基于非均匀发车间隔的大小交路时刻表优化模型

基于客流时空分布规律，考虑列车平均发车间隔、运行时间、最大载客量等约束条件，将列车在车站的停站时间与上、下车客流量相关联，建立城市轨道交通高峰时段基于非均匀发车间隔的大小交路时刻表优化模型，对乘客平均旅行时间及列车发车间隔平均偏离值进行协同优化。以某城市轨道交通线路实际运营数据验证模型的有效性。结果表明，优化后乘客在各个车站平均等待时间较优化前减少幅度为0.4%~13.1%，其中全线客流量较大的第7、8、9站优化幅度较为明显，分别为 11.7%、13.1%、11.9%。优化后列车在各个车站最大满载率较优化前降低幅度为1.8%~8.5%，且所有车站站台均无滞留乘客，体现了优化后列车运输能力与客流需求的良好匹配。灵敏度分析讨论了目标函数权重系数及列车平均发车间隔值对模型的影响，表明本模型具有良好的可用性及稳定性，能够为城市轨道交通列车时刻表优化提供参考。

Train Timetable Optimization Model for Full-length and Short-turn Routings with Irregular Departure Intervals

Considering irregular train departure interval, this paper proposes the train timetable optimization model for full-length and short-turn routings in peak hours. The model aims at collaboratively optimizing the average travel time of passengers and the average deviation value of train departure interval under temporal and spatial distribution law of passenger flow for an urban rail transit line. The model also considers the constraints on average value of train departure interval, running time, and maximum passenger capacity. In the proposed model, the train dwell time at the station is associated with the number of passengers boarding and alighting the train. The effectiveness of the model is assessed by actual data of an urban rail transit line. The results show that compared with the current regular train timetable, the reduction ratio for the average waiting time of passengers under the optimized timetable is between 0.4% and 13.1% for different stations. Among them, the optimization range of stations 7, 8 and 9 with the largest passenger flow along the entire rail transit line is obvious and the reduction ratio is respectively 11.7%, 13.1% and 11.9%. The reduction ratio for the maximum train loading rate under the optimized irregular timetable is between 1.8% and 8.5% for different stations, and there are no stranded passengers at all stations, reflecting the good match between the train capacity and passenger demands under the optimized timetable. The sensitivity analysis is performed for coefficient weight of objective function and average value of train departure interval, which shows that the proposed model has good usability and stability, and can be used for timetable optimization for an urban rail transit line.