基于Max-plus代数法的市域铁路快慢车运行特性
郑翔1,2,3徐行方2,3刘薇4鲁玉2,3
Characteristics of Municipal Railway Express/Local Train Operation Based on Maxplus Algebra Method
ZHENG XiangXU XingfangLIU WeiLU Yu
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作者信息:1.广州地铁设计研究院股份有限公司, 510010, 广州
2.同济大学道路与交通工程教育部重点实验室,201804, 上海
3.上海市轨道交通结构耐久与系统安全重点实验室, 201804, 上海
4.国家开发银行苏州市分行, 215128, 苏州
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Affiliation:Guangzhou Metro Design & Research Institute Co., Ltd., 510010, Guangzhou, China
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关键词:
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Key words:
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DOI:10.16037/j.1007-869x.2023.09.001
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中图分类号/CLCN:U292.4∶U239.5
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栏目/Col:学术专论
摘要:
为编制市域铁路快慢车模式的运行计划和检验快慢车方案的鲁棒性,针对快慢车运行特点,提出一种基于Maxplus代数法的市域铁路快慢车运行系统的闭环模型。方法:将列车运行系统作为典型的离散事件动态系统,定义其模型变量与参数,同时定义系统约束规则;基于Maxplus代数法建立列车运行系统Maxplus开环线性模型,并进行了快慢车模式下开环线性模型的变换;基于Maxplus代数法建立列车运行系统Maxplus闭环线性模型,并以一段计划开行快慢车的市域铁路作为算例,对该算例建立闭环模型,并求解与分析输出演化过程,最后通过状态转移变量矩阵的求解结果生成列车运行时刻表。结果及结论:该算例的快慢车运行系统稳定,一个周期系统的缓冲时间为291 s;通过单参数摄动情形下的鲁棒性分析获得了使快慢车运行系统保持运行一致均衡性的摄动元取值区间;首班车在始发站的出发时刻不具备鲁棒性,当第4列列车为快车时,其越行后成为第3列列车,该列车在越行站越行时刻不具备鲁棒性。
Abstracts:
To develop operation plans for municipal railway express/local train mode and assess the robustness of the proposed scheme, targeting the characteristics of express/local train operation, a closedloop model for municipal railway express/local train operation system based on Maxplus algebra method is proposed. Method: Treating the train operation system as a typical discrete event dynamic system, the model variables and parameters are defined along with system constraints. The above method is employed to establish the openloop linear model of the train operation system and to perform the transformation for the model under express/local train mode. The Maxplus algebra method is utilized to establish the train operation system Maxplus closedloop linear model. A municipal railway with planned implementation of express/local train mode is taken as calculation example, the closedloop model for which is established, and the evolution process of the output is analyzed and solved. Finally, a train timetable is generated through the solution of the state transition variable matrix. Result & Conclusion: The express/local train operation system in the calculation example is stable, with system buffer time of 291 seconds for one cycle. By analyzing the robustness under singleparameter perturbation condition, the perturbation element value range that maintains the operational equilibrium of express/local train operation system is obtained. The departure time of the first train from the originating station doesn′t have robustness. When the 4th train is an express train and becomes the 3rd after overtaking the previous train, the overtaking time of this train at the overtaking station doesn′t have robustness as well.
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