and maximizes the expected punctuality. The core method consists of iteratively re-optimizing a bi-objective mixed integer sequencing timetable model, where both planned travel time and simulated delays are taken into account. Each generated timetable is validated and re-evaluated using the micro-simulation tool RailSys. The advantage of the method is that it captures both the uncertainty of a timetable at the planning stage and the validity of the generated timetable. The method is evaluated on a unidirectional track section of the Western Main Line in Sweden and shows promising results for future research.