Cyclic train timetables as a popular mode of train operation have been successfully applied for many years in European railways, especially in highspeed railways (hereinafter referred to as 'HSR'). However, in China, most studies on the train timetables of HSR still follow the traditional mode. By analyzing the characteristics of Chinese HSR, this paper proposes an incomplete cyclic timetable mode that will be more suitable for the Chinese situation. The characteristics and process of working out incomplete a cyclic train timetable are discussed. There are four key issues involved in developing this kind of timetable: (1) Adaptability analyzing. This paper analyzes the proportion of trains that can be operated cyclically in terms of the technical condition and passenger flow of each HSR in order to determine the structure of the timetable. (2) Model developing. By analyzing the condition of the Chinese HSR, the existing model is improved to solve the problem more precisely and practically. (3) Non-cyclic train path insertion. According to the travel demand of passengers, the principles and technologies of inserting non-cyclic train paths into cyclic train paths is developed. (4) Seasonal expanding. The seasonal fluctuation of passenger flow makes more non-cyclic train paths. The ways to balance the disaccord in different periods are discussed to keep the operation efficient. Furthermore, a system using VC++ is designed with consideration of the four issues in its functions and working process, based on inputting the solution of the model. Finally, a successful case of the Beijing-Shanghai HSR shows the feasibility of the incomplete cyclic timetable and the practical value of the system.

With the aim of supporting the process of adapting railway infrastructure and future traffic needs, we have developed a method to insert additional trains efficiently to an existing timetable without introducing large consecutive delays to scheduled trains. In this work, the problem is characterized as a job-shop scheduling problem. In order to meet the limited time requirement and minimize deviations to the existing timetable, the modification that consists of retiming or reordering trains is implemented if and only if it potentially leads to a better solution. With these issues in mind, the problem of adding train paths is decomposed into two subproblems. One is finding the optimal insertion for a fixed order timetable and the other is reordering trains. The two subproblems are solved iteratively until no improvement is possible within a time limit of computation. An innovative branch and bound algorithm and iterative reordering strategy are proposed to solve this problem in real time. Unoccupied capacities are utilized as primary resources for additional trains and the transfer connections for passengers can be guaranteed in the new timetable. From numerical investigations, the proposed framework and associated techniques are tested and shown to be effective.

In order to support the process of scheduling a hybrid cyclic timetable, this paper is devoted to inserting additional non-cyclic train paths into existing cyclic timetable. The adding train paths problem is an integration of timetable scheduling and rescheduling problem. The train dispatcher can not only modify the given timetable to manage the interruptions in existing operations, but also establish schedules for additional trains. A multi-objective model minimizing both the travel time of additional trains and the variation of existing trains is proposed in this paper. In addition, we consider both general constraints and some additional practical constraints, such as the overtaking priority constraint, reasonable adjustment of initial schedules and the scheduled connections. This problem is very difficult and must be solved in practice. A heuristic algorithm is introduced to find high-quality solutions for large-scale cases within reasonable computing time. Based on high-speed railway line in China, the case studies illustrate the methodology and compare the performance of trains. Numerical experiments indicate that the proposed solution approach to the adding train paths problem is promising. INDEX TERMS High-speed railway, cyclic timetable, adding additional train paths, genetic algorithm, mixed integer programming.

Railways around the world are experiencing growth in traffic flow, but the problem concerning how to optimize the utilization of capacity is still demands significant research. To accommodate the increasing traffic demand, the high-speed railway operator in China is interested in understanding the potential benefit of adopting reasonable headway to balance the safety and efficiency of train operations. In this study, a compress timetable scheduling model based on the UIC Code 406 method is presented to evaluate the line capacity. In this model, train headway is not pre-fixed as in the existing research, but considers the actual operating conditions and is calculated using actual running data. The results of the case study show that refined headway calculations generally have positive capacity effects.

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