理解车辆在路网中的运动行为与诸多实际及理论问题密切相关。尽管近期研究聚焦于车辆运动过程中最小化的成本类型,但车辆如何运动以实现该成本最小化仍鲜有探索。本研究基于大规模真实路网中个体车辆轨迹数据,识别车辆的成本最小化运动模式,并分析路网结构对这类运动的影响。我们发现车辆运动呈现三个阶段:行程起始、中间与结束阶段。在起始与结束阶段,车辆绕行更多、方向记忆衰减更快、行驶速度低于中间阶段;而在中间阶段,车辆绕行更少、方向记忆保持更久、速度高于起始与结束阶段。此外,起始与结束阶段的绕行与速度模式相似,仅运动方向相反。为解释这些模式,我们提出一种双层网络模型,以模拟真实路网的层次化结构。我们发现,当车辆在该模型网络中以最小化通行时间为目标运动时,其路径倾向于集中于高层级道路,且上述三阶段运动模式得以复现。因此,当车辆在给定起讫点间运动时,必须进入并离开这些高层级道路,从而导致其轨迹偏离相同起讫点间距离最短的路径——尤其在行程起始与结束阶段。我们的结果揭示了看似高度多样化的个体车辆运动背后所共有的模式,表明这些模式源于车辆对路网层级化特征的利用。
Understanding vehicle movement on road networks is closely related to various practical and theoretical issues. While recent works have focused on which cost vehicles minimize while moving, how they move to minimize that cost remains less explored. In this work, we analyze large-scale data of individual vehicle trajectories in real-world road networks to identify cost-minimizing movement patterns of vehicles and the influence of road network structure on such movement. We observed that vehicle movements exhibit three phases: the beginning, middle, and end of trips. At the beginning and end, vehicles detour more, lose directional memory quickly, and travel at lower speeds than during the middle. In contrast, during the middle, they tend to detour less, maintain directional memory, and travel faster than at the beginning and end. Finally, at the beginning and end, vehicles exhibit similar detour and velocity patterns, except the direction of movement. To understand these patterns, we propose a double-layered network model mimicking the hierarchical structure of real-world road networks. We found that when vehicles move across our model network while minimizing travel time, they tend to concentrate on high-level roads, and the three observed movement phases are reproduced. Consequently, when a vehicle moves between a given origin-destination pair, it must enter and exit these high-level roads. This causes it to deviate from the trajectory that minimizes travel distance between the same origin-destination pair -- particularly at the beginning and end of the trip. Our results reveal common patterns underlying individual vehicle movements that appear highly diverse at first glance, demonstrating that these patterns emerge because vehicles leverage the characteristics of hierarchical road networks to minimize travel time.