# Double-Track One-Direction Operation Mode for Overnight Trains on High-Speed Railway
## 1 Introduction
Due to the maintenance disruption period of conventional railway lines usually being short and being arranged in any time period, the transfer to conventional railways has been used before, including the EMU trains from Shanghai to Xi'an and Lanzhou. In the section of Shanghai to Xuzhou, the traditional Beijing-Shanghai railway instead has of the Beijing-Shanghai high-speed railway, but it can easily lead to interference between the high-speed railway with the conventional railway, resulting in a decrease in punctuality. Safety issues also need to be considered. EMU trains running at high-speed cause pressure on some freight trains, but if EMU trains run at a lower speed, then there is no advantage to ordinary trains. Thus, this method is currently deprecated. Operation on a single track during maintenance disruption is unable to carry out large-scale maintenance operations, and scheduling is complicated; speed limits are also required. There is also some research on the adjustment of maintenance construction. The theoretical feasibility of set maintenance disruption every other day is demonstrated in [7], combined with construction projects and time requirements, and a linear programming model for the integration of a train diagram and a comprehensive maintenance window was established in [8]. A trapezoidal mode and a maintenance disruption during daytime hours also appeared in a number of studies, but they are more limited and have no practical application value. The demand-based periodic operation in [9] is now being used, and in the operating method currently implemented, periodic maintenance disruption was set up to realize periodic overnight train operation. An overnight sleeper EMU train on a high-speed rail runs towards two main directions, including from Beijing to Guangzhou and from Shanghai to Shenzhen, and it operates from Friday to Monday. During this period, there is only inspection without maintenance, generally maintenance disruption compressed to a minimum of 2 h, and full maintenance disruption sets from Tuesday to Thursday, which provide at least 4 h of time to complete all inspection and repair operations. The work in [10] illustrated the difficulty of expanding service hours in some sections due to the inability to further compress the maintenance disruption. Generally, the above methods cannot solve the contradiction between overnight trains and maintenance disruption, and none of them fully explored the capabilities of a high-speed rail at night. A new research idea is urgently needed. On the basis of passengers' travel preference, to obtain enough sleep, trains that leave and arrive at night are usually pointless; thus, the sunset-departure and sunrise-arrival trains usually depart from 19:00 to 23:00 and arrive from 06:00 to 09:00 the next day. In the current operating modes, all overnight trains in the same direction run in a group. Departure and arrival times are relatively concentrated, and only one-direction line is used except for the rendezvous, which leads to the resources in the opposite direction being idled as, Figure 2 shows. Meanwhile, [11] mentioned the hardware conditions of the China Train Control System (CTCS), which has five levels from 0 to 4 that allow reverse running under certain conditions on most existing lines, although minor software changes are required if there are a large number of trains running in reverse. Making full use of wasted capacity on the reverse line can be a breakthrough to solve the problem, and it is groundbreaking that we came up with our method. We propose a novel method called the \"double-track One-direction\" organization mode for the overnight train on a high-speed railway. We built a mathematical model and, according to the case study, verified the feasibility and effectiveness of our method. It can effectively solve the conflict between overnight train operation and the maintenance of a high-speed railway, and it can increase the capacity of HSRs.