Abstract: This paper proposes a quasi-dynamic stochastic user equilibrium assignment model and algorithm to grasp the temporal and spatial distribution of passenger flow in the urban rail transit network. The Origin-Destination (OD) passenger flow is allocated to different periods of the line interval, and the passenger flow distribution is calculated in each period of the line interval in the network. The transfer network is constructed to describe the passenger travel process at different departure periods. The route cost is designed to consider the waiting time, stopping time, running time, congestion benefit, transfer time and transfer penalty cost, which changes with the departure time. On this basis, a quasi-dynamic stochastic user equilibrium allocation model is designed, and the optimal solution of the model is proved to reach the stochastic user equilibrium state in each period of departure. A dynamic successive averaging algorithm based on the effective path is designed to solve the model, and the experiment is carried out in the actual Guangzhou Metro network. The algorithm convergence speed is fast, and the convergence accuracy is high. Based on the analysis of passenger route selection under different random parameters, most passengers tend to choose the least cost efficient route, which often has the least transfer times, but not necessarily the shortest travel distance. By analyzing the spatial and temporal distribution characteristics of passenger flow on the line sections, the results show that the distribution of passenger flow on some line sections has significant morning and evening peak characteristics and tidal phenomena, which reflects the regional characteristics of the line and the commuting habits of urban passengers. The study result confirms the rationality of the passenger flow distribution results and has certain practical application value.

Key words: railway transportation, stochastic user equilibrium, successive averaging algorithm, passenger flow distribution, transfer network

摘要： 为准确、快速掌握客流在城市轨道交通网络上的时空分布，本文提出适用于城市轨道交通网络的拟动态随机用户均衡分配模型及算法，将OD客流分配到线路区间上的不同时段内，获得网络上各线路区间在各时段内的客流分布。首先，设计换乘网络描述不同出发时段的乘客出行过程，综合考虑候车时间、停站时间、运行时间、拥挤效益、换乘时间和换乘惩罚费用设计路径费用，路径费用随出发时段发生变化。在此基础上，设计拟动态随机用户均衡分配模型，并通过理论推导证明了模型的最优解在各个时段内均达到随机用户均衡状态。设计基于有效路径的动态相继平均算法对模型进行求解，在广州地铁网络上进行实验，算法收敛速度较快，达到了较高的收敛精度要求。分析不同随机性参数下的乘客路径选择情况，多数乘客倾向于选择最小费用有效路径，这些路径换乘次数往往最少，但出行里程不一定最短。分析线路区间上客流的时空分布特征，结果显示，部分线路区间上的客流分布具有显著的早晚高峰特征和潮汐现象，符合线路所在的区域特征和市内乘客的通勤出行习惯，证实了客流分配结果的合理性，具有一定的实际应用价值。

关键词: 铁路运输, 随机用户均衡, 相继平均算法, 客流分配, 换乘网络