基于Max-Plus代数的列车运行图稳定性分析方法研究

Research on Stability Analysis Method of Train Working Diagram Based on Max-Plus Algebra

列车运行图是行车组织工作的基础,其稳定性关乎整个路网线路的运输效率和运营质量。为评估列车运行图的稳定性,通过分析列车运行间隔限制、接续限制、运行线路限制3类列车运行过程限制事件的逻辑关系,总结出列车运行过程具有典型离散事件动态系统(DEDS)特征;采用Max-Plus代数求解DEDS分析理论,探索Max-Plus代数与运行图限制事件的映射关联,建立列车运行图稳定性分析的Max-Plus代数模型;通过模型计算,求解Max-Plus代数最大特征值及运行余量时间矩阵、延迟传播时间矩阵,并以此定量评估列车运行图稳定性。经过实验算例的建模、计算及指标分析,表明采用Max-Plus代数可以科学评估列车运行图的稳定性。此分析方法可为铁路部门改善运行图铺画质量、降低晚点造成的影响,提供有效的参考。

Train working diagram is the basis of train operation organization,and its stability is related to the transport efficiency and operation quality of the whole railway network.In order to evaluate the stability of train working diagram,by analyzing the logical relationship between three types of train operation process limitation events:train operation interval limit,connection limit and operation line limit,it is summarized that the train operation process has typical discrete event dynamic system(DEDS)characteristics;Max-Plus algebra is used to solve the DEDS analysis theory,explore the mapping association between Max-Plus algebra and train working diagram restriction events,and establish a Max-Plus algebraic model for stability analysis of train working diagram;through model calculation,the maximum characteristic value of Max-Plus algebra,running margin time matrix and delay propagation time matrix are solved to quantitatively evaluate the stability of train working diagram.The modeling,calculation and index analysis of experimental examples show that the stability degree of train working diagram can be scientifically evaluated by using Max-Plus algebra.This analysis method can provide an effective reference for railway authority to improve the drawing quality of train working diagram and reduce the impact caused by delays.