Abstract: To alleviate the extreme congestions of local stations in oversaturated metro lines, this paper proposes a carriage capacity allocation strategy and optimization method. This method allocates the train capacity to each station by reserving and allocating carriages to ensure that all passengers at each station, especially for the congested stations, can receive fair service and the extreme congestion can be alleviated. Considering the proposed strategy, this studytakes the number of reserved carriages of each train at each station as the decision variable. A linear integer programming model for carriage capacity allocation is developedto minimize the total waiting time of all passengers at each station. A numerical experiment is carried out in Batong Line of Beijing metro for the carriage capacity allocation in the downward direction during the morning peak hour from 7:00-10:40 am on weekdays. The experimental results show that the maximum number of passengers gathered at each station in the line has fallen within an acceptable range, among which the maximum number of gathered passengers has been reduced from 3642 to 1345, a decrease of about 63% . The total waiting time of passengers only increased form 418027 minutes to 420099 minutes, an increase of 0.5%. The results show that the train capacity allocation method performed well in alleviating the extreme congestions in oversaturated metro lines and realized the balance of passenger flow gathering at each station. The method can improve overall operational safety at the line leveland ensure the quality of passenger services.

Key words: urban traffic, train capacity allocation, linear integer programming model, oversaturated metro line; carriage reservation, extreme congestion

摘要： 为缓解过饱和地铁线路的局部车站极端拥挤问题，提出一种新颖的车厢容量分配策略及优化方法，即通过预留和分配车厢的方式，将列车运力合理分配到各个车站，从而确保各车站乘客(特别是拥堵车站)均能得到公平服务，缓解极端拥堵。基于上述策略，以线路各车站所有乘客总等待时间最小为目标，以各列车在各车站的预留车厢数量为决策变量，构建关于车厢容量分配问题的线性整数规划模型。针对北京地铁八通线，对其工作日早高峰7:00-10:40下行方向的车厢容量分配进行数值实验。实验仿真结果表明，线路内各车站最大乘客聚集人数均降到安全范围内，其中最大聚集乘客数量由3642人降低至1345人，约降低63%。而全线乘客的总等待时间仅由418027 min增加至420099 min，增加0.5%。上述结果表明，列车容量分配的方法有效缓解了过饱和地铁线路内极度拥挤问题，实现各车站客流聚集均衡，在线路层面提高了总体运营安全性， 同时保证了客运服务质量。

关键词: 城市交通, 列车容量分配, 线性整数规划模型, 过饱和地铁线路, 车厢预留, 极端拥挤