具有极大时间约束的轨道交通系统的周期分析
Periodic analysis for railway transport systems with maximum timing constraints

运用极大–加代数方法研究具有极大时间约束的轨道交通系统的周期运行规律. 分别建立具有两个车站的 双回路城际轨道交通系统和具有n个车站的单回路城市轨道交通系统的极大–加线性模型. 对于前者, 运用系统状 态矩阵的周期性, 证明各个车站第k次与第(k + 2)次的发车时间间隔相同; 对于后者, 运用状态变量的线性替换, 证 明在任何初始状态下, 系统经过一次循环便可进入周期稳态运行, 即列车连续两次到达同一车站的时间间隔相同. 周期时间分析有利于轨道交通系统列车时刻表的编排和周期运行方案的设计. 为验证本文结果的实用性和有效性, 给出周期时间分析在列车调度和线路规划中的应用例子.
This paper investigates the periodic operation regulations of railway transport systems with maximum timing constraints by using max-plus algebra. The max-plus linear model of the double-loop intercity railway transport system with two stations and the single-loop urban railway transport system with n stations are established, respectively. For the former, according to the periodicity of the state matrices, it is proven that the time interval between the k-th departure and the (k + 2)-th departure of trains are the same. And for the later, through the linear transformation of the state variables, it is proven that the steady-state regime is reached with any starting state after once cycle, i.e., the time interval between two successive arrival of a train at a station are the same. The periodic analysis of railway transport systems is helpful for scheduling train timetable and designing periodic running scheme. To verify the practicability and validity of the results, this paper presents application examples in the trains scheduling and traffic lines planning.