基于Max-plus方法的列车运行图稳定性评价

Evaluation of Stability of Railway Working Diagram Based on Max-plus Algebra

列车运行图是铁路运输组织重要的技术文件,因而列车运行图质量的评估历来受到铁路部门的重视。而列车运行图稳定性是评估工作中的重要内容之一,它是指列车运行图在实施过程中出现列车晚点的概率和消除晚点以及晚点传播的能力。本文介绍max-plus方法,并将该方法引入列车运行图稳定性评估工作。建立用以评价列车运行图稳定性的恢复矩阵,提出评价的定量指标,并应用Matlab编程实现了恢复矩阵计算分析的自动化。Max-plus的应用需要与图论等方法结合,比较复杂,应进一步研究。

The railway working diagram （or timetable） specifies the arrival and departure time at stations in train services. It plays a very important role in railway transportation. Hence, the railway operators emphasize its quality assessment stringently all the time. Stability is one of the criteria in the assessment, which is defined as the ability of the timetable to eliminate the train delay and its propagation. In this paper, the max-plus alge-bra is introduced to make evaluation on the timetable stability. The method to build the recovery matrix is presented, as well as the quantitative criteria for the evaluation. Matlab programming is implemented consequently. The max-plus algebra has to work together with the graph theory. Further investigation is needed since the assessment with the max-plus algebra is very advanced.