Abstract: In urban rail systems, the high passenger flow demand in peak hours would cause a large number of passengers stranded at platforms, which will not only bring potential safety risks to the system but also reduce the comfort of passengers. Meanwhile, the imbalance of passenger flow spatial distribution leads to the mismatch of supply and demand capacity, which reduces the utilization of train resources. This paper studies the collaborative optimization of train timetables combined with the full-length and short-turning routes and passenger flow control strategy. Considering the uncertainty of passenger flow, the passenger arrival rate is set as an uncertain variable. Then, based on the dynamic relationship between passenger flow evolution and train operation, an optimization model is established to minimize the number of stranded passengers, the number of passenger flow controlled, train operation time, and to maximize the measurement value of train resources utilization. A scenario- based chance- constrained optimization algorithm is designed to solve the model. Numerical experiments are carried out to verify the effectiveness of the model based on an urban rail line in Beijing. The results show that compared with the regular strategy, the collaborative optimal strategy proposed in this paper has greatly reduced the expected number of stranded people and train operation time, and better realized the balance between passenger cost and enterprise operation cost.

Key words: urban traffic, train timetabling optimization, chance-constrained optimization, short-turning strategy; passenger flow control strategy

摘要： 高峰时段的大客流需求易造成城市轨道站台乘客大量聚集，从而给城市轨道交通系统带来安全隐患，降低乘客乘车的舒适度；同时，客流空间分布的不均衡性导致供需能力不匹配，降低 了列车资源的利用率。针对该现象，本文结合大小交路开行方案与客流控制策略研究城市轨道交通列车时刻表协同优化问题。考虑到城市轨道交通客流的不确定性，将乘客到达率设置为不确定变量，而后基于客流演化与列车运行的动态关系，建立以最小化滞留乘客数、客流控制人数、 列车运行时间，以及最大化列车资源利用率衡量值为目标的优化模型，并设计一种基于机会约束 的随机场景优化算法进行模型求解。以北京市某轨道线路为例进行数值实验验证模型的有效性。结果表明，相较于常规运营策略，本文提出的协同优化策略在期望滞留人数和列车运行时间方面有了较大改善，更好地实现了乘客成本和企业运营成本之间的均衡。

关键词: 城市交通, 列车时刻表优化, 机会约束, 小交路策略, 客流控制策略