## 1 Introduction  
The sections of a high-speed railway are the basic space units of train movement. A reasonable and accurate assessment of the carrying capacity of railway sections is an important basis for train timetabling and dispatching. As the passenger volume of high-speed railways increases year by year [1], the capacity of some lines tends to become saturated. As a result, railway companies pay increasing attention to the fine management of capacity and put forward higher requirements for the accuracy of capacity assessment results. A railway section in this paper refers to the railway line between two main stations, from which a train can depart and arrive. A railway section consists of two terminal stations and many intermediate stations. For the capacity assessment of high-speed railway sections, numerous approaches have been developed. The most relevant methods can be classified into three levels: analytical methods, optimization methods, and simulation methods [2]. Analytical methods are designed to model the railway environment by means of mathematical formulae or algebraic expressions. They usually obtain theoretical capacities and determine practical capacities either as a percentage of the theoretical capacity or by including regularity margins when they calculate the theoretical capacity. In Russia and China, some scholars have discussed the application of the deduction coefficient method in high-speed railways in the early stage [3, 4, 5, 6]. However, with the gradual in-depth study of the deduction coefficient method, due to the excessive factors affecting capacity, the situations that need to be considered and the form of the formulasare becoming increasingly complex, which makes subsequent research difficult and is not conducive to practical applications [7]. The deduction coefficient method is a calculation method based on statistical analysis to obtain the average deduction coefficient of various types of trains by simulating a train timetable under various situations to evaluate the occupancy of the trains to capacity. [PERSON] and [PERSON] [8] analyzed the essence of the deduction coefficient method and believed that the traditional deduction coefficient method is no longer suitable for the calculation of the capacity of high-speed railways. It is necessary to start with the overlap relationship between the trains and the time occupancy of the train timetable to carry out follow-up quantitative research more directly and effectively. In Germany and some other European countries, capacity assessment methods based on the average minimum headway and queuing theory are widely applied [9]. [PERSON] and [PERSON] [10] have developed several methods to calculate the absolute capacity of railway lines and networks. [PERSON], [PERSON] and [PERSON] [11] discussed a stochastic model for the capacity analysis of railway lines with applications in long-term planning, and a generalization of an approach widely used in Germany was derived that is valid for a wide range of timetable requirements. The extensions of these approach are given in [12; 13; 14; 15]. However, none of these methods consider a timetable with its scheduled arrival and departure times as an input for the capacity assessment. The International Union of Railways proposed the UIC method [16]. It calculates the capacity of line sections to identify bottlenecks and takes into account the order of trains, and a buffer time is inserted to achieve an acceptable quality of service. This method was officially dropped some years ago and is no longer recognized as a standard. It has been superseded by more general recommendations [17] that establish a link between railway capacity and railway quality. In 2004, the UIC406 leaflet [18] was published and proposed the compression method for capacity assessment. In 2013, the second edition [19] was published, a methodology was presented enabling the calculation of nodes' capacity based on the same principles.