Abstract: In order to solve the problem of low operational efficiency of traditional public transportation lines with low passenger flow, considering the spatial-temporal characteristics of passenger flow on low passenger flow public transportation lines, a combination service mode of traditional public transportation and DRT(demand response transit）were proposed, in which the optimization idea was the full time traditional bus mode (M1), segmented traditional bus + DRT mode (M2), and full time DRT mode (M3). The elements of different operation modes were analyzed. Considering the spatial and temporal characteristics of passengers, the station planning model was constructed based on three-dimensional spatial-temporal clustering. The cost of vehicle operation and passenger time were considered, with the goal of minimizing the total operating cost of each shift, a flexible DRT route and scheduling planning model with time windows was constructed, and genetic algorithm was used to solve the model. A bus line in Beijing was taken as an example to simulate and validate. The simulation results show that M2 reduces operational costs by 9.0% and 23.0% respectively compared to M1 and M3. The proposed method can provide technical reference for the formulation and optimization of operational plans for low passenger flow public transport services.

Key words: traffic engineering; demand responsive transit; low passenger flow bus; combined operation mode; three-dimensional spatial-temporal clustering

摘要： 为解决低客流传统公交线路运营效率低的问题，考虑低客流公交线路客流时空特性，提出了采用传统公交与需求响应公交（demand response transit，DRT）相结合的组合运营模式：全时段传统公交模式（M1）、分时段传统公交+DRT模式（M2）全时段DRT模式（M3）的优化思路。分析了不同运营模式的要素，考虑乘客空间、时间特征，构建基于三维时空聚类的站点规划模型；考虑车辆行驶成本、乘客时间成本，以总班次运营成本最小为目标，构建了带有时间窗的灵活型DRT线路与调度规划模型，运用遗传算法进行求解。以北京市某公交线路进行仿真实证，仿真结果表明：M2相比M1、M3分别降低了9.0%、23.0%的运营成本。研究可针对低客流公共交通服务的运营方案制定与优化提供技术参考。

关键词: 交通工程；需求响应公交；低客流公交；组合运营模式；三维时空聚类