Train scheduling and rescheduling model based oncustomer satisfaction. Application to Genoa railway network

A new method is proposed for single-track railway freight train timetable with two-stage solution of train scheduling problem. The method describes train scheduling problem in matrix with the "signaling block" concept. The matrix represents entire block occupancy of trains between inter-stations and internal-stations while decomposing individual train occupancy, making optimization method more flexible in design and use. The "two-stage solution" refers to that of train timetable with "conflict solution" and "timetable optimization." At the beginning, related data for trains are entered to build the initial timetable, which is then transferred and saved as the matrix format. All conflicts between interstations and internal-stations are located; solutions are made with manual scheduling to generate a feasible timetable. In the second stage, departure and stop time of freight trains, and passenger trains if necessary, are adjusted with Fuzzy system. Before optimization, storage is made in ascending amount of extra-time percent in freight train schedule. Execution is made subject to pre-ordered results during optimization for computer program acceleration of current manual spotting solution to find reasonable and feasible solution. The two-stage method also takes less time than the regular railway timetable design methods in cost saving of manual labor and providing higher operation performance and efficiency.

Optimisation of train schedules to minimise transit time and maximise reliability : Higgins, Andrew, Ph.D. Queensland University of Technology, 1996. 260 pp. (available from Inter-library loans, Gardens Point Campus, Queensland University of Technology, P.O. Box 2434, Brisbane 4001, Australia)

Petri nets and railway networks are considered in this paper with the aim of providing a comprehensive model to be used for analysis, optimisation, and control purposes. The overall model consists of two interconnected Petri nets that represent, respectively, the physical part of the network (stations, blocks, crossovers, tracks, and so on, as well as trains travelling on the network) and the logical part of it (train schedule over the available lines). The former Petri net has a fixed structure whereas the second one changes in accordance with the number of trains, lines, and timetable. In the paper, the main elements of the two Petri nets are described in detail, making use of an example of network which is representative of real-word railways. Moreover, some applications of the proposed model are discussed in order to highlight the effectiveness in employing Petri nets to analyse, optimise, and control railway networks and train schedules.

An integrated model for line planning and train scheduling based on the circulation of trains is proposed to reduce passenger dissatisfaction and operation costs for an urban rail transit line. The turnaround operations of trains and their departures from and arrivals at the depot were included in this model. Furthermore, binary variables were introduced to indicate whether train service existed, and a discrete event model was used to determine the order of the train services. In addition, a bi-level optimization approach is proposed to solve the integrated line-planning and train-scheduling problem, in which the number of required train services, the headways between train services, the departure times, and the arrival times were optimized simultaneously on the basis of passenger demand. The performance of the proposed integrated model and bi-level approach is illustrated with a case study of the Beijing Yizhuang line.

ABSTRACTThis study proposes a modelling framework for the demand-driven train timetable and stop pattern cooperative optimization problem on an urban rail transit line. By embedding the train stop pattern into the timetable optimization process, we consider the minimization of total passenger travel time. A binary variable determination (BVD) method, which can transform complicated linear constraints into simple logical constraints, is proposed to calculate the large number of binary variables easily, and a genetic algorithm (GA) based on the BVD method is designed to solve the proposed model. A case study of the Batong line in the Beijing subway network is conducted to test the proposed model and algorithm. This study can provide beneficial advice for the operator to improve the operational service of urban rail transit lines.

Modeling the first train timetabling problem with minimal missed trains and synchronization time differences in subway networks

A multi-objective train scheduling model and solution

The article is devoted to the analysis of the effectiveness of the DTN (Delay Tolerant Network) system in a communication network on a railway line. Trains act as moving objects, that are sending and receiving messages to/from an external network. As well trains may transmit telemetry, collected during movement. The article presents data on the effectiveness of the DTN network in terms of reducing the delay in message delivery, reducing the delay in transmitting telemetry, and increasing the total number of messages in the railway scenario. The data on the theoretical efficiency of the DTN system are presented, including the results of the generation of many maps of railway networks and the corresponding train schedules. An analysis of railway line sections of various load and having different coverage of mobile network was made. These models are based on real railway maps with real train schedules. Effectiveness of DTN during migration to networks of a higher data rate (5G) and networks with satellite connection of trains is analyzed.

Scheduling trains in order to minimize the traveling time is a challenging optimization problem. Delay may occur due to the bottleneck or many trains need to use the same track at the same time. These delays increase the journey time and may cause secondary delays to the other trains in the network. Double track railway scheduling can be modelled as a Job-Shop Scheduling Problem that can be achieved by considering the train trips as jobs which will be scheduled on tracks. This research is focus on scheduling trains in order to minimize the delay time. First Come First Serve (FCFS) dispatching rule is used to calculate the traveling time at each block section by sequencing the trains in order of starting time. The other rule is priority queue to solve the bottleneck problem by assigning the block section to the highest priority train. The simulation result is that the proposed model produce a less optimal schedule than the actual schedule due to the great average delays but the number of the delayed trains are less.

