With the continuous expansion of the railway infrastructure network, the railway operation network has become more and more complex both in time and space dimensions. In order to help railway operators formulate management measures more pertinently, this research aims to develop a method to analyze the complex operation network via quantifying and ranking the importance of stations in different periods based on the train timetable. Firstly, we propose the time-space train origin-destination (OD) service network (OD-TS network) to abstractly describe the railway transportation service. And a network construction method is designed to build the OD-TS network according to the train operation information in the timetable. We further develop an improved k-shell decomposition method to quantify the node importance for the directed-weighted networks. Case studies are carried out based on the train timetable of China's high-speed railway. We study the OD-TS network from three perspectives (the global network, the railway hubs, and the stations) and analyze the spatiotemporal details of the railway operation. These analyses show that the proposed method can help the railway operators mine the spatiotemporal characteristics of the railway operation well.

Heavy-haul railway transport is a critical mode of regional bulk cargo transport. It dramatically improves the freight transport capacity of railway lines by combining several unit trains into one combined train. In order to improve the efficiency of the heavy-haul transport system and reduce the transportation cost, a critical problem involves arranging the combination scheme in the combination station (CBS) and scheduling the train timetable along the trains’ journey. With this consideration, this paper establishes two integer programming models in stages involving the train service plan problem (TSPP) model and train timetabling problem (TTP) model. The TSPP model aims to obtain a train service plan according to the freight demands by minimizing the operation cost. Based on the train service plan, the TTP model is to simultaneously schedule the combination scheme and train timetable, considering the utilization optimal for the CBS. Then, an effective hybrid genetic algorithm (HGA) is designed to solve the model and obtain the combination scheme and train timetable. Finally, some experiments are implemented to illustrate the feasibility of the proposed approaches and demonstrate the effectiveness of the HGA.

Compared with other modes of transportation, a high-speed railway has energy saving advantages; it is environmentally friendly, safe, and convenient for large capacity transportation between cities. With the expansion of the high-speed railway network, the operation of high-speed railways needs to be improved urgently. In this paper, a hybrid approach for quickly solving the timetable of high-speed railways, inspired by the periodic model and the aperiodic model, is proposed. A space–time decomposition method is proposed to convert the complex passenger travel demands into service plans and decompose the original problem into several sub-problems, to reduce the solving complexity. An integer programming model is proposed for the sub-problems, and then solved in parallel with CPLEX. After that, a local search algorithm is designed to combine the timetables of different periods, considering the safety operation constraints. The hybrid approach is tested on a real-world case study, based on the Beijing–Shanghai high-speed railway (HSR), and the results show that the train timetable calculated by the approach is superior to the real-world timetable in many indexes. The hybrid approach combines the advantages of the periodic model and the aperiodic model; it can deal with the travel demands of passengers well and the solving speed is fast. It provides the possibility for flexible adjustment of a timetable and timely response to the change of passenger travel demands, to avoid the waste of transportation resources and achieve sustainable development.

Comparing to other modes of transportation, high-speed railway has the advantages of energy saving, environment friendly, safety and convenience for passengers, and has been more and more popular. However, unforeseen emergencies may disrupt the normal train operation. In this paper, an integrated dispatch strategy (IDS) is proposed to synergistically reschedule the train timetable and rolling stock circulation plan under single-direction disruptions. A two-objective model is formulated, aiming at minimizing both the delay time of passengers and the operation costs of railway companies, to reschedule the train operation efficiently and economically. An algorithm based on Non-dominated Sorting Genetic Algorithms-II (NSGA-II) is designed to solve the model. To accelerate the solving process, we propose a quick method to generate an assignment plan to serve disrupted passengers, and based on the practical experiences, the algorithm acceleration strategy (AAS) is proposed to improve the quality of initial solutions. The model and algorithm are tested on real-world instances of the Beijing-Shanghai high-speed railway line. The results indicate that the average minimized delay time of passengers is 6,012,386 min and the average minimized additional operation costs (operation mileage of standby rolling stocks) are 1623 km, with a decrease of 28.5% and 18.3%, respectively, indicating the model and algorithm are adaptable to handle single-direction disruptions on the railway line, and AAS can further accelerate the computing speed and improve the solutions quality. Finally, the characteristics of disrupted sections of railway lines are well studied and analyzed.

Nowadays, high-speed railway (HSR) has become one of the main choices for passengers. As the number of passengers increases, their travel demands become diverse and the fluctuation range of passenger travel demands will also increase. In order to adapt to the change of passenger travel demands, the switching frequency of timetables needs to be increased. When switching the timetable, the train-set circulation plan also needs to be considered. In this paper, a scheduling approach for quickly solving the timetable and the train-set circulation plan in the transition time is proposed. A section sequence is constructed in the integer programming model, and the primary train-set circulation plan is obtained. Then a stop plan is obtained on the basis of passenger travel demands. To obtain the final train-set circulation plan and the timetable, a genetic algorithm (GA) is designed, and a method that can ensure that the timetable meets the safety operation requirements is proposed. The scheduling approach is tested on the Beijing-Shanghai HSR. The results show that by extending the transition time, the scheduling approach can switch the train-set position from the old state to new state, without additional consumption of resources, on the premise of meeting the travel demands of passengers.

This research paper proposes a Lagrangian method to address the passing capacity of the calculation problem (PCCP) for a hub station in a high-speed railway (HSR) system. The passing capacity of a hub station is critical for determining the train timetable and maximizing the number of trains that can operate on different lines. The objective of this study is to determine the maximum number of trains that can pass through, start at, or end at a hub station. To achieve this objective, a mathematical model was introduced to solve the PCCP. The model was decomposed into two parts using a Lagrangian relaxation algorithm. The first part of the model was a simple train arrival problem (TAP) that reflected the timing of trains at the hub station with simultaneous arrival and departure time constraints. The second part of the model was a train spatio-temporal routing problem (TSRP) that aimed to solve the shortest spatio-temporal path of trains with free conflict with the train’s trajectory. A real instance was provided to demonstrate the feasibility of the proposed approach and the effectiveness of the Lagrangian method. The results showed that the proposed method can efficiently solve the PCCP and maximize the passing capacity of a hub station in an HSR system.