Key Trains Identifying and its Reasonable Ratios in the High-Speed Rail Timetable

A key train plays a important role in the rail timetable. The unreasonable key trains 47 layout greatly influences the normal train-running order, thus affecting the quality of 48 the high-speed rail (HSR) timetable. This paper studies the probability produced by 49 train paths for overcoming bottlenecks, and identifies key trains in the HSR timetable, 50 that is, key trains have greater effecter on other trains and needed to pay close 51 attention to them. Moreover, under certain capacity requirements, this paper 52 calculates reasonable key trains ratio for different combinations of speed in a HSR 53 timetable. This research demonstrates that: （a） maintaining a low speed level is 54 essential for key trains in the HSR timetable; and （b） when trains of 350km/h and 55 250km/h run on the same line, the key trains (250km/h) ratio of the 56 Beijing-Shanghai HSR should be less than 10%. Currently, for the trains running on 57 the Beijing-Shanghai HSR, whose speeds are 300km/h and 250km/h, the key trains 58 (250km/h) ratio should be no more than 20%.