Scheduling local and express trains in suburban rail transit lines: Mixed–integer nonlinear programming and adaptive genetic algorithm

Timetable Optimization for High-Speed Trains at Chinese Railways

Train scheduling has been a significant issue in the railway industry. Over the last few years, numerous approaches and tools have been developed to compute railway scheduling. In this paper, we present a set of heuristics for a constraint‐based train scheduling tool, which is a project in collaboration with the National Network of Spanish Railways (RENFE), Spain. We formulate train scheduling as constraint optimization problems. Three heuristics are developed to speed up and direct the search toward suboptimal solutions in periodic train scheduling problems. The feasibility of our problem‐oriented heuristics is confirmed with experimentation using real‐life data. The results show that these techniques enable MIP solvers such as LINGO and ILOG Concert Technology (CPLEX) to terminate earlier with good solutions.

This study investigates an integrated train stop planning and timetabling problem considering the uncertainty of passenger demand in a railway network. With the scenario-based representation of demand distribution, an integer linear programming (ILP) model is formulated to simultaneously optimise the train timetable and stop plan, in which the time-space network representation method is adopted to characterise the movements of trains and passengers. The objective is to jointly optimise the total travel time of trains and passengers, and the expected number of unsatisfied or over-satisfied passengers over all demand scenarios. By analyzing the characteristics of the model, we decompose it into two subproblems based on trains (timetabling) and passengers (assignment), respectively. Then, an iterative algorithm based on variable neighbourhood search (VNS) is designed to solve the two subproblems iteratively. Additionally, a series of numerical experiments based on the real-world instance in a high-speed railway (HSR) network are implemented to verify the effectiveness of the proposed stochastic programming (SP) model and the iterative algorithm. The results demonstrate that (i) the proposed SP model is easy to implement in practice, and (ii) the developed iterative algorithm exhibits much higher computational efficiency than the optimisation solver.

We propose a network flow model to study problems in commuting traffic in the railway network of the Tokyo Metropolitan area. Through this network, about seven million passengers commute, and about 7,500 trains transport them in morning rush hours. Trains are usually crowded and subject to delay caused by overcrowded passengers. In addition to the huge traffic volume, such facts intensify the situation that the commuters concentrate in commuting during short time period, traveling radial lines directing to the central district, and choosing a “better (higher speed)” train service. In order to relieve such conditions, not only investments in hardware but also soft approach are important to fully utilize the existing capacity of the network to average the number of passengers across the trains. Our model consists of a time–space network (or schedule-based network) and detailed traffic data on route choice of commuters. The former has been intensively studied to consider traffic problems where each vehicle service is operated according to a timetable. Using this network, every train services and actions of passengers can be represented by nodes and edges of the network. The latter is the questionnaire survey of commuting traffic in Metropolitan area being done in every five years. We use the survey conducted in 2005, which has about 140,000 respondents. Another important point of our model is that it is able to consider the whole railway network universally in one system.

In modern railway networks, real-time monitoring and secure control communications are essential for ensuring operational safety, efficiency, and reliability. Critical operations such as signal control, train scheduling, and automated track switching generate large volumes of data that must be analysed instantly to prevent system failures or malicious intrusions. Traditional approaches relying on manual inspections or rule-based systems are often slow, error-prone, and inadequate for handling highvolume, dynamic communication data. To address these limitations, this research proposes a robust, automated anomaly detection framework for accurate real-time classification. Existing methods, including Decision Tree with Cost Complexity Pruning (DTCCP) and Deep Neural Decision Tree (DNDT), offer interpretability and moderate accuracy. However, DTCCP tends to overfit complex sequential data, while DNDT struggles to capture subtle contextual relationships, resulting in missed anomalies and false alarms. The proposed framework employs a RuleFit classifier (RF) that combines linear rules with decision tree logic, enhanced by semantic embeddings generated using Sentence Bidirectional Encoder Representations from Transformers (SBERT). This hybrid model effectively learns both hierarchical decision boundaries and contextual patterns within communication sequences. Performance evaluation is conducted using metrics such as accuracy, precision, recall, F1-score, confusion matrix, and Receiver Operating Characteristic (ROC) curves. Experimental results demonstrate that the RF-based approach significantly outperforms DTCCP and DNDT, achieving improved anomaly detection accuracy, reduced false positives, and reliable real-time classification of secure and insecure rail communications, thereby enhancing overall railway network safety and operational efficiency.